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### 11th Standard Physics Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 11 Session 2020 - 2021 TN Stateboard [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 11th Standard Physics English Medium - Important 5 Mark Question Paper and Answer Key 2022 - 2023 - by Study Materials - View & Read

• 1)

(i) Explain the use of screw gauge and vernier caliper in measuring smaller distances.
(ii) Write a note on triangulation method and radar method to measure larger distances

• 2)

Derive the equation of motion, range and maximum height reached by the particle thrown at an oblique angle $\theta$ with respect to the horizontal direction.

• 3)

Describe the method of measuring angle of repose.

• 4)

State and explain work energy principle. Mention any three examples for it.

• 5)

Explain the method to find the center of gravity of a irregularly shaped lamina?

#### 11th Standard Physics English Medium - Important 3 Mark Question Paper and Answer Key 2022 - 2023 - by Study Materials - View & Read

• 1)

In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 sec. If the speed of sound in water is 1460 ms-1. What is the distance of enemy submarine?

• 2)

If the value of universal gravitational constant in SI is 6.6 x 10−11 Nm2 kg−2, then find its value in CGS System?

• 3)

Calculate the average velocity of the particle whose position vector changes from $\overrightarrow { { r }_{ 1 } } =5\hat { i } +6\hat { j }$ to $\overrightarrow { { r }_{ 2 } } =2\hat { i } +3\hat { j }$  in a time 5 second.

• 4)

The following velocity-time graph represents a particle moving in the positive x-direction. Analyse its motion from 0 to 7 s. Calculate the displacement covered and distance travelled by the particle from 0 to 2 s.

• 5)

Given two vectors $\vec A=2\hat i+4\hat j+5\hat k$ and $\vec B=\hat i+3\hat j+6\hat k$. Find the product $\vec A.\vec B$, and the magnitudes of $\vec A$ and $\vec B$ . What is the angle between them?

#### 11th Standard Physics English Medium - Important 2 Mark Question Paper and Answer Key 2022 - 2023 - by Study Materials - View & Read

• 1)

Write the rules for determining significant figures.

• 2)

Explain what is meant by Cartesian coordinate system?

• 3)

A particle has its position moved from $\overset { \rightarrow }{ { r }_{ 1 } } =3\hat { i } +4\hat { j }$ to $\overset { \rightarrow }{ { r }_{ 2 } } =\hat { i } +2\hat { j }$ Calculate the displacement vector ($\Delta$$\overrightarrow { r }$) and draw the $\overrightarrow { { r }_{ 1 } }$, $\overrightarrow { { r }_{ 2 } }$ and $\Delta \overrightarrow { r }$ vector in a two dimensional cartesian coordinate system.

• 4)

If the position vector of the particle is given by $\vec { r } ={ 3t }^{ 2 }\hat { i } +5t\hat { j } +4\hat { k }$, Find the
(a) The velocity of the particle at t = 3 s
(b) Speed of the particle at t = 3 s
(c) Acceleration of the particle at time t = 3s

• 5)

The position vector of a particle is given by $\vec { r } =3t\hat { i } +5t^{ 2 }\hat { j } +7\hat { k }$. Find the direction in which the particle experiences net force?

#### 11th Standard Physics English Medium - Important 1 Mark MCQ's Question Paper and Answer Key 2022 - 2023 - by Study Materials - View & Read

• 1)

One of the combinations from the fundamental physical constants is ${{hc}\over{G}},$ The unit of this expression is

• 2)

The dimensional formula for gravitational constant G is

• 3)

Which one of the following Cartesian coordinate systems is not followed in physics?

• 4)

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

• 5)

An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is

#### 11th Standard Physics English Medium - Revision Model Question Paper with Answer Key 2022 - 2023 - by Study Materials - View & Read

• 1)

If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be

• 2)

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

• 3)

Choose appropriate free body diagram for the particle experiencing net acceleration along negative y direction. (Each arrow mark represents the force acting on the system).

• 4)

A uniform force of (2$\hat { i }$+$\hat { j }$) N acts on a particle of mass 1 kg. The particle displaces from position (3$\hat { j }$+$\hat { k }$) m to (5$\hat { i }$+3$\hat { j }$) m. The work done by the force on the particle is

• 5)

A disc of the moment of inertia Ia is rotating in a horizontal plane about its symmetry axis with a constant angular speed $\omega$Another disc initially at rest of moment of inertia Ib is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

#### 11th Standard Physics Work, Energy and Power English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A uniform force of (2$\hat { i }$+$\hat { j }$) N acts on a particle of mass 1 kg. The particle displaces from position (3$\hat { j }$+$\hat { k }$) m to (5$\hat { i }$+3$\hat { j }$) m. The work done by the force on the particle is

• 2)

A body of mass 1 kg is thrown upwards with a velocity 20 ms-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?(Take g = 10 ms-2)

• 3)

The coefficient of restitution e for a perfectly elastic collision is ______________.

• 4)

The work done by the conservative force for a closed path is

• 5)

If the potential energy of the particle is $\alpha -\frac { \beta }{ 2 } { x }^{ 2 }$, then force experienced by the particle is

#### 11th Standard Physics Motion of System of Particles and Rigid Bodies English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A couple produces,

• 2)

A system consisting of two masses connected by a massless rod lies along the x axis. If 0.2 kg mass is at a distance x = 0.5m while a 0.3 kg mass is at a distance x = 1m, then the x - co-ordinate of the centre of mass will be at ______________.

• 3)

The angular momentum of a rotating body is doubled, its K.E. of rotation becomes ________________

• 4)

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

• 5)

A disc of the moment of inertia Ia is rotating in a horizontal plane about its symmetry axis with a constant angular speed $\omega$Another disc initially at rest of moment of inertia Ib is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

#### 11th Standard Physics Properties of Matter English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

If a wire is stretched to double of its original length, then the strain in the wire is

• 2)

For a given material, the rigidity modulus is $\left( \frac { 1 }{ 3 } \right)$rd of Young’s modulus. Its Poisson’s ratio is

• 3)

Two wires are made of the same material and have the same volume. The area of cross sections of the first and the second wires are A and 2A respectively. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

• 4)

The young’s modulus for a perfect rigid body is

• 5)

A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

#### 11th Standard Physics Heat and Thermodynamics English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

In hot summer after a bath, the body’s

• 2)

An ideal gas is taken from (Pi, Vi) to (P$\rho$ , Vf) in three different ways. Identify the process in which the work done on the gas the most.

• 3)

A distant star emits radiation with maximum intensity at 350 nm. The temperature of the star is

• 4)

In an isochoric process, we have

• 5)

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy applied which increases the internal energy of gas is _____________.

#### 11th Standard Physics Work, Energy and Power English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

• 2)

A particle of mass m is being rotated on a vertical circle of radius r. If the speed of particle at the highest point be v, then ______________.

• 3)

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

• 4)

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

• 5)

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

#### 11th Standard Physics Motion of System of Particles and Rigid Bodies English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

The center of mass of a system of particles does not depend upon,

• 2)

The angular momentum of a system of particles is conserved _____________.

