For how many kilometre the journey on LTC performed by a private/personal transport be regulated, assuming that the place is not connected by any public transport?

For medical reimbursement, advance is paid direct to the hospital and the employee wants to submit the adjustment bills for final settlement . Within how many days the employee can apply in the Vidyalaya?

Hard area allowances for the central government employees residing at Nicobar Group of islands is

The special allowances for child care for women with disabilities is

The range of  $f\left(x\right)=\frac{\left|x\right|-x}{2x}\ is$  

Solution of  $\left|1+i\right|^x\ =\ 2\ \ \ \ \ is\$  

If 2 + 3 i   is a root of  $x^2+px+q\ =\ 0\ \ then\ values\ of\ p\ and\ q\ are$  

The sum of the digits in the unit place of all the numbers formed using the digits 3, 4, 5 and 6 taken all at a time is

Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. the value of n is

If a, b, c , d and e are in arithmetic progressions, then the value of

a - 4b + 6c - 4d + e is

The inverse of the function  $f\left(x\right)=\ \frac{a^x\ -\ a^{-x}}{a^x\ +\ a^{-x}}\ \ \ is$  

Let
  $f\left(x\right)=\ \sin^{-1}x\ +\cos^{-1}x,\ then\ \frac{\pi}{2}\ \$  
is equal to 

if  $\cot^{-1}\left(\frac{n^2-10n\ +21\cdot6}{\pi}\right)\ >\frac{\pi}{6}$  
n is a natural number, then the minimum value of n is 

Let A, B be two square matrices such that A + B = AB. Then

The system of equations x + 2y + 3z = 4, 2x + 3y + 4z = 5, 3x +4y +5z = 6 has

The differential coefficient of  $\tan^{-1}\left(\frac{\sin x\ +\ \cos x}{\sin x\ -\ \cos x}\right)\$  with respect to x is 

If  $f\left(x\right)=\ \frac{\left(a^x-1\right)^3}{\sin\left(x\log a\right)\log\left(1+x^2\log a^2\right)}$  
is continuous at x = 0 then f(0) is 

The second derivative of  $a\ \sin^3t\ \ with\ respect\ to\ a\cos^3t$  
at  $t\ =\ \frac{\pi}{4}\$  is 

 $g\left(x\right)=\frac{1}{x-1}\ f\left(x\right)=\frac{1}{x^2+x-2}$  
The points of discontinuity of the function fog  are

The equation of motion of a stone thrown vertically upwards is $s=ut\ -\ 4\cdot9t^2$ . The maximum height attained by it is 

Angle between the curves y = sin x

and y = cos x is

The equation x log x = 3 - x in the interval (1,3) has

 $\int_0^{\frac{\pi}{2}}\ \frac{\cos x}{1\ +\ \sin^2x}\ dx\ \ is$  

The area of the region bounded by $y\ =\ 2x\ -\ x^2$  
and x - axis is 

Solution of

( 3x + 2y + 1) dx - ( 3x + 2y - 1) dy = 0 is

If G is the centroid of the triangle ABC then 
 $\overrightarrow{GA}$  +  $\overrightarrow{GB}$  +  $\overrightarrow{GC}$   is

The equation of the plane through the line of intersection of the planes x + y + z - 6 = 0, 2x + 3y + 4z + 5 = 0 and passing through the point (1,1,1) is

A coin is tossed. If head comes up, a die is thrown but if tail comes up the coin is tossed again. The probability of obtaining a head and an even number is

The two curves $x^3-3xy^2+2\ =0\ and\$  
 $3x^2y-y^3=2$