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### Tamilnadu Board Maths Question papers for 10th Standard EM (English Medium) Question paper & Study Materials

#### 10th Standard Maths English Medium Model Question Paper Part - V - by Indumathi - Namakkal - May 13, 2020 - View & Read

• 1)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 2)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

• 3)

The value of (13+23+33+...153) - (1+2+3+...+15)is

• 4)

How many terms are there in the G.P::5,20,80,320,...,20480:

• 5)

Graph of a linear polynomial is a

#### 10th Standard Maths English Medium Model Question Paper Part - IV - by Indumathi - Namakkal - May 13, 2020 - View & Read

• 1)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 2)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

• 3)

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

The sum of first n terms of the series a,3a,5a...is :

• 5)

Find the matrix X if 2X + $\left( \begin{matrix} 1 & 3 \\ 5 & 7 \end{matrix} \right) =\left( \begin{matrix} 5 & 7 \\ 9 & 5 \end{matrix} \right)$

#### 10th Standard Maths English Medium Model Question Paper Part - III - by Indumathi - Namakkal - May 13, 2020 - View & Read

• 1)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 2)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

• 3)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

• 4)

If pth,qth and rth terms of an A.P.are a,bc respestively, then(a(q-r)+b(r-p)+c(p-q)is:

• 5)

If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

#### 10th Standard Maths English Medium Model Question Paper Part - II - by Indumathi - Namakkal - May 13, 2020 - View & Read

• 1)

If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

• 2)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 3)

The value of (13+23+33+...153) - (1+2+3+...+15)is

• 4)

Sum of first n terms of the series $\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...$ is

• 5)

The number of points of intersection of the quadratic polynomial x2 + 4x + 4 with the X axis is

#### 10th Standard Maths English Medium Important 8 Marks Questions - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

Draw the graph of y = x2 + 4x + 3 and hence find the roots of x2 + x + 1 = 0

• 2)

Graph the following quadratic equations and state their nature of solutions.
x2 - 9x + 20 = 0

• 3)

Draw the graph of y = x2 - 4 and hence solve x2 - x - 12 = 0

• 4)

Draw the graph of y = x2 - 4 and hence solve x2 + 1 = 0

• 5)

Draw the graph of y = 2x2 - 3x - 5 and hence solve 2x2 - 4x - 6 = 0

#### 10th Standard Maths English Medium Creative Important 5 Marks Questions - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

A functionf: [-7,6) $\rightarrow$ R is defined as follows.

find 2f(-4) + 3f(2)

• 2)

A functionf: [-7,6) $\rightarrow$ R is defined as follows.

f(-7) -f(-3)

• 3)

f(x) = (1+ x)
g(x) = (2x-1)
Show that fo(g(x)) = gof(x)

• 4)

A functionf: (1,6) $\rightarrow$R is defined as follows:

Find the value of f(5),

• 5)

If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and

#### 10th Standard Maths English Medium Book back Important 5 Marks Questions  - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

Let A = {x $\in$ N| 1 < x < 4}, B={x $\in$ W| 0 ≤ x < 2) and C={x $\in$ N| x < 3} Then verify that
(i) A x (B U C) = (A x B) U (A x C)
(ii) A x (B ∩ C) = (A x B) ∩ (A x C)

• 2)

Given A={1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5}, check if (A ∩ C) x (B ∩ D) =(A x B) ∩ (C x D) is true?

• 3)

Forensic scientists can determine the height (in cms) of a person based on the length of their thigh bone. They usually do so using the function h(b)=2.47b+54.10 where b is the length of the thigh bone.
(i) Check if the function h is one – one
(ii) Also find the height of a person if the length of his thigh bone is 50 cms.
(iii) Find the length of the thigh bone if the height of a person is 14796 cms.

• 4)

If the function f: R⟶ R defined by

(i) f(4)
(ii) f(-2)
(iii) f(4)+2f(1)
(iv) $\frac { f(1)-3f(4) }{ f(-3) }$

• 5)

Find the domain of the function f(x) = $\sqrt { 1+\sqrt { 1-\sqrt { 1-x^{ 2 } } } }$.

#### 10th Standard Maths English Medium Book back Important 2 Marks Questions - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R1={(3,7), (4,7), (7,10), (8,1)}

• 2)

Let f{(x,y)| x,y$\in$ N and y=2x}. be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?

• 3)

Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.

• 4)

If f(x)=3x-2, g(x)=2x+k and if f o g = f o f, then find the value of k..

• 5)

Find the value of k, such that f o g = g o f
(i) f(x) =x+2, g(x)=6x-k

#### 10th Standard Maths English Medium Creative Important 2 Marks Questions - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

LetA= {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} $\subseteq$ A x B bea relation. Show that R is a function and find its domain, co-domain and the range of R.

• 2)

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

• 3)

State whether the graph represent a function. Use vertical line test.

• 4)

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as  a table .

• 5)

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

#### 10th Standard Maths English Medium Creative Important 1 Marks Questions - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

A={a,b,C},B={2,3},C={a,b,C,d}then n[(A∩C)XB] is:

• 2)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 3)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

• 4)

If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

• 5)

If(x)=2-3x, then f of(1-x)=?

#### 10th Standard Maths English Medium Book back Important 1 Mark Questions - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 2)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 3)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is

• 4)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

• 5)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

#### 10th Standard Maths English Medium Model Question Paper - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

• 2)

Let f and g be two functions given by
f={(0,1), (2,0), (3,-4), (4,2), (5,7)}
g={(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 3)

74k $\equiv$ ________ (mod 100)

• 4)

The difference between the remainders when 6002 and 601 are divided by 6 is:

• 5)

A system of three linear equations in three variables is inconsistent if their planes

#### 10th Standard Maths English Medium Public Exam Model Question Paper  - II July 2020 - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 2)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 3)

74k $\equiv$ ________ (mod 100)

• 4)

The difference between the remainders when 6002 and 601 are divided by 6 is:

• 5)

If number of columns and rows are not equal in a matrix then it is said to be a

#### 10th Standard Maths English Medium Public Exam Model Question Paper - II June 2020 - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 2)

f(x) = (x+1)3 - (x-1)3 represents a function which is

• 3)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

• 4)

How many terms are there in the G.P::5,20,80,320,...,20480:

• 5)

Which of the following should be added to make x4 + 64 a perfect square

#### 10th Standard Maths English Medium Public Exam Model Question Paper July 2020 - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 2)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

• 3)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 4)

If(x)=mx+n,when m and n are integers f(-2)=7, and f(3)=2 then m and n are equal to :

• 5)

If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

#### 10th Standard Maths English Medium Public Exam Model Question Paper June 2020 - by Indumathi - Namakkal - May 09, 2020 - View & Read

• 1)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

• 2)

If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

• 3)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 4)

If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

• 5)

If(x)=2-3x, then f of(1-x)=?

#### 10th Standard Maths (English Medium) Important Questions Bookback and Creative - by 10th maths English Medium - New syllabus 2019 - May 08, 2020 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

• 3)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

• 4)

If f:R⟶R is defined by(x)=x2+2, then the premiage 27 are:

• 5)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

#### 10th Standard Maths (English Medium) Imporant Questions - by 10th maths English Medium - New syllabus 2019 - May 08, 2020 - View & Read

• 1)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 2)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 3)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is

• 4)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 5)

Let f and g be two functions given by
f={(0,1), (2,0), (3,-4), (4,2), (5,7)}
g={(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

#### 10th Standard Maths (English Medium) Model Question Paper - by 10th maths English Medium - New syllabus 2019 - May 08, 2020 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 3)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 4)

If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

• 5)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

#### 10th standard Maths One Mark important Questions Book back and Creative - 2020 - by Indumathi - Namakkal - Mar 19, 2020 - View & Read

• 1)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is

• 2)

Let f and g be two functions given by
f={(0,1), (2,0), (3,-4), (4,2), (5,7)}
g={(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 3)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 4)

If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

• 5)

f(x) = (x+1)3 - (x-1)3 represents a function which is

#### 10th Standard Mathematics English Medium All Chapter Book Back and Creative One Marks Questions 2020 - by Indumathi - Namakkal - Mar 12, 2020 - View & Read

• 1)

If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

• 2)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 3)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

• 4)

If f is constant function of value $\cfrac { 1 }{ 10 }$, the value of f(1)+f(2)+...+f(100) is:

• 5)

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

#### 10th Standard Mathematics English Medium All Chapter Book Back and Creative Two Marks Questions 2020 - by Indumathi - Namakkal - Mar 12, 2020 - View & Read

• 1)

In electrical circuit theory, a circuit C(t) is called a linear circuit if it satisfies the superposition principle given by C(at1+ bt2) = aC(t1) + bC(t2)  where a,b are constants. Show that the circuit C(t) = 3t is linear.

• 2)

Let A={9,10,11,12,13,14,15,16,17} and let f: A ⟶ N be defined f(n) = the highest prime factor of n $\in$ A. Write f as a set of ordered pairs and find the range of f.

• 3)

State whether the graph represent a function. Use vertical line test.

• 4)

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as  a table .

• 5)

Find the next three terms of the sequences.
1,0.1,0.01,...