• 3)

If earth suddenly contracts to 0.75 times of its present radius, then the length of the day becomes _______________

• 4)

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

• 5)

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

#### 11th Standard Physics Gravitation English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

The linear momentum and position vector of the planet is perpendicular to each other at

• 2)

A planet moving along an elliptical orbit is closest to the Sun at distance r1 and farthest away at a distance of r2. If v1 and v2 are linear speeds at these points respectively. Then the ratio ${v_1\over v_2}$ is

• 3)

The gravitational potential energy of the Moon with respect to Earth is

• 4)

The work done by the Sun’s gravitational force on the Earth is

• 5)

An object of mass 10 kg is hanging on a spring scale which is attached to the roof of a lift. If the lift is in free fall, the reading in the spring scale is

#### 11th Standard Physics Gravitation English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

If the masses of the Earth and Sun suddenly double, the gravitational force between them will

• 2)

According to Kepler’s second law, the radial vector to a planet from the Sun sweeps out equal areas in equal intervals of time. This law is a consequence of

• 3)

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then

• 4)

If the mass and radius of the Earth are both doubled, then the acceleration due to gravity g'

• 5)

If a person moves from Chennai to Trichy, his weight

#### 11th Standard Physics Properties of Matter English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

If a wire is stretched to double of its original length, then the strain in the wire is

• 2)

For a given material, the rigidity modulus is $\left( \frac { 1 }{ 3 } \right)$rd of Young’s modulus. Its Poisson’s ratio is

• 3)

Two wires are made of the same material and have the same volume. The area of cross sections of the first and the second wires are A and 2A respectively. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

• 4)

The young’s modulus for a perfect rigid body is

• 5)

If the temperature of the wire is increased, then the Young’s modulus will

#### 11th Standard Physics Heat and Thermodynamics English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

The graph between volume and temperature in Charles’ law is

• 2)

When food is cooked in a vessel by keeping the lid closed, after some time the steam pushes the lid outward. By considering the steam as a thermodynamic system, then in the cooking process

• 3)

A hot cup of coffee is kept on the table. After some time it attains a thermal equilibrium with the surroundings. By considering the air molecules in the room as a thermodynamic system, which of the following is true

• 4)

Identify the state variables given here?

• 5)

The efficiency of a heat engine working between the freezing point and boiling point of water is

#### 11th Standard Physics Oscillations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to B, it returns to B after another 3 s. The time period is

• 2)

A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is

• 3)

A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is

• 4)

A simple pendulum has a time period T1. When its point of suspension is moved vertically upwards according as y = k t2, where y is vertical distance covered and k = 1 ms−2, its time period becomes T2. Then, $\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } }$ is (g = 10 m s−2).

• 5)

A pendulum is hung in a very high building oscillates to and fro motion freely like a simple harmonic oscillator. If the acceleration of the bob is 16 ms−2 at a distance of 4 m from the mean position, then the time period is

#### 11th Standard Physics Kinetic Theory of Gases English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

An ideal gas is maintained at constant pressure. If the temperature of an ideal gas increases from 100K to 1000K then the rms speed of the gas molecules

• 2)

The average translational kinetic energy of gas molecules depends on

• 3)

A container has one mole of monoatomic ideal gas. Each molecule has f degrees of freedom. What is the ratio of $\gamma =\frac { { C }_{ p } }{ { C }_{ V } }$

• 4)

If sP and sV denote the specific heats of nitrogen gas per unit mass at constant pressure and constant volume respectively, then

• 5)

For a given gas molecule at a fixed temperature, the area under the Maxwell-Boltzmann distribution curve is equal to

#### 11th Standard Physics Oscillations English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be

• 2)

The length of a second’s pendulum on the surface of the Earth is 0.9 m. The length of the same pendulum on surface of planet X such that the acceleration of the planet X is n times greater than the Earth is

• 3)

The time period for small vertical oscillations of block of mass m when the masses of the pulleys are negligible and spring constant k1 and k2 is

• 4)

An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is

• 5)

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will

#### 11th Standard Physics Kinetic Theory of Gases English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

An ideal gas is maintained at constant pressure. If the temperature of an ideal gas increases from 100K to 1000K then the rms speed of the gas molecules

• 2)

The average translational kinetic energy of gas molecules depends on

• 3)

The ratio $\gamma =\frac { { C }_{ p } }{ { C }_{ V } }$ for a gas mixture consisting of 8 g of helium and 16 g of oxygen is

• 4)

If the temperature and pressure of a gas is doubled the mean free path of the gas molecules

• 5)

A sample of gas consists of $\mu$1 moles of monoatomic molecules, $\mu$2 moles of diatomic molecules and $\mu$3 moles of linear triatomic molecules. The gas is kept at high temperature. What is the total number of degrees of freedom?

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - by Question Bank Software - View & Read

• 1)

The dimensional formula for gravitational constant G is

• 2)

The dimension of a quantity $hy \over c$ where h is the planck's constants, $\gamma$ is the frequency and c is the velocity of light are _______________.

• 3)

Identify the pair of physical quantities having the same dimensions.

• 4)

If E and B respectively, represent electric field and magnetic induction field, then the ratio $\frac{E}{B}$ has the dimensions of _____________.

• 5)

Which two of the following five physical parameters have the same dimensions?
1. energy density
2. refractive index
3. dielectric constant
4. Young's modulus
5. magnetic field

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Nine - by Question Bank Software - View & Read

• 1)

Which of the following pairs of physical quantities have same dimension?

• 2)

The fractional error $\left( {{\triangle x}\over{x}} \right)$  _____________.

• 3)

Ihe density of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and length are 3% and 2% respectively, the maximum error in the measurement of density is ________________.

• 4)

The numbers 3.665 and 3.635 on rounding off to 3 significant figures will give____________

• 5)

Which of the following statements is/are not true?

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Two - by Question Bank Software - View & Read

• 1)

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

• 2)

The amount of work done by the centripetal force on the object moving in a circular path is ______________.

• 3)

The kinetic energy is not conserved in ______________.

• 4)

For inelastic collision co-efficient of restitution is ______________.

• 5)

If the momentum of a body increases by 25% its kinetic energy will increase by _____________.

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Eight - by Question Bank Software - View & Read

• 1)

The term used to mention study of macroscopic system to microscopic constituents is _____________.

• 2)

In equation of motion S = ut+$1\over 2$kt2 the dimensional formula for K is______________

• 3)

When a body undergoes an oblique projection, maximum range of it is ____________.

• 4)

Two cars P and Q start fun a point at the same time in a straight line and their positions are represented by X p(t) = (at + bt2) and xQ(t) = (ft - ft2). At what time do the cars have the same velocity?

• 5)

A body is projected vertically upward with the velocity v = $3\hat{i}+4\hat{j} \ ms^{-1}$The maximum height attained by the body is __________ (g = 10 ms-2)

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - by Question Bank Software - View & Read

• 1)

If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

• 2)

If a circle with 10 m radius and angle 60° at centre, then what will be the length of arc?

• 3)

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

• 4)

Which of the following graph represents the equation y = mx + C?

• 5)

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F1 is applied from the left. Later only a force F2 is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F1 :F2 is

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Two - by Question Bank Software - View & Read

• 1)

The velocity of a particle v at an instant t is given by v = at + br2. The dimensions of b is

• 2)

Which unit is used to measure size of a nucleus?

• 3)

The diameter of the steel ball is measured using a vernier calipers which has divisions of 0.5 cm on its main scale and 10 division of its vernier scale match 9 division on the main scale. Three such measurements for a ball are as follows.

 S.No MS (cm) VS (divisions) 1 0.5 8 2 0.5 4 3 0.5 6

If the zero error is - 0.03 em, then mean corrected diameter is__________________ cm.

• 4)

One degree of arc is_______________.

• 5)

If $\bar A$and $\bar B$ are two vectors, $\bar A.\bar B=\bar A\times\bar B$ then resultant vector is ____________.

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Three - by Question Bank Software - View & Read

• 1)

A length-scale (I) depends on the permittivity (e) of a dielectric material,  Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for I is dimensionally correct?

• 2)

The dimensions of K.E. is _______________.

• 3)

The fraction of $1\over 273.16$ temperature of the triple point of water represents __________.

