A patient following head injury was admitted in intensive care ward with signs of raised intracranial pressure. He was put on a ventilator and started on intravenous fluids and diuretics. Twenty-four hours later his urine output was 3.5 litres, serum sodium 156 mEq/I and serum osmolarity of 316 mOsm/kg. The most likely diagnosis based on these parameters is -
Laboratory abnormalities seen in this patient

Increased serum sodium       →  (N-135-145 meq/dL)
Increased serum osmolarity  →   (N-275-293 mosm/kg)
Polyuria                                 →   (Urine output > 3L/day sometimes assumed to be 70 kg, the

criteria forpolyuria is > 3.5L/day)
Usually when the diagnosis of polyuria is Established the next step is to assess urine osmolality
Urine osmolarity
> 300 mosmol/L           Solute diuresis due to diabetes Mellitus or Diuretics (Osmotic diuretics and loop diuretics)
< 300 mosm/L              Water diuretis (Now, it should be further evaluated to determine which type of diabetes insipidus is present)

In the question there is no information regarding the urine osmolality and specific gravity
The other clues given in the question -

-H/O head injury
-Raised intracranial tension
-Patient is on diuretic (Usually is given to reduce pressure) 
-L V. fluid administration intracranial
 

The history and the laboratory abnormalities suggests either diabetes insipidus or diuresis due to osmotic diuretics.
The features of Hypernatrenzia, Increased osmolality and increased urine output indicates diuresis due to mannitol.
Pts with head injury and increased intracranial pressure requires mannitol adminstration (to reduce intracranial pressure).
Mannitol is an osmotic diuretic, it is freely filtered at glomerulus and undergoes limited reabsorption.
Presence of mannitol in the tubular fluid reduces the corticomedullary gradiant and retains water isoosmatically in the proximal tubular fluid.
So, the primary function of mannitol is to increase urinary volume.
The loss of water in the urine can cause Hypernatremia and increase in serum osmolarity.

"Whenever mannitol is administered in cases of head trauma to reduce the intracranial tension, serum osmolarity should always be monitored (it should never be allowed to go beyond 320 mosmol/kg.)"
Diabetes insipidus

Hypernatremia and increase in Serum osmolarity can also occur in Diabetes insipidus (due to increased water loss).
Presence of head injury too, suggests Diabetes insipidus
But, this is not a case of diabetes insipidus

To establish the diagnosis of diabetes insipidus urinary osmolarity and specific gravity is needed
- urine osmolarity < 300 mosmol/kg and
- specific gravity < 1.02
Urine output in cases of diabetes insipidus is generally in the range of 6-7 L/day.
(Here, the urine output is 3.5 L/day which is just adequate to meet the criteria of polyuria)
Remember,
The pt is on a diruretic i.e., mannitol

Mannitol will prevent reabsorption of water in                →        Proximal tubule
. Diabetes insipidus will prevent reabsorption water in   →      Collecting duct of 


 
So the presence of diabetes insipidus in patients on diuretic will lead to huge loss of water through urine which will certainly be much more than 3.5 L/day
Note :
The patients is on ventilator

Significant loss of water also occurs through ventilation by evaporation. This may also contribute to hypernatremia and increase in serum osmolarity.

Too much infusion of normal saline

Too much infusion of normal saline will never increase sodium and serum osmolarity in physiologically normal patient
Hypernatremia can be caused by administration of hypertonic saline and NaHCO3.
High output due to diuretics
Diabetes insipidus
Too much infusion of normal saline
Cerebral salt retaining syndrome