#### 10th Standard Mathematics English Medium All Chapter Book Back and Creative Five Marks Questions 2020 - by Indumathi - Namakkal - Mar 12, 2020 - View & Read

• 1)

Let f be a function f:N ⟶ N be defined by f(x) = 3x+2, x$\in$N
(i) Find the images of 1, 2, 3
(ii) Find the pre-images of 29, 53
(ii) Identify the type of function

• 2)

A function f: [-5,9] ⟶ R is defined as follows:

Find
i. f(-3)+f(2)
ii. f(7)-f(1)
iii. 2f(4)+f(8)
iv. $\frac { 2f(-2)-f(6) }{ f(4)+f(-2) } \\$

• 3)

A functionf: (1,6) $\rightarrow$R is defined as follows:

Find the value of f(5),

• 4)

If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and

• 5)

Find the sum to n terms of the series
3 +33 + 333 + ...to n terms

#### 10th Standard Mathematics English Medium All Chapter Book Back and Creative Eight Marks Questions 2020 - by Indumathi - Namakkal - Mar 12, 2020 - View & Read

• 1)

Draw the graph of y = x2 + x - 2 and hence solve x2 + x - 2 = 0

• 2)

Graph the following quadratic equations and state their nature of solutions.
x2 - 4x + 4 = 0

• 3)

Draw a triangle ABC of base BC = 5.6 cm, $\angle$A=40o and the bisector of $\angle$A meets BC at D such that CD = 4 cm.

• 4)

Draw a circle of radius 4 cm. At a point L on it draw a tangent to the circle using the alternate segment.

#### 10th Standard Mathematics All Chapter Creative Questions-I-2019-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If $f(x)=\cfrac { 1 }{ x }$, and $g(x)=\cfrac { 1 }{ { x }^{ 3 } }$ then fogo(y),is:

• 2)

Given a1=-1, $a=\cfrac { { a }_{ n } }{ n+2 }$,then a4 is :

• 3)

The square root of 4m2-24m+36 is

• 4)

In figure $\angle OAB={ 60 }^{ o }$ and OA=6cm then radius of the circle is

• 5)

Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

#### 10th Standard Mathematics All Chapter Creative Questions-I-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If $\\ \\ (x)=\cfrac { x+1 }{ x-2 } ,g(x)=\cfrac { 1+2x }{ x-1 }$ then f og(x) is :

• 2)

Sum of infinite terms of G.P is 12 and the first term is 8.what is the fourth term of the G.P?

• 3)

(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

• 4)

Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

• 5)

Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two if the sides of the triangle are 2cm,3cm and 4 cm. find the diameter of the smallest circle.

#### 10th Standard Mathematics All Chapter Important Creative  Questions-I- 2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 2)

44≡8 (mod12), 113≡85 (mod 12),thus 44X113≡______(mod 12):

• 3)

The real roots of the quardractic equation x2-x-1 are

• 4)

If the angle between two radil of a circle is o, the angle between the tangents at the end of the radii is

• 5)

Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

#### 10th Standard Mathematics All Chapter Important Creative  Questions-I- 2019-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If functionf:N⟶N,f(x)=2x then the function is, then the function is

• 2)

The difference between the remainders when 6002 and 601 are divided by 6 is:

• 3)

The parabola y=-3x2 is

• 4)

If triangle PQR is similar to triangle LMN such that 4PQ=LM and QR=6 cm then MN is equal to :

• 5)

If ABC is a triangle and AD bisects ረA ,AB=4cm,BD=6cm,DC=8cm then the value of AC is

#### 10th Standard Mathematics All Chapter Creative Questions-II-2019-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

• 2)

In the arithemetic series Sn=k+2k+3k+...+100, k is positive integer and k is a factor 100 then Sn is:

• 3)

If $A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right] _{ 3\times 2 }$ $B=\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \right] _{ 2\times 3 }$ then which of the following products can be made from these matrices
(i) A2
(ii) B2
(iii) AB
(iv) BA

• 4)

In the given figure if OC=9 cm and OB=15 cm then OB+BD is equal to

• 5)

Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

#### 10th Standard Mathematics All Chapter Creative Questions-II-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

• 2)

44≡8 (mod12), 113≡85 (mod 12),thus 44X113≡______(mod 12):

• 3)

Graphically an infinite number of solutions represents

• 4)

The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the traiangle is

• 5)

In figure $\angle OAB={ 60 }^{ o }$ and OA=6cm then radius of the circle is

#### 10th Standard Mathematic All Chapter Important Creative Questions-II- 2019-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If $\\ \\ (x)=\cfrac { x+1 }{ x-2 } ,g(x)=\cfrac { 1+2x }{ x-1 }$ then f og(x) is :

• 2)

If p,q,r,x,y,z are in A.P, then 5p+3,5r+3,5x+3,5y+3,5z+3 form

• 3)

Which of the following is correct
(i) Every polynomial has finite number of multiples
(ii) LCM of two polynimials of degree 2 may be a constant
(iii) HCF of 2 polynomials may be constant
(iv) Degree of HCF of two polynomials is always less then degree of LCM

• 4)

If triangle PQR is similar to triangle LMN such that 4PQ=LM and QR=6 cm then MN is equal to :

• 5)

Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two if the sides of the triangle are 2cm,3cm and 4 cm. find the diameter of the smallest circle.

#### 10th Standard Mathematics All Chapter Important Creative Questions-II-2020 - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

If(x)=2-3x, then f of(1-x)=?

• 2)

How many terms are there in the G.P::5,20,80,320,...,20480:

• 3)

Which of the following are linear equation in three variables

• 4)

If triangle PQR is similar to triangle LMN such that 4PQ=LM and QR=6 cm then MN is equal to :

• 5)

The ratoi of the areas of two similar triangles is equal to

#### 10th Standard Mathematics Creative Test Model - by Indumathi - Namakkal - Feb 07, 2020 - View & Read

• 1)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

• 2)

Sum of first n terms of the series $\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...$ is

• 3)

If $2A+3B=\left[ \begin{matrix} 2 & -1 & 4 \\ 3 & 2 & 5 \end{matrix} \right]$ and $A+2B=\left[ \begin{matrix} 5 & 0 & 3 \\ 1 & 6 & 2 \end{matrix} \right]$ then B=[hint:B=(A+2B)-(2+3B)]

• 4)

The ratoi of the areas of two similar triangles is equal to

• 5)

Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

#### 10th Standard Mathematics Book Back and Important Questions-II-2019-2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

f(x) = (x+1)3 - (x-1)3 represents a function which is

• 3)

$(x-\cfrac { 1 }{ x } )={ x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } }$ then f(x)=

• 4)

A={a,b,C},B={2,3},C={a,b,C,d}then n[(A∩C)XB] is:

• 5)

If functionf:N⟶N,f(x)=2x then the function is, then the function is

#### 10th Standard Mathematics Book Back and Important Questions-I-2019-2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

• 2)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

• 3)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 4)

If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

• 5)

If $f(x)=\cfrac { 1 }{ x }$, and $g(x)=\cfrac { 1 }{ { x }^{ 3 } }$ then fogo(y),is:

#### 10th Standard Mathematics Book back and Creative Important Questions-II- 2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

• 2)

If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

• 3)

If f:R⟶R is defined by(x)=x2+2, then the premiage 27 are:

• 4)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 5)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

#### 10th Standard Mathematics Book back and Creative Important Questions-I- 2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 2)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 3)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

• 4)

If f(x)=x+1 then f(f(f(y+2)) is :

• 5)

If(x)=2-3x, then f of(1-x)=?

#### 10th Standard Mathematics Questions -II- 2019-2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

• 3)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

• 4)

If $f(x)=\cfrac { 1 }{ x }$, and $g(x)=\cfrac { 1 }{ { x }^{ 3 } }$ then fogo(y),is:

• 5)

if f(x)+f(1-x)=2 then $f\left( \cfrac { 1 }{ 2 } \right)$ is

#### 10th Standard Mathematics Questions -I- 2019-2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

• 2)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

• 3)

If f:R⟶R is defined by(x)=x2+2, then the premiage 27 are:

• 4)

A={a,b,C},B={2,3},C={a,b,C,d}then n[(A∩C)XB] is:

• 5)

If functionf:N⟶N,f(x)=2x then the function is, then the function is

#### 10th Standard Mathematics Important Question All Chapter Questions -II- 2019-2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

• 2)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 3)

If f:R⟶R is defined by(x)=x2+2, then the premiage 27 are:

• 4)

If functionf:N⟶N,f(x)=2x then the function is, then the function is

• 5)

If(x)=2-3x, then f of(1-x)=?

#### 10th Standard Mathematics Important Question All Chapter-I- 2020 - by Indumathi - Namakkal - Feb 06, 2020 - View & Read

• 1)

Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

• 2)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 3)

If f:R⟶R is defined by(x)=x2+2, then the premiage 27 are:

• 4)

$(x-\cfrac { 1 }{ x } )={ x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } }$ then f(x)=

• 5)

If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

#### 10th Standard Maths Important Questions - by Indumathi - Namakkal - Feb 04, 2020 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

• 3)

If f:R⟶R is defined by(x)=x2+2, then the premiage 27 are:

• 4)

The function t which maps temperature in degree Cesius into tmperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C $t(C)=\cfrac { 9c }{ 5 } +32$ is :

• 5)

If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

#### 10th Maths - Full Portion Eight Marks Question Paper - by 8682895000 - Jan 20, 2020 - View & Read

• 1)

Let A={1,2} and B={1,2,3,4}, C={5,6} and D={5,6,7,8}, Verify whether A x C is a subset of B x D?

• 2)

A functionf: (1,6) $\rightarrow$R is defined as follows:

Find the value of f(2) - f( 4).

• 3)

Show that 107 is of the form 4q +3 for any integer q.

• 4)

Discuss the nature of solutions of the following quadratic equations.x2 + 2x + 5 = 0

• 5)

Graph the following quadratic equations and state their nature of solutions.
x2 - 9 = 0

#### 10th Maths - Full Portion Five Marks Question Paper - by 8682895000 - Jan 20, 2020 - View & Read

• 1)

Represent each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set in roster form, wherever possible.
i. {(x,y)|x = 2y, x $\in$ {2,3,4,5}, y $\in${1,2,3,4}
ii. {(x,y)|y = x+3, x, y are natural numbers < 10}.

• 2)

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown Fig. Express the volume V of the box as a function of x.