• 4)

1 CSL is the largest practical unit of _____________.

• 5)

The diameter of the steel ball is measured using a vernier calipers which has divisions of 0.5 cm on its main scale and 10 division of its vernier scale match 9 division on the main scale. Three such measurements for a ball are as follows.

 S.No MS (cm) VS (divisions) 1 0.5 8 2 0.5 4 3 0.5 6

If the zero error is - 0.03 em, then mean corrected diameter is__________________ cm.

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Three - by Question Bank Software - View & Read

• 1)

How many light years make 1 per sec?

• 2)

The density of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and length are 5% and 3% respectively, the maximum error in the measurement of density is _____________.

• 3)

Which pair do not have equal dimensions?

• 4)

During a projectile motion if the maximum height equals the horizontal range, then the angle of projection with the horizontal is ______________.

• 5)

In which direction of the motion of the particle does centripetal force act?

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Four - by Question Bank Software - View & Read

• 1)

If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be

• 2)

If E & B respectively, represent electric field and magnetics induction field, then the ratio E & B has the dimensions of ______________.

• 3)

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be ______________.

• 4)

The pair of quantities having same dimensions is ______________.

• 5)

If the percentage error in the measurement of mass and momentum of a body are 3% and 2% respectively, then maximum possible error in kinetic energy is ______________

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Four - by Question Bank Software - View & Read

• 1)

The dimensional formula for gravitational constant G is

• 2)

High precision instruments are used to eliminate ______________.

• 3)

If the energy E = GPhqCr where G is the universal gravitational constant, h is the planck's constant and C is the velocity of light, then the values of p, q and r are respectively ______________.

• 4)

A force F is applied on to a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, the percentage error in pressure is ____________.

• 5)

TIle dimensional formula of torque is _____________.

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Five - by Question Bank Software - View & Read

• 1)

Which relation is wrong?

• 2)

Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful?

• 3)

The ratio of one nanometer to one micron is__________________

• 4)

Zero error of an instrument is a______________.

• 5)

Dimensions [M L-1T-1] are related to_____________

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Five - by Question Bank Software - View & Read

• 1)

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

• 2)

While measuring acceleration due to gravity, by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error , of 3% in the value of time period. The percentage error in the measurement of 'g' is _______________.

• 3)

If 'am' and '$\triangle a_m$' are true value and mean absolute error respectively, then the magnitude of the quantity may lie between____________.

• 4)

The unit of moment of force_______

• 5)

Odd one out ________

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Six - by Question Bank Software - View & Read

• 1)

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

• 2)

Which is deals with the study of materials of an intermediate length scale?

• 3)

The Van der Waal equation for n moles of a real gas is $(P+\frac{a}{V^2})(V-b)=RT$ where P is the pressure. V is the volume. T is the absolute temperature. R is the molar gas constant and 'a' and 'b' are Van der Waal constants. The dimensions of 'a' are the same as those of _______________.

• 4)

Dimensional formula of self inductance is _______________.

• 5)

If a particle executes uniform circular motion, choose the correct statement

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Six - by Question Bank Software - View & Read

• 1)

The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figure is _____________.

• 2)

If the percentage error in the measurement of mass and momentum of a body are 3% and 2% respectively, then maximum possible error in kinetic energy is ______________

• 3)

The horizontal range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at angle of 45°, its range will be

• 4)

Retardation means ____________.

• 5)

A passenger in the moving train tosses a coin. If the coin falls behind him, train must be moving with _____________.

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Seven - by Question Bank Software - View & Read

• 1)

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

• 2)

If a circle with 10 m radius and angle 60° at centre, then what will be the length of arc?

• 3)

___________ system of units was accepted by the scientists of the general conference on weights and measures.

• 4)

One degree of arc is equal to_______

• 5)

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula p =$F\over l^2$ .If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is _________________

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Seven - by Question Bank Software - View & Read

• 1)

How many AU makes one metre?

• 2)

Which pair do not have equal dimensions?

• 3)

The word physics is derived from the word____________.

• 4)

If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms-2

• 5)

What is the resultant vectors, when 2 vectors are at right angles to each other?

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Eight - by Question Bank Software - View & Read

• 1)

If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

• 2)

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

• 3)

The law of electricity and magnetism is used to ____________

• 4)

The fraction of $1\over 273.16$ temperature of the triple point of water represents __________.

• 5)

Which of the following is the most accurate?

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Nine - by Question Bank Software - View & Read

• 1)

A student measures the distance traversed in free fall of a body, initially at rest, in a given time, He uses this data to estimate g, the acceleration due to gravity, If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is ______________.

• 2)

If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant t is

• 3)

When a body moves once circular path, the ______________

• 4)

In the absence of air resistance, horizontal velocity of the projectile is _____________.

• 5)

With increase of temperature, the frictional force acting between two surfaces ______________.

#### 11th Standard Physics English Medium Free Online Test 1 Mark Questions 2020 - Part Ten - by Question Bank Software - View & Read

• 1)

If the force is proportional to square of velocity, then the dimension of proportionality constant is

• 2)

If the error in the measurement of radius of a sphere is 3% then the error in the measurement of volume of the sphere will be ________________.

• 3)

Random error can be eliminated by ______________.

• 4)

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula p =$F\over l^2$ .If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is _________________

• 5)

Slope of displacement-time graph at any instant gives ____________.

#### 11th Standard Physics English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Ten - by Question Bank Software - View & Read

• 1)

If $\pi=3.14,$ then the value of ${\pi}^{2}$ is

• 2)

Which unit is used to measure size of a nucleus?

• 3)

A student measures the distance traversed in free fall of a body, initially at rest, in a given time, He uses this data to estimate g, the acceleration due to gravity, If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is ______________.

• 4)

In a vernier caliper, n divisions of vernier scale coincides with (n - 1) divisions of main scale. The least count of the instrument is ______________

• 5)

If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant t is

#### 11th Standard Physics Waves English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A student tunes his guitar by striking a 120 Hertz with a tuning fork, and simultaneously plays the 4th string on his guitar. By keen observation, he hears the amplitude of the combined sound oscillating thrice per second. Which of the following frequencies is the most likely the frequency of the 4th string on his guitar?

• 2)

A person standing between two parallel hills fires a gun and hears the first echo after t1 sec and the second echo after t2 sec. The distance between the two hills is

• 3)

The displacement y of a wave travelling in the x direction is given by y = (2$\times$10 -3) sin (300t - 2x + $\frac{\pi}{4}$), where x and y are measured in metres and t in second. The speed of the wave is

• 4)

Which of the following represents a wave

• 5)

Let y = $\frac{1}{1+x^2}$ at t = 0 s be the amplitude of the wave propagating in the positive x-direction. At t = 2 s, the amplitude of the wave propagating becomes $y=\frac{1}{1+(x-2)^{2}}.$ Assume that the shape of the wave does not change during propagation. The velocity of the wave is

#### 11th Standard Physics Waves English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. Which of the following plots shows the correct variation of speed v with height h from the lower end?

• 2)

With propagation of longitudinal waves through a medium, the quantity transmitted is ______________.

• 3)

The speed ofsound in oxygen (O2) at a certain temp is 460 ms-1 the speed of sound in helium at the same temperature will be _______________.

• 4)

The ratio of the velocity of sound in a monatomic gas to that in a triatomic gas having same molar mass, under similar conditions of temperature and pressure, is _________.

• 5)

The path difference between the two waves Y1 = a1 sin $\left( \omega t-\frac { 2\pi x }{ \lambda } \right)$ and Y2 = a2 cos$\left( \omega t-\frac { 2\pi x }{ \lambda } +\phi \right)$is _________.