• 3)

A functionf: [-7,6) $\rightarrow$ R is defined as follows.

f(-7) -f(-3)

• 4)

A functionf: [-7,6) $\rightarrow$ R is defined as follows.

$\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) }$

• 5)

Let A = {1, 2, 3, 4, 5}, B = N and f: A $\rightarrow$B be defined by f(x) = x2. Find the range of f. Identify the type of function.

#### 10th Maths - Full Portion Two Marks Question Paper - by 8682895000 - Jan 20, 2020 - View & Read

• 1)

If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

• 2)

The arrow diagram shows a relationship between the sets P and Q. Write the relation in (i) Set builder form (ii) Roster form (iii) What is the domain and range of R.

• 3)

A plane is flying at a speed of 500 km per hour. Express the distance d travelled by the plane as function of time t in hours.

• 4)

If f(x)=3x-2, g(x)=2x+k and if f o g = f o f, then find the value of k..

• 5)

State whether the graph represent a function. Use vertical line test.

#### 10th Maths - Revision Model Question Paper 2 - by Indumathi - Namakkal - Jan 17, 2020 - View & Read

• 1)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 2)

Let f and g be two functions given by
f={(0,1), (2,0), (3,-4), (4,2), (5,7)}
g={(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 3)

If A = 265 and B = 264+263+262+...+20 Which of the following is true?

• 4)

For the given matrix A = $\left( \begin{matrix} 1 \\ 2 \\ 9 \end{matrix}\begin{matrix} 3 \\ 4 \\ 11 \end{matrix}\begin{matrix} 5 \\ 6 \\ 13 \end{matrix}\begin{matrix} 7 \\ 8 \\ 15 \end{matrix} \right)$ the order of the matrix AT is

• 5)

The two tangents from an external points P to a circle with centre at O are PA and PB.If $\angle APB$=70o then the value of $\angle AOB$ is

#### 10th Maths - Public Exam Model Question Paper 2019 - 2020 - by Indumathi - Namakkal - Jan 17, 2020 - View & Read

• 1)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 2)

Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

• 3)

An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

• 4)

For the given matrix A = $\left( \begin{matrix} 1 \\ 2 \\ 9 \end{matrix}\begin{matrix} 3 \\ 4 \\ 11 \end{matrix}\begin{matrix} 5 \\ 6 \\ 13 \end{matrix}\begin{matrix} 7 \\ 8 \\ 15 \end{matrix} \right)$ the order of the matrix AT is

• 5)

If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

#### 10th Maths - Statistics and Probability Model Question Paper - by Indumathi - Namakkal - Dec 06, 2019 - View & Read

• 1)

If are event occurs surely, then its probability is

• 2)

Two dice are through simultaneously the probability if getting a double is:

• 3)

The standard deviation is the ____ of variance

• 4)

The mean of a observation x1, x2, x3, .........xn is $\bar { x }$. If each observation is multiplied by p, there the mean of the new observations is

• 5)

If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

#### 10th Maths - Mensuration Model Question Paper - by Indumathi - Namakkal - Dec 06, 2019 - View & Read

• 1)

The radio of base of a one 5 cm and to height 12cm. The slant height of the cone.

• 2)

A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

• 3)

• 4)

The volume of a frustum if a cone of height L and ends -radio and r1 and r2 is

• 5)

The ratio of the volumes of two cones is 2:3. Find the ratio of their radii if the height of second cone is double the height of the first.

#### 10th Maths - Trigonometry Model Question Paper - by Indumathi - Namakkal - Dec 06, 2019 - View & Read

• 1)

If sinθ-cosθ=0, then the value of (sin4θ+cos4θ) is

• 2)

The value of sin2θ +$\frac { 1 }{ 1+{ tan }^{ 2 }\theta }$ of

• 3)

(cosec2θ-cot2θ) (1-cos2θ) is equal to

• 4)

9 sec2A -9tam2A=

• 5)

$1+\frac { { cot }^{ 2 }\alpha }{ 1+cosex\alpha } =cosec\alpha$

#### 10th Maths - Coordinate Geometry Model Question Paper - by Indumathi - Namakkal - Dec 06, 2019 - View & Read

• 1)

The slope of the line which is perpendicular to line joining the points (0, 0) and (–8, 8) is

• 2)

A straight line has equation 8y = 4x + 21. Which of the following is true

• 3)

When proving that a quadrilateral is a parallelogram by using slopes you must find

• 4)

(2, 1) is the point of intersection of two lines.

• 5)

Find the value of ‘a’ for which the given points are collinear.
(2, 3), (4, a) and (6, –3)

#### 10th Maths - Geometry Important Questions - by Indumathi - Namakkal - Nov 29, 2019 - View & Read

• 1)

If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

• 2)

if $\triangle$ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

• 3)

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

• 4)

In figure if PR is tangent to the circle at P and O is the centre of the circle, then $\angle PQR$ is

• 5)

Is $\triangle$ABC~$\triangle$PQR?

#### 10th Maths - Algebra Model Questions - by Indumathi - Namakkal - Nov 29, 2019 - View & Read

• 1)

A system of three linear equations in three variables is inconsistent if their planes

• 2)

$\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 }$ gives

• 3)

The square root of $\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } }$ is equal to

• 4)

If the roots of the equation q2x2 + p2x + r2 = 0 are the squares of the roots of the equation qx2 + px + r = 0, then q, p, r are in __________.

• 5)

Solve $\frac { x }{ 2 } -1=\frac { y }{ 6 } +1=\frac { z }{ 7 } +2$$\frac { y }{ 3 } +\frac { z }{ 2 } =13$

#### 10th Maths - Numbers and Sequences Model Questions - by Indumathi - Namakkal - Nov 29, 2019 - View & Read

• 1)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

• 2)

If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is

• 3)

The next term of the sequence $\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 }$, ..... is

• 4)

If the sequence t1,t2,t3...are in A.P. then the sequence t6,t12,t18,....is

• 5)

Find the HCF of 396, 504, 636.

#### 10th Maths - Relations and Functions Model Question Paper - by Indumathi - Namakkal - Nov 29, 2019 - View & Read

• 1)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 2)

Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

• 3)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 4)

f(x) = (x+1)3 - (x-1)3 represents a function which is

• 5)

Let X={1,2,3,4} and Y={2,4,6,8,10} and R={(1,2),(2,4),(3,6),(4,8)} Show that R is a function and find its domain, co-domain and range?

#### 10th Maths - Half Yearly Model Question Paper 2019 - by Indumathi - Namakkal - Nov 13, 2019 - View & Read

• 1)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 2)

If the sequence t1,t2,t3...are in A.P. then the sequence t6,t12,t18,....is

• 3)

Which of the following should be added to make x4 + 64 a perfect square

• 4)

In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP=11 cm andBC =7 cm, then the length of BR is

• 5)

A straight line has equation 8y = 4x + 21. Which of the following is true

#### 10th Standard Maths - Term II Model Question Paper - by Selvamary - Erode - Oct 29, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

f(x) = (x+1)3 - (x-1)3 represents a function which is

• 3)

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

A system of three linear equations in three variables is inconsistent if their planes

• 5)

If $\triangle$ABC is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

#### 10th Standard Maths - Statistics and Probability Model Question Paper - by Selvamary - Erode - Oct 12, 2019 - View & Read

• 1)

Which of the following is not a measure of dispersion?

• 2)

If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

• 3)

The probability of getting a job for a person is $\frac{x}{3}$. If the probability of not getting the job is $\frac{2}{3}$  then the value of x is

• 4)

A purse contains 10 notes of Rs.2000, 15 notes of Rs.500, and 25 notes of Rs.200. One note is drawn at random. What is the probability that the note is either a Rs.500 note or Rs.200 note?

• 5)

A girl Calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game

#### 10th Maths - Mensuration Model Question Paper - by Selvamary - Erode - Oct 12, 2019 - View & Read

• 1)

If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

• 2)

If the radius of the base of a cone is tripled and the height is doubled then the volume is

• 3)

A shuttle cock used for playing badminton has the shape of the combination of

• 4)

The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

• 5)

The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

#### 10th Maths - Coordinate Geometry Five Marks Questions - by Indumathi - Namakkal - Oct 09, 2019 - View & Read

• 1)

The line r passes through the points (–2, 2) and (5, 8) and the line θ passes through the points (–8, 7) and (–2, 0). Is the line r perpendicular to θ ?

• 2)

The line p passes through the points (3, - 2), (12, 4) and the line q passes through the points (6, -2) and (12, 2). Is parallel to q ?

• 3)

Show that the straight lines 2x + 3y - 8 = 0 and 4x + 6y + 18 = 0 are parrel.

• 4)

Show that the straight lines x - 2y + 3 = 0 and 6x + 3y + 8 = 0 are perpendicular.

• 5)

A(1, -2), B(6, -2), C(5, 1) and D(2, 1) be four points

#### 10th Maths - Trigonometry Five Marks Questions - by Indumathi - Namakkal - Oct 09, 2019 - View & Read

• 1)

If sin (A - B) = $\frac12$,  cos (A + B) = $\frac12$, 0o < A + ≤  90°, A > B, find A and B.

• 2)

Express the ratios cos A, tan A and see A in terms-of sin A.

• 3)

If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.

• 4)

If ATB=90o then prove that
$\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA$

• 5)

P.T (1+tan∝tan∝tanβ)2 +(tan∝-tanβ)2 =sec2 ∝sec2β.

#### 10th Standard Maths - Statistics and Probability Five Marks Questions - by Indumathi - Namakkal - Oct 09, 2019 - View & Read

• 1)

The mean of a data is 25.6 and its coefficient of variation is 18.75. Find the standard deviation.

• 2)

The consumption of number of guava and orange on a particular week by a family are given below.

 Number of Guavas 3 5 6 4 3 5 4 Number of Oranges 1 3 7 9 2 6 2

Which fruit is consistently consumed by the family?

• 3)

If P(A).=037, P(B).=0.42, P(A∩B) =009 then find P(AUB).

• 4)

What is the probability of drawing either a king or a queen in a single draw from a well shuffled pack of 52 cards?

• 5)

A card is drawn from a pack of 52 cards. Find the probability of getting a king or a heart or a red card.

#### 10th Standard Maths - Mensuration Five Marks Questions - by Indumathi - Namakkal - Oct 09, 2019 - View & Read

• 1)

Find the volume of a cylinder whose height is 2 m and whose base area is 250 m2.

• 2)

The volume of a cylindrical water tank is 1.078×106 litres. If the diameter of the tank is 7m, find its height.

• 3)

The volume of a solid right circular cone is 11088 cm3. If its height is 24 cm then find the radius of the cone.

• 4)

The volume of a solid hemisphere is 29106 cm3. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

• 5)

Calculate the weight of a hollow brass sphere if the inner diameter is 14 cm and thickness is 1mm, and whose density is 17.3 g/ cm3.

#### 10th Standard Maths - Geometry Five Marks Questions - by Indumathi - Namakkal - Oct 09, 2019 - View & Read

• 1)

D and E are respectively the points on the sides AB and AC of a DABC such that AB=5.6 cm, AD=1.4 cm, AC=7.2 cm and AE = 1.8 cm, show that DE||BC

• 2)

DE||AC and DC||AP. Prove that $\cfrac { BE }{ CE } =\cfrac { BC }{ CP }$

• 3)

Construct a triangle $\triangle$PQR such that QR = 5 cm, $\angle$P=30 and the altitude from P to QR is of length 4.2 cm.

• 4)

Draw a triangle ABC of base BC = 8 cm, $\angle$A=60o and the bisector of $\angle$A meets BC at D such that BD = 6 cm.

• 5)

In Fig, ABC is a triangle with $\angle$B=90o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.

#### 10th Standard Maths - Trigonometry Model Question Paper - by Selvamary - Erode - Oct 04, 2019 - View & Read

• 1)

tan$\theta$cosec2$\theta$-tan$\theta$ is equal to

• 2)

(1+tan$\theta$+sec$\theta$) (1+cot$\theta$-cosec$\theta$) is equal to

• 3)

If the ratio of the height of a tower and the length of its shadow is $\sqrt { 3 }$:1 then the angle of elevation of the sun has measure

• 4)

The angle of elevation of a cloud from a point h metres above a lake is $\beta$. The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

• 5)

The value of the expression [cosec(75o+θ)-sec (15o-θ)-tan(55o+θ)+cot(35o-θ] is

#### 10th Standard Maths - Coordinate Geometry Model Question Paper - by Selvamary - Erode - Oct 04, 2019 - View & Read

• 1)

The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

• 2)

The slope of the line joining (12, 3) , (4, a) is $\frac 18$The value of ‘a’ is

• 3)

If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

• 4)

A straight line has equation 8y = 4x + 21. Which of the following is true

• 5)

(2, 1) is the point of intersection of two lines.

#### 10th Science - Relations and Functions Five Marks Questions - by Indumathi - Namakkal - Oct 03, 2019 - View & Read

• 1)

The arrow diagram shows a relationship between the sets P and Q. Write the relation in (i) Set builder form (ii) Roster form (iii) What is the domain and range of R.

• 2)

Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}  be a function from A to B. Show that f is one – one but not onto function.

• 3)

If A={-2,-1,0,1,2} and f: A ⟶ B is an onto function defined by f(x)=x2+x+1 then find B.

• 4)

If the function f: R⟶ R defined by

(i) f(4)
(ii) f(-2)
(iii) f(4)+2f(1)
(iv) $\frac { f(1)-3f(4) }{ f(-3) }$

• 5)

Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this (i) an one-one function (ii) an onto function, (iii) both oneone and onto function?

#### 10th Science - Numbers and Sequences Five Marks Questions - by Indumathi - Namakkal - Oct 03, 2019 - View & Read

• 1)

How many terms of the series 1 + 5 +9 + ....must be taken so that their sum is 190?

• 2)

The 13th term of an A.P is 3 and the sum of the first 13 terms is 234.Find the common difference and the sum of first 21 terms.

• 3)

Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

• 4)

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
4,10,16,22, ...

• 5)

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
1,-1,-3, -5, ...

#### 10th Maths - Algebra Five Marks Questions - by Indumathi - Namakkal - Oct 03, 2019 - View & Read

• 1)

Find the square root of the following expressions
256(x - a)2 (x - b)4 (x - c)16 (x - d)20

• 2)

Find the zeroes of the quadratic expression x2 + 8x + 12

• 3)

Write down the quadratic equation in general form for which sum and product of the roots are given below.
9, 14

• 4)

Solve x2 - 3x - 2 = 0

• 5)

Draw the graph of y = 2x2 and hence solve 2x2 - x - 6 = 0

#### 10th Standard Maths - Geometry Model Question Paper - by Selvamary - Erode - Sep 30, 2019 - View & Read

• 1)

If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

• 2)

if $\triangle$ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

• 3)

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

• 4)

How many tangents can be drawn to the circle from an exterior point?

• 5)

In figure if PR is tangent to the circle at P and O is the centre of the circle, then $\angle PQR$ is

#### 10th Standard Maths - Algebra Model Question Paper - by Selvamary - Erode - Sep 30, 2019 - View & Read

• 1)

A system of three linear equations in three variables is inconsistent if their planes

• 2)

$\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}$ is

• 3)

Which of the following should be added to make x4 + 64 a perfect square

• 4)

Graph of a linear polynomial is a

• 5)

Transpose of a column matrix is

#### 10th Standard Maths - Numbers and Sequences Model Question Paper - by Selvamary - Erode - Sep 25, 2019 - View & Read

• 1)

Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

• 2)

74k $\equiv$ ________ (mod 100)

• 3)

An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

• 4)

The next term of the sequence $\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 }$, ..... is

• 5)

The value of (13+23+33+...153) - (1+2+3+...+15)is

#### 10th Standard Maths - Relations and Functions Model Question Paper - by Selvamary - Erode - Sep 25, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

• 3)

If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

• 4)

If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

• 5)

f(x) = (x+1)3 - (x-1)3 represents a function which is

#### 10th Maths - Statistics and Probability Two Marks Questions - by Indumathi - Namakkal - Sep 21, 2019 - View & Read

• 1)

The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find its standard deviation.

• 2)

Find the mean and variance of the first n natural numbers.

• 3)

48 students were asked to write the total number of hours per week they spent on watching television. With this information find the standard deviation of hours spent for watching television.

 x 6 7 8 9 10 11 12 f 3 6 9 13 8 5 4
• 4)

Marks of the students in a particular subject of a class are given below:

 Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Number of students 8 12 17 14 9 7 4

Find its standard deviation.

• 5)

Two coins are tossed together. What is the probability of getting different faces on the coins?

#### 10th Maths - Mensuration Two Marks Questions - by Indumathi - Namakkal - Sep 21, 2019 - View & Read

• 1)

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2 . Find the diameter of the cylinder.

• 2)

A garden roller whose length is 3 m long and whose diameter is 2.8 m is rolled to level a garden. How much area will it cover in 8 revolutions?

• 3)

If the total surface area of a cone of radius 7cm is 704 cm2, then find its slant height.

• 4)

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and base is hollowed out (Fig.7.13). Find the total surface area of the remaining solid.

• 5)

The radius of a spherical balloon increases from 12 cm to 16 cm as air being pumped into it. Find the ratio of the surface area of the balloons in the two cases.

#### 10th Maths - Trigonometry Two Marks Questions - by Indumathi - Namakkal - Sep 21, 2019 - View & Read

• 1)

prove that$\left( \frac { co{ s }^{ 3 }A-si{ n }^{ 3 }A }{ cosA-sinA } \right) -\left( \frac { co{ s }^{ 3 }A+si{ n }^{ 3 }A }{ cosA+sinA } \right) =2sinAcosA$

• 2)

prove that $\frac { sinA }{ secA+tanA-1 } +\frac { cosA }{ cosecA+cotA-1 } =1$

• 3)

As observed from the top of a 60 m high light house from the sea level, the angles of depression of two ships are 28° and45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
(tan28°=0.5317)

• 4)

A man is watching a boat speeding away from the top of a tower. The boat makes an angle of depression of 60° with the man’s eye when at a distance of 200 m from the tower. After 10 seconds, the angle of depression becomes 45°. What is the approximate speed of the boat (in km / hr), assuming that it is sailing in still water?($\sqrt { 3 }$=1.732)

• 5)

If tan A=$\frac{3}{4}$, then sin A cos A=$\frac{12}{15}$

#### 10th Maths - Coordinate Geometry Two Marks Questions - by Indumathi - Namakkal - Sep 21, 2019 - View & Read

• 1)

Show that the points P(-1.5,3), Q(6,-2) , R(-3,4) are collinear.

• 2)

If the area of the triangle formed by the vertices A(-1,2) , B(k,-2) and C(7,4) (taken in order) is 22 sq. units, find the value of k.

• 3)

Find the area of the quadrilateral formed by the points (8, 6), (5, 11), (-5, 12) and (-4, 3).

• 4)

The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost Rs. 1300 per square feet. What will be the total cost for making the parking lot?

• 5)

Calculate the slope and y intercept of the straight line 8x − 7y + 6=0

#### 10th Maths - Term 1 Model Question Paper - by Selvamary - Erode - Sep 20, 2019 - View & Read

• 1)

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 2)

If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

• 3)

Graph of a linear polynomial is a

• 4)

If $\triangle$ABC is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

• 5)

The point of intersection of 3x − y = 4 and x + y = 8 is

#### 10th Maths - Geometry Two Marks Question - by Indumathi - Namakkal - Sep 19, 2019 - View & Read

• 1)

Is $\triangle$ABC~$\triangle$PQR?