#### 11th Standard Physics English Medium Free Online Test Book Back One Mark Questions - by Question Bank Software - View & Read

• 1)

One of the combinations from the fundamental physical constants is ${{hc}\over{G}},$ The unit of this expression is

• 2)

Which one of the following Cartesian coordinate systems is not followed in physics?

• 3)

When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to

• 4)

A uniform force of (2$\hat { i }$+$\hat { j }$) N acts on a particle of mass 1 kg. The particle displaces from position (3$\hat { j }$+$\hat { k }$) m to (5$\hat { i }$+3$\hat { j }$) m. The work done by the force on the particle is

• 5)

The center of mass of a system of particles does not depend upon,

#### 11th Standard Physics English Medium Free Online Test Book Back One Mark Questions - Part Two - by Question Bank Software - View & Read

• 1)

If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

• 2)

Which one of the following physical quantities cannot be represented by a scalar?

• 3)

A vehicle is moving along the positive x direction, if sudden brake is applied, then

• 4)

A body of mass 1 kg is thrown upwards with a velocity 20 ms-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?(Take g = 10 ms-2)

• 5)

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

#### 11th Standard Physics English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - by Question Bank Software - View & Read

• 1)

If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be

• 2)

Identify the unit vector in the following?

• 3)

An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure.The minimum value of the force F is

• 4)

A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

• 5)

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

#### 11th Standard Physics English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Two - by Question Bank Software - View & Read

• 1)

The length of a body is measured as 3.51 m, if the accuracy is 0.01 mm, then the percentage error in the measurement is

• 2)

Two objects of masses m1 and m2 fall from the heights h1 and h2 respectively. The ratio of the magnitude of their momenta when they hit the ground is

• 3)

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

• 4)

A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

• 5)

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

#### 11th Standard Physics English Medium Free Online Test Book Back One Mark Questions - Part Three - by Question Bank Software - View & Read

• 1)

The dimensional formula of Planck's constant h is

• 2)

If a particle has negative velocity and negative acceleration, its speed

• 3)

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

• 4)

The potential energy of a system increases, if work is done

• 5)

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

#### 11th Standard Physics English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Three - by Question Bank Software - View & Read

• 1)

Which of the following pairs of physical quantities have same dimension?

• 2)

If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant t is

• 3)

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F1 is applied from the left. Later only a force F2 is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F1 :F2 is

• 4)

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

• 5)

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

#### 11th Standard Physics English Medium Free Online Test Creative 1 Mark Questions - by Question Bank Software - View & Read

• 1)

The word scientia is meaning to ___________.

• 2)

Which one of the following satatement is true?

• 3)

A ball is thrown vertically upward. It is a speed of 10 m/s. When it has reached one half of its maximum height. How high does the ball rise? (g = 10 ms-2)

• 4)

A rocket with a lift off mass 2.5 $\times$ 10kg is blast upward with an initial acceleration of 5m/s2. Then the initial thrust of the blast is ______________.

• 5)

A body of mass 3 kg hits a wall at an angle of 60° and returns at the same angle. The impact time was 0.2 sec. The force exerted on the wall

#### 11th Standard Physics English Medium Free Online Test Creative One Mark Questions with Answer Key - by Question Bank Software - View & Read

• 1)

Microscopic group of Physics dealt with the study of ____________.

• 2)

Retardation means ____________.

• 3)

The unit of momentum is ____________.

• 4)

When is the speed of a moving body doubled?

• 5)

A metal ball of mass 2 kg moving with speed of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after collision, both the balls move as a single mass, then the loss in K.E. due to collision is ________________.

#### 11th Standard Physics English Medium Free Online Test Creative 1 Mark Questions - Part Two - by Question Bank Software - View & Read

• 1)

Microscopic group of Physics dealt with the study of ____________.

• 2)

The speed of a train is reduced from 60 kmh-1 to 15 kmh-1 in a distance of 450 m. If the retardation is uniform is the distance, it will travel further before coming to rest is _______________.

• 3)

When a projectile is at its maximum height, the direction of its velocity and acceleration are _____________.

• 4)

A marble block of mass 3 kg lying on ice when given a velocity of 5 ms-1 is stopped by friction in 10s. Then the coefficient of friction is ______________.

• 5)

A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 ms-1. The final velocity acquired by the person and the average force exerted on the person are ________________.

#### 11th Standard Physics English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Two - by Question Bank Software - View & Read

• 1)

What is the value of one light year in tera metre?

• 2)

Distance is a scalar quantity and ______________ is a vector.

• 3)

The position vector of a particle is $\vec r=4t^2\hat i+2t\hat j+3\hat k$ . The speed of the particle at t = 5s is ____________.

• 4)

When a horse pulls a wagon, the force that causes the horse to move forward is the force?

• 5)

A body of mass 3 kg hits a wall at an angle of 60° and returns at the same angle. The impact time was 0.2 sec. The force exerted on the wall

#### 11th Standard Physics English Medium Free Online Test Creative 1 Mark Questions - Part Three - by Question Bank Software - View & Read

• 1)

One parallactic second is ______________

• 2)

Which of the following is having same dimensional formula?

• 3)

The cross product of two vectors $\vec A\times\vec B$ is _____________

• 4)

The scalar product of two vectors will be minimum. When $\theta$ is equal to _______________

• 5)

A 1 kg stationary bomb is exploded in three parts having mass 1 : 1 : 3 respectively. Parts having same mass move in perpendicular direction with velocity 30 m/s, then the velocity of bigger part will be ______________.

#### 11th Standard Physics English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Three - by Question Bank Software - View & Read

• 1)

The term used to mention study of macroscopic system to microscopic constituents is _____________.

• 2)

Kinematics deals with the motion of objects without taking____________into accounts.

• 3)

Spinning of the earth about its own axis is known as _______________.

• 4)

A body of mass M moving with velocity V explodes into two equal parts. If one comes to rest and the other body moves with velocity v, what is the value of v?

• 5)

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0  m/s-2. If g = 10 ms-2, the tension in the supporting cable is _____________.

#### 11th Standard Physics English Medium Free Online Test Creative 1 Mark Questions - Part Four - by Question Bank Software - View & Read

• 1)

A scientific way of doing things involve _____________.

• 2)

The numerical ratio of average velocity to average speed is ________________.

• 3)

The angle between anti parallel vectors is _____________

• 4)

A particle revolves round a circular pattern. The acceleration of the particle is inversely proportional to ______________

• 5)

The accelerated train is an example for _____________.

#### 11th Standard Physics English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Four - by Question Bank Software - View & Read

• 1)

How many AU present in one light year?

• 2)

If $\bar A$and $\bar B$ are two vectors, $\bar A.\bar B=\bar A\times\bar B$ then resultant vector is ____________.

• 3)

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two bails are in the sky at any time? (Given g = 9.8m/s2)

• 4)

The position vector of a particle is $\vec r=4t^2\hat i+2t\hat j+3\hat k$ . The speed of the particle at t = 5s is ____________.

• 5)

Unit of momentum _______________.

#### 11th Standard Physics English Medium Free Online Test Creative 1 Mark Questions - Part Five - by Question Bank Software - View & Read

• 1)

If force |F|, velocity |V| and time |T| are taken as to fundamental units then the dimensions of mass are _______________.

• 2)

The vectors $\vec A$ and $\vec B$ to be mutually orthogonal when _________.

• 3)

If a reaction is R and coefficient of friction is μ, what is work done against friction in moving a body by distance d?

• 4)

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius $\frac { r }{ 3 }$ and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier. stone when they experience same centripetal forces. The value of n is _______________.

• 5)

For a particle revolving in a circular path, the acceleration of the particle is _____________.

#### 11th Standard Physics English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Five - by Question Bank Software - View & Read

• 1)

Least count of screw gauge _____________.

• 2)

Resultant of two vectors which are parallel to each other and are in the same direction is obtained by of vectors.

• 3)

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is _____________.

• 4)

The angle between parallel vectors is _____________.

• 5)

Inertia is that property of a body by virtue of which the body is ____________.

#### 11th Standard Physics English Medium Free Online Test Volume 1 One Mark Questions 2020 - by Question Bank Software - View & Read

• 1)

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

• 2)

One parallactic second is ______________

• 3)

The same error repeated every time in the series of observation is known as _____________error.

• 4)

One Angstrom is______________.

• 5)

In a system of units, if force (F), acceleration (A) and time (T) are taken as fundamental units then the dimensional formula of energy is____________

#### 11th Standard Physics English Medium Free Online Test Volume 1 One Mark Questions with Answer Key 2020 - by Question Bank Software - View & Read

• 1)

If the force is proportional to square of velocity, then the dimension of proportionality constant is

• 2)

If A = 2.331cm and C = 2.1cm, then A + C = ______________cm

• 3)

Which two of the following five physical parameters have the same dimensions?
1. energy density
2. refractive index
3. dielectric constant
4. Young's modulus
5. magnetic field

• 4)

In equation of motion S = ut+$1\over 2$kt2 the dimensional formula for K is______________

• 5)

Number of significant digits in 3256 ____________.

#### 11th Standard Physics English Medium Free Online Test Volume 2 One Mark Questions 2020 - by Question Bank Software - View & Read

• 1)

A planet moving along an elliptical orbit is closest to the Sun at distance r1 and farthest away at a distance of r2. If v1 and v2 are linear speeds at these points respectively. Then the ratio ${v_1\over v_2}$ is

• 2)

A body is suspended from a spring balance kept in a satellite the reading of the balance is W1 when the satellite goes in an orbit of radius R and is W2 when it goes in an orbit of radius 2R

• 3)

Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is Δl. If Y represents the Young’s modulus, then which of the following graphs is a straight line?

• 4)

Two fluids 1 and 2 have mass densities of P1 and P2 respectively. If P1> P2, which one of the following expressions will represent the relation between their specific volumes V1 and V2?

• 5)

If the tension on a wire is removed at once, then _______.

#### 11th Standard Physics English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 2020 - by Question Bank Software - View & Read

• 1)

In the following, what are the quantities which that are conserved?

• 2)

Viscosity is a property of ______________.

• 3)

A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

• 4)

The molar specific heats of an ideal gas at a constant pressure & volume are denoted by Cp&Cv if r =$\frac{C_{p}}{C_{v}}$ & R the universal gases constant then Cv is equal _____________.

• 5)

Two capillaries of lengths L & 2L and of radius R & 2R are connected in series the net rate of flow of fluid through them will (rate of the flow through singe capillary,$x=\pi R^{4}/8 \eta L$) be ____________.

#### 11th Standard Physics Nature of Physical World and Measurement English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

One of the combinations from the fundamental physical constants is ${{hc}\over{G}},$ The unit of this expression is

• 2)

Which of the following has the highest number of significant figures?

• 3)

Which of the following pairs of physical quantities have same dimension?

• 4)

The velocity of a particle v at an instant t is given by v = at + br2. The dimensions of b is

• 5)

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

#### 11th Standard Physics Nature of Physical World and Measurement English Medium Free Online Test 1 Mark Questions with Answer Key 2020-2021 - by Question Bank Software - View & Read

• 1)

If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be

• 2)

The dimensional formula of Planck's constant h is

• 3)

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

• 4)

Astromical Scale is dealt with the _________ Physics

• 5)

Which is deals with the study of materials of an intermediate length scale?

#### 11th Standard Physics Kinematics English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

Which one of the following Cartesian coordinate systems is not followed in physics?

• 2)

Which one of the following physical quantities cannot be represented by a scalar?

• 3)

If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant t is

• 4)

An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is

• 5)

The component of position vector $\overrightarrow { r }$ along x-axis will maximum value if ____________

#### 11th Standard Physics Kinematics English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

Identify the unit vector in the following?

• 2)

If the velocity is $\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k }$, then the magnitude of acceleration at t = 0.5s is

• 3)

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

• 4)

A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

• 5)

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R30° and R30°. Choose the correct relation from the following

#### 11th Standard Physics Laws of Motion English Medium Free Online Test One Mark Questions 2020 - 2021 - by Question Bank Software - View & Read

• 1)

When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to

• 2)

Two masses m1 and m2 are experiencing the same force where m1 < m2.The ration of their acceleration $\frac { { a }_{ 1 } }{ { a }_{ 2 } }$ is _____________.

• 3)

Force acting on the particle moving with constant speed is

• 4)

The centrifugal force appears to exist

• 5)

Physical independence of force is a consequence of _______________.

#### 11th Standard Physics Laws of Motion English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Question Bank Software - View & Read

• 1)

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

• 2)

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F1 is applied from the left. Later only a force F2 is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F1 :F2 is

• 3)

When an object is at rest on the inclined rough surface ____________.

• 4)

Action and reaction ___________

• 5)

A heavy iron rod of weight W is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle ፀ with the horizontal. What is the weight experienced by the man?

#### 11th Standard Physics English Medium All Chapter Book Back and Creative One Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

• 2)

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

• 3)

Which of the following pairs of quantities and their units is a proper match?

• 4)

The dimension of a quantity $hy \over c$ where h is the planck's constants, $\gamma$ is the frequency and c is the velocity of light are _______________.

• 5)

If a particle executes uniform circular motion, choose the correct statement

#### 11th Standard Physics English Medium All Chapter Book Back and Creative Two Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

The measurement value of length of a simple pendulum is 20cm known with 2mm accuracy. The time for 50 oscillations was measured to be 40 s within is resolution. Calculate the percentage accuracy in the determination of acceleration due to gravity 'g' from the above measurement.

• 2)

What is meant by Range of masses?

• 3)

How Physics is related to technology and define technology with respect to Physics.

• 4)

A RADAR signal is beamed towards a planet and its echo is received 7 minutes later. If the distance between the planet and the Earth is 6.3$\times$1010 m. Calculate the speed of the signal?

• 5)

The following velocity-time graph represents a particle moving in the positive x-direction. Analyse its motion from 0 to 7 s. Calculate the displacement covered and distance travelled by the particle from 0 to 2 s.

#### 11th Standard Physics English Medium All Chapter Book Back and Creative Three Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

If humans were to settle on other planets, which of the fundamental quantities will be in trouble? Why?

• 2)

Calculate the angle of
(i) 10 (degree)
(ii) 1' (minute of arc or arc min) and
(iii) 1" (second of arc or arc second) in radians. Use 3600 = 2$\pi$ rad, 10 =60 and 1' = 60"

• 3)

Arrive at Einstein's mass-energy relation by dimensional method (E = mc2).

• 4)

Convert
G = 6.67$\times$10-11 N m2kg-2 to cm3g-1s-2

• 5)

Define displacement and distance.

#### 11th Standard Physics English Medium All Chapter Book Back and Creative Five Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

Briefly explain the different types of errors and their causes with an example. How can these error be minimised?