• 2)

A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.

• 3)

$\angle A=\angle CED$ prove that $\Delta\ CAB \sim \Delta CED$ Also find the value of x.

• 4)

If $\triangle$ABC is similar to$\triangle$DEFsuch that BC=3 cm, EF=4 cm and area of $\triangle$ABC= 54 cm2. Find the area of $\triangle$DEF.

• 5)

An insect 8 m away initially from the foot of a lamp post which is 6 m tall, crawls towards it moving through a distance. If its distance from the top of the lamp post is equal to the distance it has moved, how far is the insect away from the foot of the lamp post?

#### 10th Science - Algebra Two Marks Question - by Indumathi - Namakkal - Sep 19, 2019 - View & Read

• 1)

The father’s age is six times his son’s age. Six years hence the age of father will be four times his son’s age. Find the present ages (in years) of the son and father.

• 2)

Find $\frac { { x }^{ 2 }+20x+36 }{ { x }^{ 2 }-3x-28 } -\frac { { x }^{ 2 }+12x+4 }{ { x }^{ 2 }-3x-28 }$

• 3)

Find the square root of 64x4 - 16x3 + 17x2 - 2x + 1

• 4)

If 9x4 + 12x3 + 28x2 + ax + b is a perfect square, find the values of a and b.

• 5)

Solve 2m2+ 19m + 30 = 0

#### 10th Maths Unit 2 Numbers and Sequences Two Marks Question - by Indumathi - Namakkal - Sep 19, 2019 - View & Read

• 1)

We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?

• 2)

Find the remainders when 70004 and 778 is divided by 7

• 3)

Find the number of integer solutions of 3x $\equiv$ 1 (mod 15).

• 4)

Write an A.P. whose first term is 20 and common difference is 8.

• 5)

Find the number of terms in the A.P. 3, 6, 9, 12,…, 111.

#### 10th Maths Chapter 1 Relations and Functions Two Marks Question - by Indumathi - Namakkal - Sep 19, 2019 - View & Read

• 1)

If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

• 2)

Let A = {x $\in$ N| 1 < x < 4}, B={x $\in$ W| 0 ≤ x < 2) and C={x $\in$ N| x < 3} Then verify that
(i) A x (B U C) = (A x B) U (A x C)
(ii) A x (B ∩ C) = (A x B) ∩ (A x C)

• 3)

Let X={1,2,3,4} and Y={2,4,6,8,10} and R={(1,2),(2,4),(3,6),(4,8)} Show that R is a function and find its domain, co-domain and range?

• 4)

A relation ‘f’ is defined by f(x)=x2-2 where x$\in${-2,-1,0,3}
(i) List the elements of f
(ii) Is f a function?

• 5)

If f(x)=3x-2, g(x)=2x+k and if f o g = f o f, then find the value of k..

#### 10th Maths - Term 1 Five Mark Model Question Paper - by Indumathi - Namakkal - Sep 16, 2019 - View & Read

• 1)

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R1={(3,7), (4,7), (7,10), (8,1)}

• 2)

Let A = {1,2,3,4} and B ={2,5,8,11,14} be two sets. Let f: A ⟶ B be a function given by f(x)=3x−1. Represent this function
(i) by arrow diagram
(ii) in a table form
(iii) as a set of ordered pairs
(iv) in a graphical form

• 3)

The general term of a sequence is defined as
an = {$\begin{matrix} n\left( n+3 \right) ;n\epsilon N\quad is\quad odd \\ { n }^{ 2 }+1;n\epsilon N\quad is\quad even \end{matrix}$
Find the eleventh and eighteenth terms.

• 4)

In an A.P. the sum of first n terms is $\frac { { 5n }^{ 2 } }{ 2 } +\frac { 3n }{ 2 }$. Find the 17th term

• 5)

Find the GCD of 6x3 - 30x2 + 60x - 48 and 3x3 - 12x2 + 21x - 18.

#### 10th Maths Quarterly Model Questions Paper - by Indumathi - Namakkal - Sep 14, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

• 3)

If $\triangle$ABC is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

• 4)

if $\triangle$ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

• 5)

The slope of the line which is perpendicular to line joining the points (0, 0) and (–8, 8) is

#### 10th Standard Maths Unit 8 Statistics and Probability Book Back Questions - by Indumathi - Namakkal - Sep 04, 2019 - View & Read

• 1)

Which of the following is not a measure of dispersion?

• 2)

The range of the data 8, 8, 8, 8, 8. . . 8 is

• 3)

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is

• 4)

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

• 5)

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

#### 10th Standard Maths Unit 7 Mensuration Book Back Questions - by Indumathi - Namakkal - Sep 04, 2019 - View & Read

• 1)

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

• 2)

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

• 3)

Th e height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

• 4)

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is

• 5)

A shuttle cock used for playing badminton has the shape of the combination of

#### 10th Standard Maths Unit 6 Trigonometry Book Back Questions - by Indumathi - Namakkal - Sep 04, 2019 - View & Read

• 1)

The value of is $si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta }$ equal to

• 2)

if sin$\theta$=cos$\theta$=a and sec$\theta$+cosec$\theta$=b, then the value of b (a2-1) is equal to

• 3)

(1+tan$\theta$+sec$\theta$) (1+cot$\theta$-cosec$\theta$) is equal to

• 4)

The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the tower is 60°. The height of the tower (in metres) is equal to

• 5)

A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

#### 10th Standard Maths Unit 5 Coordinate Geometry Book Back Questions - by Indumathi - Namakkal - Sep 04, 2019 - View & Read

• 1)

The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

• 2)

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

• 3)

The straight line given by the equation x = 11 is

• 4)

If slope of the line PQ is $\frac { 1 }{ \sqrt { 3 } }$ then the slope of the perpendicular bisector of PQ is

• 5)

The equation of a line passing through the origin and perpendicular to the line

#### 10th Standard Maths Unit 4 Geometry Book Back Questions - by Indumathi - Namakkal - Sep 03, 2019 - View & Read

• 1)

If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

• 2)

In $\angle$LMN, $\angle$L=60o,$\angle$M=50o, If $\triangle$LMN~$\triangle$PQR then the value of $\angle$R is

• 3)

if $\triangle$ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

• 4)

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

• 5)

The two tangents from an external points P to a circle with centre at O are PA and PB.If $\angle APB$=70o then the value of $\angle AOB$ is

#### 10th Standard Maths - Numbers and Sequences Book Back Questions - by Indumathi - Namakkal - Sep 02, 2019 - View & Read

• 1)

Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

• 2)

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 3)

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

Given F1 = 1, F2 = 3 and Fn = Fn-1+Fn-2 then F5 is

• 5)

If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is

#### 10th Standard Maths - Algebra Book Back Questions - by Indumathi - Namakkal - Sep 02, 2019 - View & Read

• 1)

A system of three linear equations in three variables is inconsistent if their planes

• 2)

The solution of the system x + y − 3x = −6, −7y + 7z = 7 , 3z = 9 is

• 3)

If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

• 4)

$\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 }$ gives

• 5)

The solution of (2x - 1)2 = 9 is equal to

#### 10th Maths Unit 1 Relations and Functions Book Back Questions - by Indumathi - Namakkal - Aug 30, 2019 - View & Read

• 1)

If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

• 2)

Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

• 3)

If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

• 4)

f(x) = (x+1)3 - (x-1)3 represents a function which is

• 5)

Represent the function f(x)=$\sqrt { 2x^{ 2 }-5x+3 }$ as a composition of two functions.

#### 10th Standard Maths Chapter 1 Relations and Functions One Mark Question with Answer Key - by Indumathi - Namakkal - Aug 29, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 3)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 4)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 5)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is

#### 10th Standard Maths Unit 8 Statistics and Probability One Mark Question and Answer - by Indumathi - Namakkal - Aug 29, 2019 - View & Read

• 1)

Which of the following is not a measure of dispersion?

• 2)

The range of the data 8, 8, 8, 8, 8. . . 8 is

• 3)

The sum of all deviations of the data from its mean is

• 4)

A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4 find the probability that |x|≤4

• 5)

which of the following is true?

#### 10th Maths - Mensuration One Mark Question with Answer - by Indumathi - Namakkal - Aug 28, 2019 - View & Read

• 1)

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

• 2)

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

• 3)

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

• 4)

If the radius of the base of a cone is tripled and the height is doubled then the volume is

• 5)

The total surface area of a hemi-sphere is how much times the square of its radius.