• 2)

Write the rules for "Rounding off" with example

• 3)

The force F acting on a body moving in a circular path depends on mass of the body (m), velocity (v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method. (Take the value of k = 1)

• 4)

Two resistors of resistances R1= 150 ± 2 Ohm and R2 = 220 ± 6 Ohm are connected in parallel combination. Calculate the equivalent resistance.
Hint:$\frac{1}{R'}=\frac{1}{R_1}+\frac{1}{R_2}$

• 5)

A car moving uniform motion with speed 120 kmh-2 is brought to a stop within a distance of 200 m. How long does it take for the car to stop?

#### 12th Physics - Full Portion Five Marks Question Paper - by 8682895000 - View & Read

• 1)

What do you mean by propagation of errors? Explain the propagation of errors in addition and multiplication.

• 2)

A body starting from rest has an acceleration of 25 ms-2. Find the distance travelled by it in 20th second.

• 3)

Two vectors $\vec A$ and $\vec B$ of magnitude 5 units and 7 units respectively make an angle 60° with each other as shown below. Find the magnitude of the resultant vector and its direction with respect to 7 unit the vector $\vec A$.

• 4)

A three storey building of height 100m is located on Earth and a similar building is also located on Moon. If two people jump from the top of these buildings on Earth and Moon simultaneously, when will they reach the ground and at what speed? (g = 10m s-2)

• 5)

Describe Galileo's experiments concerning motion of objects on inclined planes?

#### 12th Physics - Full Portion Three Marks Question Paper - by 8682895000 - View & Read

• 1)

Write the rules for determining significant figures.

• 2)

How many parallactic second are there in one Astronomical unit?
Given data:
1 parallactic second = 3.08$\times$1016m
1 Astronomical unit = 1.496$\times$1011m

• 3)

Calculate the number of times a human heart beats in the life of 100 years old man. Time of one heart beat = 0.8s.

• 4)

A bullet going with speed 350 m/s enters in a concrete wall and penetrates a distance of 5 cm before coming to rest. Find the deceleration.

• 5)

Two vectors $\vec A$ and $\vec B$ are given in the component form as $\overrightarrow { A } =5\hat { i } +7\hat { j } -4\hat { k }$ and $\overrightarrow { B } =6\hat { i } +3\hat { j } +2\hat { k }$. Find $\vec { A } +\vec { B } ,\vec { B } +\vec { A } ,\vec { A } -\vec { B } ,\vec { B } -\vec { A }$

#### 12th Physics - Full Portion Two Marks Question Paper - by 8682895000 - View & Read

• 1)

The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.

• 2)

Assuming that the frequency y of a vibrating string may depend upon
(i) applied force (F)
(ii) length (I)
(ill) mass per unit length (m), prove that $\gamma\alpha{{1}\over{l}}\sqrt{{{F}\over{m}}}$using dimensional analysis.

• 3)

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Calculate
(i) the mean value of the period of oscillation
(ii) the absolute error in each measurement
(iii) the mean absolute error
(iv) the relative error
(v) the percentage error.
(vi) Express the result in proper form.

• 4)

Two resistances R1 = (100 ± 3) $\Omega$, R2 = (150 ± 2)$\Omega$, are connected in series. What is their equivalent resistance?

• 5)

Round off the following numbers as indicated 19.45 up to 3 digits

#### 11th Physics - Public Exam Model Question Paper 2019 - 2020 - by Question Bank Software - View & Read

• 1)

How many AU present in one light year?

• 2)

Two objects of masses m1 and m2 fall from the heights h1 and h2 respectively. The ratio of the magnitude of their momenta when they hit the ground is

• 3)

$\hat i\times \hat j$ is ______________.

• 4)

Choose appropriate free body diagram for the particle experiencing net acceleration along negative y direction. (Each arrow mark represents the force acting on the system).

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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2 kg moves with 8 ms-1 speed. If the third part flies off with 4 ms-1 speed, then its mass is ____________.

#### 11th Physics - Revision Model Question Paper 2 - by Question Bank Software - View & Read

• 1)

Dimensions [M L-1T-1] are related to_____________

• 2)

Which one of the following physical quantities cannot be represented by a scalar?

• 3)

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• 4)

An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure.The minimum value of the force F is

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No force is required for ____________.

#### 11th Physics - Motion of System of Particles and Rigid Bodies Model Question Paper - by Question Bank Software - View & Read

• 1)

A couple produces,

• 2)

The angular momentum of a rotating body is doubled, its K.E. of rotation becomes ________________

• 3)

A particle undergoes uniform circular motion. The angular momentum of the particle remain conserved about,

• 4)

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• 5)

Two blocks of masses 20 kg and 5 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 15 m/s to the heavier block in the direction of lighter block. The velocity of centre of mass is _____________.

#### 11th Physics - Work, Energy and Power Model Question Paper - by Question Bank Software - View & Read

• 1)

A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

• 2)

The coefficient of restitution e for a perfectly elastic collision is ______________.

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What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

• 4)

A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = kx + ax3. Here, k and a are positive constants. For x ≥ 0, the functional form of the potential, energy U(x) of the particles

• 5)

A cricket ball falls from a height of 40 m. What is the velocity with which the ball hits the ground?

#### 11th Physics - Laws of Motion Model Question Paper - by Question Bank Software - View & Read

• 1)

A vehicle is moving along the positive x direction, if sudden brake is applied, then

• 2)

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

• 3)

A particle of mass m sliding on the smooth double inclined plane (shown in figure) will experience

• 4)

A heavy iron rod of weight W is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle ፀ with the horizontal. What is the weight experienced by the man?

• 5)

A ship of mass 3$\times$ 106 kg initially at rest is pulled by a force of 6 $\times$ 104 N through a distance of 4m. The speed of the ship is (Assume resistive of water is negligible)

#### 11th Physics - Nature of Physical World and Measurement Important Questions - by Question Bank Software - View & Read

• 1)

Which of the following has the highest number of significant figures?

• 2)

If $\pi=3.14,$ then the value of ${\pi}^{2}$ is

• 3)

The velocity of a particle v at an instant t is given by v = at + br2. The dimensions of b is

• 4)

Which is deals with the study of materials of an intermediate length scale?

• 5)

What is the range of astronomical time scales to microscopic scales?

#### 11th Physics - Kinematics Important Questions - by Question Bank Software - View & Read

• 1)

If a particle has negative velocity and negative acceleration, its speed

• 2)

If the velocity is $\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k }$, then the magnitude of acceleration at t = 0.5s is

• 3)

If a particle executes uniform circular motion, choose the correct statement

• 4)

Choose the motion in two dimension from the following.

• 5)

A train is moving towards east and a car is along north, both with same speed. The passenger in the train is observed the car moving in which of the following direction?

#### 11th Physics Half Yearly Model Question Paper 2019 - by Question Bank Software - View & Read

• 1)

One of the combinations from the fundamental physical constants is ${{hc}\over{G}},$ The unit of this expression is

• 2)

How many light years make 1 per sec?

• 3)

A car moves from X to Y with a uniform speed Vn and returns to Y with a uniform speed VThe average speed for this round trip is _____________.

• 4)

The centrifugal force appears to exist

• 5)

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of heaviest fragment in m/s will be _____________.

#### 11th Standard Physics - Term II Model Question Paper - by Ravikumar - Kumbakonam - View & Read

• 1)

One of the combinations from the fundamental physical constants is ${{hc}\over{G}},$ The unit of this expression is

• 2)

The dimension of ${\left( {\mu}_{0}{\epsilon}_{0} \right)}^{{{1}\over{2}}}$ is

• 3)

If a particle has negative velocity and negative acceleration, its speed

• 4)

When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to

• 5)

Force acting on the particle moving with constant speed is

#### 11th Physics - Properties of Matter Three Marks Questions - by Question Bank Software - View & Read

• 1)

A solid sphere has a radius of 1.5 cm and a mass of 0.038 kg. Calculate the specific gravity or relative density of the sphere.