#### 10th Maths Chapter 6 Trigonometry - One Mark Question with Answer Key - by Indumathi - Namakkal - Aug 27, 2019 - View & Read

• 1)

The value of is $si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta }$ equal to

• 2)

if sin$\theta$=cos$\theta$=a and sec$\theta$+cosec$\theta$=b, then the value of b (a2-1) is equal to

• 3)

(1+tan$\theta$+sec$\theta$) (1+cot$\theta$-cosec$\theta$) is equal to

• 4)

a cot$\theta$+b cosec$\theta$ =p and b cot $\theta$+a cosec$\theta$ =q then p2-qis equal to

• 5)

If sin A=$\frac{1}{2}$, then the value of cot A is

#### 10th Maths Unit 5 Coordinate Geometry One Mark Question and Answer - by Indumathi - Namakkal - Aug 27, 2019 - View & Read

• 1)

The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

• 2)

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

• 3)

The straight line given by the equation x = 11 is

• 4)

If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

• 5)

The point of intersection of 3x − y = 4 and x + y = 8 is

#### 10th Maths - Geometry One Mark Question with Answer - by Indumathi - Namakkal - Aug 27, 2019 - View & Read

• 1)

If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

• 2)

In $\angle$LMN, $\angle$L=60o,$\angle$M=50o, If $\triangle$LMN~$\triangle$PQR then the value of $\angle$R is

• 3)

If $\triangle$ABC is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

• 4)

In a given figure ST||QR,PS=2cm and SQ=3 cm.
Then the ratio of the area of $\triangle$PQR to the area $\triangle$PST is

• 5)

The perimeters of two similar triangles$\triangle$ABC and $\triangle$PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is

#### 10th Maths Unit 3 Algebra - One Mark Question Paper with Answer Key - by Indumathi - Namakkal - Aug 26, 2019 - View & Read

• 1)

A system of three linear equations in three variables is inconsistent if their planes

• 2)

The solution of the system x + y − 3x = −6, −7y + 7z = 7 , 3z = 9 is

• 3)

y2 + $\frac {1}{y^{2}}$ is not equal to

• 4)

The square root of $\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } }$ is equal to

• 5)

The solution of (2x - 1)2 = 9 is equal to

#### 10th Maths Unit 2 Numbers and Sequences One Mark Questions With Answer - by Indumathi - Namakkal - Aug 24, 2019 - View & Read

• 1)

Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

• 2)

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 3)

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

The sum of the exponents of the prime factors in the prime factorization of 1729 is

• 5)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

#### 10th Maths Relations and Functions One Mark Questions Paper - by Indumathi - Namakkal - Aug 23, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 3)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 4)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 5)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is

#### 10th Maths Quarterly Exam Model Two Marks Question Paper - by Indumathi - Namakkal - Aug 20, 2019 - View & Read

• 1)

If X = {–5,1,3,4} and Y = {a,b,c}, then which of the following relations are functions from X to Y ? R1= {(–5,a), (1,a), (3,b)}

• 2)

If f(x)=2x+3, g(x)=1-2x and h(x)=3x. Prove that f 0 (f o g) o h.

• 3)

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

• 4)

Find the HCF of 396, 504, 636.

• 5)

Determine the general term of an A.P. whose 7th term is -1 and 16th term is 17.

#### 10th Maths August Monthly Model Test Paper - by Indumathi - Namakkal - Aug 19, 2019 - View & Read

• 1)

A system of three linear equations in three variables is inconsistent if their planes

• 2)

y2 + $\frac {1}{y^{2}}$ is not equal to

• 3)

The square root of $\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } }$ is equal to

• 4)

Transpose of a column matrix is

• 5)

In $\angle$LMN, $\angle$L=60o,$\angle$M=50o, If $\triangle$LMN~$\triangle$PQR then the value of $\angle$R is

#### SSLC Maths Chapter 5 Coordinate Geometry Model Question Paper - by Indumathi - Namakkal - Aug 05, 2019 - View & Read

• 1)

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

• 2)

The slope of the line which is perpendicular to line joining the points (0, 0) and (–8, 8) is

• 3)

The equation of a line passing through the origin and perpendicular to the line

• 4)

When proving that a quadrilateral is a trapezium, it is necessary to show

• 5)

(2, 1) is the point of intersection of two lines.

#### 10th Standard Maths First Mid Term Model Question Paper - by Indumathi - Namakkal - Aug 01, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

• 3)

74k $\equiv$ ________ (mod 100)

• 4)

An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

• 5)

The value of (13+23+33+...153) - (1+2+3+...+15)is

#### 1. RELATIONS AND FUNCTIONS - by 9444441210 - Jul 31, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 3)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 4)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 5)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is

#### 10th Standard Maths Geometry Model Question Paper - by Indumathi - Namakkal - Jul 31, 2019 - View & Read

• 1)

If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

• 2)

If $\triangle$ABC is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

• 3)

if $\triangle$ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

• 4)

A tangent is perpendicular to the radius at the

• 5)

In figure if PR is tangent to the circle at P and O is the centre of the circle, then $\angle PQR$ is

#### 10th Standard Maths Chapter 3 Algebra Important Question Paper - by Indumathi - Namakkal - Jul 26, 2019 - View & Read

• 1)

A system of three linear equations in three variables is inconsistent if their planes

• 2)

The solution of the system x + y − 3x = −6, −7y + 7z = 7 , 3z = 9 is

• 3)

If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

• 4)

$\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}$ is

• 5)

y2 + $\frac {1}{y^{2}}$ is not equal to

#### 10th Standard Maths Chapter 2 Numbers and Sequences Important Question Paper - by Indumathi - Namakkal - Jul 25, 2019 - View & Read

• 1)

Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

• 2)

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 3)

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

The sum of the exponents of the prime factors in the prime factorization of 1729 is

• 5)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

#### SSLC Maths Chapter 1 Important Question Paper - by Indumathi - Namakkal - Jul 18, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 3)

Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

• 4)

If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

• 5)

Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

#### frequently asked five mark questions in maths chapter one for state board english mesium - by Karthik - Jun 28, 2019 - View & Read

• 1)

Let A = {1,2,3,4} and B ={2,5,8,11,14} be two sets. Let f: A ⟶ B be a function given by f(x)=3x−1. Represent this function
(i) by arrow diagram
(ii) in a table form
(iii) as a set of ordered pairs
(iv) in a graphical form

• 2)

Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.

• 3)

Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}  be a function from A to B. Show that f is one – one but not onto function.

• 4)

If A={-2,-1,0,1,2} and f: A ⟶ B is an onto function defined by f(x)=x2+x+1 then find B.

• 5)

Let f be a function f:N ⟶ N be defined by f(x) = 3x+2, x$\in$N
(i) Find the images of 1, 2, 3
(ii) Find the pre-images of 29, 53
(ii) Identify the type of function

#### Maths chapter one important questions for state board english medium - by Karthik - Jun 28, 2019 - View & Read

• 1)

A relation ‘f’ is defined by f(x)=x2-2 where x$\in${-2,-1,0,3}
(i) List the elements of f
(ii) Is f a function?

• 2)

If X = {–5,1,3,4} and Y = {a,b,c}, then which of the following relations are functions from X to Y ? R1= {(–5,a), (1,a), (3,b)}

• 3)

Given f(x) =2x-x2, find
(i) f (1)
(ii) f (x+1)
(iii) f (x) + f (1)

• 4)

Find f o g and g o f when f(x)=2x+1 and g(x)=x2-2

• 5)

Represent the function f(x)=$\sqrt { 2x^{ 2 }-5x+3 }$ as a composition of two functions.

#### 10th standard new syllabus creative multiple choice questions in chapter one maths - by Karthik - Jun 28, 2019 - View & Read

• 1)

If n(A x B) =6 and A={1,3} then n(B) is

• 2)

A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

• 3)

If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

• 4)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 5)

The range of the relation R ={(x,x2) |x is a prime number less than 13} is


text:
Save up to $499! Grab all Python courses for$49 or all online courses we’ve ever launched for only \$169. Only Feb 11-16. Happy Valentine's!
Introduction
Grouping
12. Statistical functions in groups
Summary

Instruction

Great. Apart from size(), we can use all the other statistical functions that we got to know. For instance, if we want to find the average number of aces based on players’ height, we can use:

players_by_height['aces'].mean()

The result looks something like:

height
180 1689.000000
185 5060.000000
191 2366.500000
198 3658.666667
203 5837.000000
Name: aces, dtype: float64

Note that we can refer to specific columns using the brackets operator. In this case, we specified the aces column and calculated the mean for each height group.

Exercise

Calculate the total revenue from ticket sales in each country. To that end, use the sum() function on the box_office column.

Stuck? Here's a hint!

movies_by_country['box_office']

format: plain


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## Found 234 Documents (Results 1–100)

100
MathJax

### Derivations and identities for Chebyshev polynomials. (English. Ukrainian original)Zbl 07491004

Ukr. Math. J. 73, No. 8, 1175-1188 (2022); translation from Ukr. Mat. Zh. 73, No. 8, 1011-1022 (2021).
MSC:  11B83 05A19 33C45
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### “Interpolated factored Green function” method for accelerated solution of scattering problems. (English)Zbl 07506526

MSC:  65Dxx 65Cxx 65Rxx
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### Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints. (English)Zbl 07468437

MSC:  65L05 34K06 34K28
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### A differential analogue of Favard’s theorem. (English)Zbl 07456830

Gesztesy, Fritz (ed.) et al., From operator theory to orthogonal polynomials, combinatorics, and number theory. A volume in honor of Lance Littlejohn’s 70th birthday. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 285, 239-263 (2021).
MSC:  47-XX 33-XX
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### On Jacobi polynomials and fractional spectral functions on compact symmetric spaces. (English)Zbl 07383717

MSC:  33D15 33D45
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MSC:  33C45
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### Modified Chebyshev collocation method for delayed predator-prey system. (English)Zbl 07490962

MSC:  65L60 92D25
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### A new collocation method using near-minimal Chebyshev quadrature nodes on a square. (English)Zbl 07193927

MSC:  65Dxx 41Axx
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### The faster methods for computing Bessel functions of the first kind of an integer order with application to graphic processors. (English)Zbl 07150899

MSC:  65-XX 41-XX
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### Fractional pseudospectral integration/differentiation matrix and fractional differential equations. (English)Zbl 1428.74225

MSC:  74S25 65M70 34A08
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### A new estimate for a quantity involving the Chebyshev polynomials of the first kind. (English)Zbl 1417.65218

MSC:  65N55 33C45 65N12
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### Accurate and efficient evaluation of Chebyshev tensor product surface. (English)Zbl 1426.65020

MSC:  65D10 41A10 65G50
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### Five themes in Chebyshev spectral methods applied to the regularized Charney eigenproblem: extra numerical boundary conditions, a boundary-layer-resolving change of coordinate, parameterizing a curve which is singular at an endpoint, extending the tau method to log-and-polynomials and finding the roots of a polynomial-and-log approximation. (English)Zbl 1443.65104

MSC:  65L60 33C45 86A10
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### Incremental modeling of a new high-order polynomial surrogate model. (English)Zbl 1459.62149

MSC:  62J99 65C20
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### Numerical solutions of elliptic partial differential equations using Chebyshev polynomials. (English)Zbl 1359.65275

MSC:  65N35 35J25 65N80
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MSC:  33C45
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### Extension of generalized recursive tau method to non-linear ordinary differential equations. (English)Zbl 1353.65070

MSC:  65L05 34A34
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### Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: restrictions and two improvements. (English)Zbl 1416.65478

MSC:  65N35 65N12
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### The Chebyshev points of the first kind. (English)Zbl 1334.65055

MSC:  65D20 33C45 41A50
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### Numerical approximations of Sturm-Liouville eigenvalues using Chebyshev polynomial expansions method. (English)Zbl 1339.65099

MSC:  65L15 65L60
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### Reduced-order extrapolation spectral-finite difference scheme based on POD method and error estimation for three-dimensional parabolic equation. (English)Zbl 1327.65210

MSC:  65N12 65N30 65M60
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### Powers of complex persymmetric antitridiagonal matrices with constant antidiagonals. (English)Zbl 1306.65197

MSC:  65F30 15B05
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### Post-buckling analysis of skew plates subjected to combined in-plane loadings. (English)Zbl 1302.74070

MSC:  74G60 74K20 74A40
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### On solution of Fredholm integrodifferential equations using composite Chebyshev finite difference method. (English)Zbl 1470.65219

MSC:  65R20 65L60 45J05
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### Prediction of frequencies of free axisymmetric vibration of two-directional functionally graded annular plates on Winkler foundation. (English)Zbl 1406.74309

MSC:  74H45 70J50 74K20
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### A wavelet-based approach for vibration analysis of framed structures. (English)Zbl 1329.70054

MSC:  70J50 74H45 65T60
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MSC:  65D30
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### Three-dimensional vibrations of annular thick plates with linearly varying thickness. (English)Zbl 1293.74220

MSC:  74H45 74K20 74H15
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### Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials. (English)Zbl 1266.65115

MSC:  65L03 34K28 65L70
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### Asymptotics on Laguerre or Hermite polynomial expansions and their applications in Gauss quadrature. (English)Zbl 1259.65058

MSC:  65D32 41A55
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### Efficient spectral-Petrov-Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials. (English)Zbl 1242.65148

MSC:  65L60 34B05 65L10
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MSC:  41A25
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### On the three-dimensional vibrations of a hollow elastic torus of annular cross-section. (English)Zbl 1271.74207

MSC:  74H45 74H10
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### Analytical and chpdm analysis of MHD mixed convection over a vertical flat plate embedded in a porous medium filled with water at 4$$^{\circ}$$C. (English)Zbl 1228.76190

Appl. Math. Modelling 35, No. 10, 5182-5197 (2011); corrigendum ibid. 40, No. 13-14, 6785-6786 (2016).
MSC:  76W05
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### On the Chebyshev spectral continuous time approximation for constant and periodic delay differential equations. (English)Zbl 1221.65158

MSC:  65L03 34K07
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### Nonlinear dynamic response of laminated composite plates subjected to pulse loading. (English)Zbl 1392.74046

MSC:  74H10 74K20 74E30
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### Orthogonal polynomial expansions for the matrix exponential. (English)Zbl 1217.65078

MSC:  65F30 15A16
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### On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials. (English)Zbl 1207.65098

MSC:  65L10 34B15 34B10
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### Three-dimensional vibration analysis of prisms with isosceles triangular cross-section. (English)Zbl 1271.74206

MSC:  74H45 74B05 74S30
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MSC:  45E10
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### Using piecewise polynomials for faster potential function evaluation. (English)Zbl 1182.65018

MSC:  65D05 65C05 82B80
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MSC:  45B05
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MSC:  65R20
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### Exponential fitting BDF-Runge-Kutta algorithms. (English)Zbl 1196.65118

MSC:  65L06 65L04
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### Evaluating of Dawson’s integral by solving its differential equation using orthogonal rational Chebyshev functions. (English)Zbl 1157.65331

MSC:  65D20 33B20 33F05
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### A numerical method for solving a class of functional and two-dimensional integral equations. (English)Zbl 1137.65065

MSC:  65R20 45B05 45D05
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### Solving integral equations with logarithmic kernels by Chebyshev polynomials. (English)Zbl 1136.65126

MSC:  65R20 45G05
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### Similarity solutions of a MHD boundary-layer flow past a continuous moving surface. (English)Zbl 1213.76234

MSC:  76W05 76D10 76M55
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### A Chebyshev approximation for solving the optimal production inventory problem of deteriorating multi-item. (English)Zbl 1173.90311

MSC:  90B05 90B25 49N90
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MSC:  65D15
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### Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration. (English)Zbl 1117.65178

MSC:  65T60 65L05
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### Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.’s. (English)Zbl 1117.65106

MSC:  65L05 34A34 65L50
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MSC:  65M70
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### A basic class of symmetric orthogonal polynomials using the extended Sturm-Liouville theorem for symmetric functions. (English)Zbl 1131.33005

MSC:  33C45 33C47 42C05
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### On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis. I. (English)Zbl 1106.65312

MSC:  65F30 65F50 15B57 15A21
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### A new eighth-order A-stable method for solving differential systems arising in chemical reactions. (English)Zbl 1103.92057

MSC:  92E20 65L06 65L05
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### A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor polynomials. (English)Zbl 1106.65110

MSC:  65Q05 39A10
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### Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation. (English)Zbl 1253.76076

MSC:  76M20 65N06 76W05
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### An approximation method for the solution of nonlinear integral equations. (English)Zbl 1089.65134

MSC:  65R20 45G10
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### Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade. (English)Zbl 1323.74051

MSC:  74K20 74E30 74H10
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### Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations. (English)Zbl 1086.65121

MSC:  65R20 45J05 45F05
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### Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study). (English)Zbl 1105.76006

MSC:  76A05 76M55 76M20 80A20
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### Trouble with Gegenbauer reconstruction for defeating Gibbs’ phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. (English)Zbl 1071.65189

MSC:  65T40 42C10
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### Delayed state feedback and chaos control for time-periodic systems via a symbolic approach. (English)Zbl 1082.93048

MSC:  93D15 93C30
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### A computational method for solving the branched channel flow problem. (English)Zbl 1102.76058

MSC:  76M40 76M22 76D05
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### Chebyshev finite difference method for MHD flow of a micropolar fluid past a stretching sheet with heat transfer. (English)Zbl 1299.76170

MSC:  76M20 76W05 76S05 80A20
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### Thermal-diffusion and diffusion-thermo effects on mixed free-forced convection and mass transfer boundary layer flow for non-Newtonian fluid with temperature-dependent viscosity. (English)Zbl 1077.76066

MSC:  76R99 76A05 76M20 80A20
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# Is this the correct way to compute the last $n$ digits of Graham's number?

For the following question, all what is needed to know about Graham's number is that it is a power tower with many many many $3's$

Consider the following pseudocode :

input n

Start with $s=1$ and $p=7$ (the last digit of $3^3$)

Repeat

$s=s+1$

$p=3^p$ modulo $10^s$

Until $s=n$

output p

Questions :

• Does this algorithm return the $n$ last digits of Graham's number ?
• If I take another base and $p$ happens to get smaller than $s$. Do I have to add $\lambda(10^s)$ to $p$ ?
• Can I calculate the $n$ last digits of Graham's number (or another tetrated number) easier ?
• When you say "take another base", do you mean the base 3 of your power tower, or the base 10 that you are taking modulo? – Deedlit Jun 10 '16 at 22:06
• I mean the $3$. – Peter Jun 10 '16 at 22:47

Yes, this algorithm will return the last $n$ digits of Graham's number, and as far as I know it is the simplest way of doing so.

As for when $p$ gets smaller than $s$, you don't have to worry if the base of your power tower is relatively prime to 10. However, if your base does contain factors of 2 or 5, then you could theoretically have a problem if $p < s$; say if the base were 2, then if $p < s$ the next number $2^p$ would not be divisible by $2^s$ as it should be. However, it seems to me that this will never happen; if your base is divisible by 2, then each calculation of $p$ will result in a number divisible by $2^s$, and therefore will not be less than $s$. Similarly for when the base is divisible by 5. So even in such cases, you don't need to worry.

Your algorithm produces the first $n$ digits of OEIS sequence A133613, but only a small proportion of the digits of Graham's number are given by this sequence; that is, your algorithm produces the rightmost $n$ digits of Graham's number only if $n$ is not too big. (But even the "small proportion" corresponds to a number whose size is literally "out of this world".)

Let $T_k=b\uparrow\uparrow k$ with integers $b\ge 2\ (b\neq 10),\ k\ge 3$. The interesting phenomenon is that, for fixed $b$, a certain number of rightmost decimal digits of $T_{k+1}$ are the same as those of $T_k$, and this number of "stabilized" digits grows steadily as $k$ increases. However, the growth rate of the number of stabilized digits is miniscule compared to the super-exponential growth rate of the total number of digits, so for any given $T_k$ -- e.g., Graham's number -- the vast majority of its digits are not stabilized.

For $b=3$, the infinite sequence of stabilized digits is the above-linked OEIS sequence. Similar digit sequences for other values of $b$ are cross-referenced in the OEIS article.