• 2)

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• 3)

A cube of wood floating in water supports a 300 g mass at the centre of its top face. When the mass is removed, the cube rises by 3 cm. Determine the volume of the cube.

• 4)

A metal plate of area 2.5$\times$10-4m2 is placed on a 0.25$\times$10-3m thick layer of castor oil. If a force of 2.5 N is needed to move the plate with a velocity 3$\times$10-2m s-1, calculate the coefficient of viscosity of castor oil.
Given: A = 2.5$\times$10-4 m2, dx = 0.25$\times$10-3 m, F = 2.5N and dv = 3×10-2 m s-1

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Let 2.4$\times$10−4 J of work is done to increase the area of a film of soap bubble from 50 cm2 to 100 cm2. Calculate the value of surface tension of soap solution.

#### 11th Physics - Kinetic Theory of Gases Three Marks Questions - by Question Bank Software - View & Read

• 1)

Write down the postulates of kinetic theory of gases.

• 2)

Derive the expression of pressure exerted by the gas on the walls of the container.

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Explain in detail the kinetic interpretation of temperature.

• 4)

Describe the total degrees of freedom for monoatomic molecule, diatomic molecule and triatomic molecule.

• 5)

Derive the ratio of two specific heat capacities of monoatomic, diatomic and triatomic molecules.

#### 11th Physics - Oscillations Three Marks Questions - by Question Bank Software - View & Read

• 1)

A nurse measured the average heart beats of a patient and reported to the doctor in terms of time period as 0.8 s. Express the heart beat of the patient in terms of number of beats measured per minute.

• 2)

A spring balance has a scale which ranges from 0 to 25 kg and the length of the scale is 0.25m. It is taken to an unknown planet X where the acceleration due to gravity is 11.5 m s−1. Suppose a body of mass M kg is suspended in this spring and made to oscillate with a period of 0.50 s. Compute the gravitational force acting on the body.

• 3)

Consider two springs with force constants 1 N m−1 and 2 N m−1 connected in parallel. Calculate the effective spring constant (kp) and comment on kp.

• 4)

If the length of the simple pendulum is increased by 44% from its original length, calculate the percentage increase in time period of the pendulum.

• 5)

Write down the kinetic energy and total energy expressions in terms of linear momentum, For one-dimensional case.

#### 11th Physics - Waves Three Marks Questions - by Question Bank Software - View & Read

• 1)

Write about the formation of waves in a tuning fork.

• 2)

Write the characteristics of wave motion.

• 3)

Distinguish between transverse and longitudinal waves.

• 4)

Define angular frequency, wave number and wave vector.

• 5)

What is the relation between the velocity and temperature?

#### 11th Physics - Heat and Thermodynamics Three Marks Questions - by Question Bank Software - View & Read

• 1)

A person does 30 kJ work on 2 kg of water by stirring using a paddle wheel. While stirring, around 5 kcal of heat is released from water through its container to the surface and surroundings by thermal conduction and radiation. What is the change in internal energy of the system?

• 2)

Jogging every day is good for health. Assume that when you jog a work of 500 kJ is done and 230 kJ of heat is given off. What is the change in internal energy of your body?

• 3)

Give an example of a quasi-static process.

• 4)

A 0.5 mole of gas at temperature 300 K expands isothermally from an initial volume of 2 L to 6 L
(a) What is the work done by the gas?
(b) Estimate the heat added to the gas?
(c) What is the final pressure of the gas?
(The value of gas constant, R = 8.31 J mol-1 K-1)

• 5)

The following PV curve shows two isothermal processes for two different temperatures and. Identify the higher temperature of these two.

### TN Stateboard Education Study Materials

#### 11th Stateboard Physics 2019 - 2020 Academic Monthly Syllabus - by Question Bank Software Aug 01, 2019 Aug 01, 2019

Physics 2019 - 2020 Academic Monthly Syllabus

#### How to Score High marks and Centum in 11th Physics Exam?? நூற்றுக்கு நூறு மதிப்பெண் பெற டிப்ஸ் - by boopal Jan 18, 2019 Jan 18, 2019

• கல்வி சூழலில் மருத்துவம...

#### Plus One Physics Public Exam Tips! - by Sathish.C Jan 12, 2019 Jan 12, 2019

• கல்வி சூழலில் மருத்துவம...

### TN Stateboard Updated Class 11th Physics Syllabus

#### Nature of Physical World and Measurement

Science Introduction-Physics Introduction-Physics in Relation to Technology and Society-Measurement-Measurement of Basic Quantities-Theory of Errors-Significant Figures-Dimensional Analysis

#### Kinematics

Introduction-Concept of Rest and Motion-Elementary Concepts of Vector Algebra-Components of a Vector-Multiplication of Vector by a Scalar-Position Vector-Distance and Displacement-Differential Calculus-Integral Calculus-Motion along One Dimension-Projectile Motion

#### Laws of Motion

Introduction-Newton’s Laws-Application of Newton’s Laws-Lami’s Theorem-Law of Conservation of Total Linear Momentum-Friction-Dynamics of Circular Motion

#### Work, Energy and Power

Introduction-Work-Energy-Power-Collisions

#### Motion of System of Particles and Rigid Bodies

Introduction-Torque and Angular Momentum-Equilibrium of Rigid Bodies-Moment of Inertia-Rotational Dynamics-Rolling Motion

#### TN StateboardStudy Material - Sample Question Papers with Solutions for Class 11 Session 2020 - 2021

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# What is the solution set for 4x^2 - 5x < 6?

Aug 7, 2015

Solve $4 {x}^{2} - 5 x < 6$

Ans: $\left(- \frac{3}{4} , 2\right)$

#### Explanation:

Bring the inequality to standard form:
$f \left(x\right) = 4 {x}^{2} - 5 x - 6 < 0$
First, solve $f \left(x\right) = 4 {x}^{2} - 5 x - 6 = 0$ (1) to get the 2 real roots.
I use the new Transforming Method. (Google, Yahoo)
Transformed equation $f ' \left(x\right) = {x}^{2} - 5 x + 24$ (2). Roots have opposite signs.
Factor pairs of 24 -> ...(-2, 12)(-3, 8). This sum is 5 = -b. Then, the 2 real roots of (2) are: -3 and 8.
Back to original equation (1), the 2 real roots are: $- \frac{3}{4}$ and $\frac{8}{4} = 2.$
Find the solution set of the inequality. Since a > 0, the parabola opens upward. Between the 2 real roots $\left(- \frac{3}{4}\right)$ and (2), a part of the parabola is below the x-axis, meaning f(x) < 0.
Answer by open interval:$\left(- \frac{3}{4} , 2\right)$


text:
1. Apr 8, 2010

### dirtywater101

1. Two radio stations have the same power output from their antennas. one broadcasts on FM band at 105.2 MHz and other on the AM band at 701kHz. Which one emits more photons per second? Or do they emit the same amount of photons per second? Explain answer

2. I don't know if i've been doing it right. I've been using einstein's photoelectric effect to get the energy of each (E=hf), but I don't know how to relate this to the actual emition of photons. Please help! I'm the biggest novice :(

3. (105.2 x 10^6 s^-1) x (6.626 x 10^-34) = 6.97 x 10^-26

(701 x 10^3 s^-1) x (6.626 x 10^-34) = 4.64 x 10^-28

2. Apr 8, 2010

### RoyalCat

You've found the energy of the FM station's photons, and the energy of the AM station's photons.

If you know that they both have the same power output, that means that each station is pumping out enough photons of energy $$E=hf$$ every second, so that the energy per unit time, equals the output, $$P$$. How would you relate that mathematically? Try using an arbitrary symbol like $$n$$ for the number of photons emitted per second.