• Yes, it is clear that only the last digits stabilize and that it is hopeless to calculate the FIRST digits of Graham's number. But one more thing : When I use a large number $a$ (Say $3^{27}$) and want to know the last $n$ digits of $a\uparrow\uparrow m$ with sufficiently large $m$, which number must be starting number of my algorithm ? Does $a^a$ always suffice ? – Peter Jun 14 '16 at 8:46


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Unlimited Plugins, WordPress themes, videos & courses! Unlimited asset downloads! From $16.50/m Advertisement # Functional Programming in PHP With Lambda Functions Read Time:9 minsLanguages: One of the nice things about programming is that the same problem can be solved using multiple methods. This allows people to show their creativity and come up with incredibly efficient and unique solutions. Examples of this can be seen in action when you look for programs that list or find prime numbers. Similarly, there are different styles of writing a program. Two common types of styles are functional programming and object-oriented programming. The functional style of programming is based on dividing tasks into separate functions. These functions take some arguments and then return a single value. The returned value is based only on the provided input. This tutorial will teach you how to use functional programming in PHP with lambda functions. ## Functional Programming in PHP Functions are used in programming to group a bunch of instructions that act on optional input to produce a result. There is a special class of functions called first-class functions, where a programming language treats its functions as first-class citizens. In simple terms, this means that functions in those programming languages can be passed around as arguments to other functions, used as return values, or assigned to other variables. Support for first-class functions was introduced in PHP with version 5.3. This allows us to create anonymous functions (also called lambdas) and closures in PHP. In this tutorial, you will learn all the important concepts that you need to know about lambda functions in PHP. ## Anonymous or Lambda Functions in PHP The terms "anonymous functions" and "lambda functions" are often used interchangeably, which can be confusing for people because the PHP manual does not use the term lambda functions anywhere in their entry about anonymous functions. However, dig a bit deeper and you will find an RFC page about closures that discusses lambda functions. The usefulness of lambda functions can be best understood with the help of some examples. As you already know, there are some built-in functions in PHP that accept other functions as arguments. These callback functions act on provided data and produce a final result. For example, the array_map() function accepts a callback function as its first parameter. Without lambda functions, you will be limited to one of the following three options: 1. Define the function somewhere else and then refer to it inside array_map() by its name. This will force you to move back and forth in your file to see the function definition whenever needed. 2. Define the callback functions inside array_map() and specify a name. However, you will still need to check that there is no name clash by using function_exists(). 3. Just create the function at run time using create_function() in PHP. This might seem like a good idea at first, but it isn't. It can result in lower readability, performance drop, and security issues. In fact, PHP 8.0.0 has removed create_function() from the language. Lambda or anonymous functions get rid of all these drawbacks by allowing you to define functions in place, without requiring a name. They also compile before run time, so you don't get any performance drop. Here is an example of anonymous functions in PHP: In the above example, we create a new array with squares of original numbers using array_map(). As you can see, there was no need to specify a unique name for the callback function, and its definition was provided in place, so we didn't have to jump around to see what it does. ## Understanding Closures in PHP Closures are basically lambda functions that can access variables in their parent scope. We have already covered the basics of variable scope in PHP in an earlier tutorial. This increases the usefulness of closures by allowing us to write more flexible and general-purpose functions. Let's try to rewrite the function in the previous section so that it can calculate the exponentiation value to any number instead of just 2. At first, you might try to write it in the following manner: This will give you a warning about an undefined variable $pow and output an array with the wrong values. You can solve this problem by using the global keyword to access the variable inside the callback function. However, that approach has its own drawbacks, which I have already discussed in the tutorial about variable scope.

PHP has a special keyword called use that gives you access to the variables in the parent scope. These lambda functions, which take advantage of the use keyword to access variables that are outside their scope, are called closures. The following code example illustrates their use:

One important thing to remember is that variables are passed inside the function as values. This means that any changes you make to a variable from the parent scope will not be visible outside the closure. Here is an example:

In the above example, we go through the for loop three times and then increment the value of $calls by 1 during each of the five calls to our anonymous function. Therefore, the final value of $calls should have been 15. However, it simply stays at 0.

One way to make the value of \$calls stick across iterations as well as outside the closure is to pass it as a reference.

## Arrow Functions in PHP

Arrow functions were introduced in PHP 7.4, and they simply provide a way of writing anonymous or lambda functions more concisely. They take the concept of closures one step further and automatically pass all the variables from the parent scope to the scope of our lambda function. This means that you no longer need to import variables with the use keyword.

Keep in mind that the variables are passed by value instead of reference by default. You can still pass them by reference if you want.

## Higher-Order Functions

Those functions which either take a function as an argument or return a function as their value are called higher-order functions. As we learned at the beginning of this tutorial, PHP has proper support for first-class functions. This means that we can also write our higher-order functions in PHP.

Let's use everything we have learned so far to create a higher-order function that generates simple sentences from passed values.

The above function accepts a single parameter that specifies the topic for generating our sentences. Inside the function, we use some conditional statements to return an arrow function, which in turn returns a concatenated string.

We will now create three different arrays that contain the names of people, fruit, and planets. These arrays will be passed two at a time to the array_map() function, along with our function make_sentences() as the callback.

As you can see, we were able to generate some simple sentences by taking the corresponding elements from two different arrays and joining them in a string. You should try introducing an additional variable inside the make_sentences() function, which will then be used in the arrow functions to create slightly more complicated sentences.

## Final Thoughts

In this tutorial, we have covered many topics which are related to each other in one way or another. We started with a brief introduction to functional programming in PHP. Then we moved on to some useful language features in PHP like lambdas or anonymous functions, closures, and arrow functions. You should now have a good idea of all these terms and how they are different but still related to each other. Finally, we learned how to create our own higher-order functions in PHP.


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# I How do we justify "Natural" Units

Tags:
1. Sep 11, 2018

### quickAndLucky

How is it that when using "natural" units we drop the units themselves. I understand that you can arbitrarily change the magnitude of a parameter by choosing a new unit. For example Oliver R. Smoot is exactly 1 smoot tall.

However, in natural units with [c]=[h/(2π)]=1 the "smoot" part is left off. Furthermore, leaving off the units allows us to conflate speed and action, which to me have always been different physical quantities.

How do we justify this as it seems like its common practice?

2. Sep 12, 2018

### Staff: Mentor

I don’t understand. Units don’t need to be justified. They are a convention, you simply use them (or not, whatever your preference).

3. Sep 12, 2018

### Staff: Mentor

I think that the OP is perplexed by the fact that if you calculate something using $c \approx 3 \times 10^8\, \mathrm{m/s}$, then $c$ has dimensions of length/time, but if you use natural units, then $c$ is dimensionless. Where have the units gone?

To answer the OP, the thing is that dimensioned fundamental constants can be seen as conversion factors between different dimensions. Take mass for instance: in the SI system, it has units of kg, but by the relation $E=mc^2$, we have that mass is just a form of energy, so we could also express mass as an energy, which is done all the time in particle physics, where masses are often given in MeV. So the constant $c^2$ appears as a conversion factor between mass and energy.

Similarly, it is arbitrary that we measure temperature in units of kelvin, instead of simply stating the temperature as an energy. The Boltzmann constant is the factor that allows to convert between the two (if you look closely, in thermodynamics you will rarely find $T$ by itself, whereas $kT$ is ubiquitous).

4. Sep 12, 2018

### Staff: Mentor

Perhaps the confusion is that not only the size of the units, but also the dimension of the unit is a matter of convention. For example, the dimension of charge is different in MKS and CGS units. In MKS it has its own dimension, Q, and in CGS it is $\sqrt{L^3 M T^{-2}}$

5. Sep 12, 2018

### quickAndLucky

I like the examples of temperature and mass measured as energy and get
but one of the confusing things with natural units is that the fundamental constants are unitless. Also it is intuitively clear that temperature and energy should be related quantities as they are essentially the macro and micro versions of the same physical phenomina. But it is not clear to me that h bar and c are the same physical quantity.

6. Sep 13, 2018

### Staff: Mentor

Don’t look at converting h into c, look at the things that they each convert. For c, it is used to convert time into length, and when you work with spacetime it is clear that those should be the same. It is also used to convert E into B, and since E and B are both part of the overall electromagnetic field they should also have the same units. Similarly for h.

7. Sep 13, 2018

### Staff: Mentor

As @Dale pointed out, they are not. There can be some confusion coming from the sloppiness of writing
This is simply a shorthand for $c=1$ and $\hbar = 1$, not a statement about a relation between $c$ and $\hbar$.

I confused a student a few days ago by writing something like $P(+) = P (-) = 1/2$, which brought up the question "Why should the two probabilities be equal?" In general the two probabilities I was considering are not related, but they just had the same value for the situation at hand.

8. Sep 13, 2018

### f95toli

Also, note that when some people say "natural units" they simply mean setting "unimportant" parameters equal to 1 since they do not affect the qualitative properties of the solution. A good example would be to set the mass equal to 1 in a mechanics problem where you are really only interested in solving the resulting differential equation.
Some theorists/mathematician love doing this and it can be very confusing.

9. Sep 13, 2018

### bobob

You can justify different ways for different reasons. Sometimes, it's just convenient. Sometimes there is a good physical reason for doing so to try to identify which units are fundamental and which are derived. When doing relativity, you are talking about geometry so that all of your coordinates should be on equal footing. (You use the same units for measuring, length, width and height. If you did not, then there would be a conversion constant that is physically meaningless to deal with.) We measure distance and time with different instruments and therefore we have c as a conversion constant, but it's physically meaningless in relativity. You can just as easily use meters to measure time and in that case, velocities are dimensionless.

10. Sep 20, 2018 at 7:13 PM

### Mister T

One smoot of time would be the time it takes light to travel a distance of 1 smoot. Thus the speed of light is one smoot per smoot, or simply 1.

What I did above was conflate distance and time by measuring them in the same unit, even though I fully realize that distance and time are different physical quantities.

There's nothing wrong with it, so in that sense it needs no justification. But in fact the justification is that it's convenient to do it.