3. Apr 8, 2010

### dirtywater101

hmmm... would it be

N photons/sec = Power / photon energy

i'm new to making equations so i don't really know how to write it out, but it is making some sense in my head and it's working. thanks alot! I justdon't know how to put it into an acceptable equation form, aka what the value of P should be.

4. Apr 8, 2010

### ideasrule

Just think about it. E=hf gives the energy EACH photon has. Which radio station gives off lower-energy photons? Since the photons have lower energy, does the station have to give off more or less photons to emit with the same power as the other station?


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# Möbius transformations form a simple group

How to show the group $M$ of Möbius transformations is a simple group?

I know: $SL_2(\mathbb C)/\{+I,-I\}\cong M$ then if $A \lhd M \implies \phi^{-1}(A) \lhd SL_2(\mathbb C)/\{+I,-I\}$.

So if I can show $SL_2(\mathbb C)/\{+I,-I\}$ is simple probably that answers the question.

• Actually you want a proof for this: PSL$(2,\mathbb C)$ is a simple group. Try google!
– user26857
Mar 3 '13 at 12:38
• What is $\phi$? Jun 24 '13 at 19:11
• I do not understand the votes to close - is it merely because this is an old, yet unanswered question? Personally, I think it should be left open and that someone should, you know, answer it... Jun 24 '13 at 19:36
• @user1729 I completely agree. Jun 25 '13 at 18:12
• Look at this Apr 5 '18 at 23:29

You can prove this without having to look at $$PSL_2 (\mathbb{C})$$. First, consider that any Möbius transformation can be expressed as the composition of dilations, translations and the inversion. In particular, if $$T(z) =\dfrac{az+b}{cz+d}$$, then $$T = S_4 \circ S_3 \circ S_2 \circ S_1$$, where $$S_1$$ and $$S_4$$ are translations, $$S_3$$ a dilation and $$S_2$$ the inversion. Now, let $$N \trianglelefteq M$$ be non-trivial and suppose $$T \in N$$ is a translation, i.e., $$T(z) = z+b$$, with $$b \in \mathbb{C^{*}}$$ (we don't have to consider $$b=0$$ because the identity is always there). Let $$S(z)=az$$, with $$a \in \mathbb{C}^{*}$$. We have that $$S^{-1}\circ T \circ S = z+\dfrac{b}{a} \in N$$, so, for any $$c \in \mathbb{C^{*}}$$, we may choose $$a=b/c$$ and obtain every translation. In particular, $$R(z) = z-1 \in \mathbb{C^{*}}$$ and if we take $$I(z) = 1/z$$ to be the inversion, we can obtain that

$$I\circ R \circ I^{-1} = \dfrac{z}{1-z}$$

$$\left(\dfrac{z}{1-z}\right)\circ R = \dfrac{z-1}{-z}$$

$$(-I)\circ \left(\dfrac{z-1}{-z}\right) \circ (-I) = \dfrac{1}{z+1}$$

$$\left(\dfrac{1}{z+1}\right) \circ R = \dfrac{1}{z} \in N$$

Then, if we take $$I \circ S \circ I \circ S^{-1} = a^2 z$$, we can obtain every dilation and so $$N=M$$. Now, suppose we have $$S(z)=az \in N$$, $$a\in \mathbb{C^{*}-\{1\}}$$. If we take $$T(z) = z+b$$, $$b \in \mathbb{C^{*}}$$, then $$S^{-1} \circ T \circ S \circ T^{-1} = z+ab-b \in N$$ $$\Rightarrow z+c \in N, \forall c \in \mathbb{C^{*}}$$. We have proved the following implications, for $$N \trianglelefteq M$$:

$$(\text{i) }z+b \in N$$, for some $$b \in \mathbb{C^{*}} \Rightarrow$$ $$z+c \in N, \forall c \in \mathbb{C^{*}} \Rightarrow 1/z \in N \Rightarrow az \in N, \forall a \in \mathbb{C^{*}} \Rightarrow N = M;$$

$$(\text{ii) }az \in N$$, for some $$a \in \mathbb{C^{*}-\{1\}} \Rightarrow$$ $$z+ab-b \in N \Rightarrow$$ $$N=M;$$

$$(\text{iii) }1/z \in N\Rightarrow$$ $$az \in N, \forall a \in \mathbb{C^{*}} \Rightarrow$$ $$N=M;$$

Finally, it suffices to prove that if we have a general Mobius transformation $$T(z) =\dfrac{az+b}{cz+d} \in N$$, then we can obtain a dilation, a translation or an inversion. We have that $$T = S_4 \circ S_3 \circ S_2 \circ S_1$$. This implies that $$S_1 \circ S_4 \circ S_3 \circ S_2 \in N$$ and $$S_2 \circ S_1 \circ S_4 \circ S_3 \in N$$, so $$L = (S_1 \circ S_4 \circ S_3)^2 \in N$$. Since $$L$$ is the composition of translations and dilations, it has the form $$L(z)=xz+y$$, with $$x,y \in \mathbb{C^{*}}$$. If $$x=1$$ and $$y=0$$, this would imply that $$S_1 \circ S_4 \circ S_3 = z \Rightarrow S_4 \circ S_3 = S_1^{-1}$$ $$\Rightarrow T = S_1^{-1} \circ S_2 \circ S_1 \Rightarrow 1/z \in N$$ $$\Rightarrow N=M$$. If $$x=1$$ or $$y=0$$, we are done. Finally, if $$x\neq 1$$ and $$y \neq 0$$, then $$L \circ (z-y) \circ L^{-1} \circ (z+y) = z-xy+y \in N$$ and, since $$-xy+y \neq 0$$, $$N=M$$.

• Great answer. It is hard to find a proof of the fact that $PSL_2(\mathcal{C})$ is simple, and this proof is easy to understand. I think that there is a typo in the line "This implies that $S_1 \circ S_4\circ S_3\circ S_2\in N$...", the second element should be $S_2\circ S_1\circ S_4\circ S_3$ or am I wrong? Dec 27 '19 at 4:46
• You are correct, thank you! Dec 28 '19 at 5:45


text:
# Math Help - More Proving

1. ## More Proving

$cos^2(2x)-cos^2(x)=sin^2(x)-sin^2(2x)$

2. Originally Posted by Dragon
$cos^2(2x)-cos^2(x)=sin^2(x)-sin^2(2x)$
Typically we do stuff to one side to make it equal to the other, but this one is much faster using standard manipulations:
$cos^2(2x)-cos^2(x)=sin^2(x)-sin^2(2x)$

$sin^2(2x) + cos^2(2x) = sin^2(x) + cos^2(x)$

$1 = 1$

-Dan


text:
# Find the proportion of professional male golfers-drive on an average of 280 yards or less. Approximately 5 percent of professional male golfers are found to be less than an average of 280 yards.

Question
Find the proportion of professional male golfers-drive on an average of 280 yards or less.
Approximately 5 percent of professional male golfers are found to be less than an average of 280 yards.

2021-03-03

Calculation:
The proportion of professional male golfers-drive on an average of 280 yards or less is,
$$\text{(Proportion of male golf drives less than average of 280 yards)}=$$

$$\frac{\text{(number of golfers found to be less than 280 yards)}}{\text{Total number of yards}}\times 100 = =\frac{1+1+6+2}{186}\times 100$$
$$=\frac{10}{186}\times100\approx5.38$$
Therefore, the proportion of professional male golfers-drive on an average of 280 yards or less. is found to be approximately 5 percent.

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c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and$100 per foot along theland.


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