Question 1 :
If $cot^{-1} x - cot^{-1} (x+2) = 15^0$ then x is equal to
Question 2 : <div><span>Let $\displaystyle f:A\rightarrow B$ be a function defined by $\displaystyle y=f(x)$ where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping $\displaystyle g:B\rightarrow A$ such that $\displaystyle f(x)=y$ if and only if $\displaystyle g(y)=x\forall x \epsilon A,y \epsilon B $ Then function g is said to be inverse of f and vice versa so we write $\displaystyle g=f^{-1}:B\rightarrow A[\left \{ f(x),x \right \}:\left \{ x,f(x) \right \}\epsilon f^{-1}] $when branch of an inverse function is not given (define) then we consider its principal value branch.</span><br/></div><div><span><br/></span></div>If $\displaystyle -1<x<0$,then $\displaystyle \tan^{-1}x $ equals?<br/>
Question 3 :
Let the population of rabbits surviving at a time $ t$ be governed by the differential equation $ \displaystyle \frac{dp(t)}{dt}=\displaystyle \frac{1}{2}p(t)-200$. If $ p(0)=100$, then $ p(t)$ equals:
Question 5 :
If A and B are the points $(2,1,-2),(3,-4,5)$, then the angle that $OA$ makes with $OB$ is:
Question 6 :
If  $2\overline a  - 4\widehat i - 2\widehat j + \widehat k = 0$ then find $\overline a $.
Question 7 :
Let $2\hat{i}+\hat{k}=\vec{\mathrm{a}},\ 3\hat{j}+4\hat{k}=\vec{{b}}$, $8\hat{i}-3\hat{j}$ $=\vec{\mathrm{c}}$. If $\vec{a}={x}\vec{b}+{y}\vec{{c}}$, then $(x,y) $ is equal to<br/>
Question 8 :
The figure formed by the four points i + j - k, 2i + 3j, 3i + 5j -2k and k - j is
Question 9 :
Namita walks 14 metres towards west, then turns to her right and walks 14 metres and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and the present position ?
Question 10 :
$\vec{A} \ and \ \vec{B}$ are two vectors, find the angle between them, if <br/>$\left | \vec{A}\times \vec{B} \right |=\sqrt{3}(\vec{A.}\vec{B})$ the value of is :-<br/>
Question 12 :
If $\vec{a} = (2, 1, -1), \vec{b} = (1,-1,0), \vec{c} = (5, -1, 1) $ , then what is the unit vector parallel to $ \vec{a} + \vec{b} - \vec{c} $ in the opposite direction ?
Question 14 :
If $|\overrightarrow{a}| = 5, |\overrightarrow{a} - \overrightarrow{b}|=8$ and $|\overrightarrow{a} + \overrightarrow{b}| = 10$, then $|\overrightarrow{b}|$ is equal to:
Question 15 : <div><span>Conclude from the following:</span><br/></div>$n^2 > 10$, and n is a positive integer.<div>A: $n^3$</div><div>B: $50$</div>
Question 16 :
Find the output of the program given below if$ x = 48$<br/>and $y = 60$<br/>10  $ READ x, y$<br/>20  $Let x = x/3$<br/>30  $ Let y = x + y + 8$<br/>40  $ z = \dfrac y4$<br/>50  $PRINT z$<br/>60  $End$
Question 17 :
The rate of change of surface area of a sphere of radius $r$ when the radius is increasing at the rate of $2 cm/sec$ is proportional to
Question 18 :
The side of a square sheet is increasing at the rate of $4 cm$ per minute. The rate by which the area increasing when the side is $8 cm$ long is.
Question 19 :
<i></i>A point on the parabola $y^{2}=18x$ at which the ordinate increases at twice the rate of the abscissa is <br/>
Question 20 :
Time period $T$ of a simple pendulum of length $l$ is given by $T=2\pi \sqrt{\dfrac{l}{g}}$. If the length is increased by $2\%$, then an approximate change in the time period is
Question 21 :
Water flows at the rate of $10$ metres per minute from cylindrical pipe $5mm$ in diameter. How long it will take to fill up a conical vessel whose diameter at the base is $30cm$and depth $24cm$<br><br>
Question 22 :
If the radius of a circle is doubled, its area is increased by :
Question 23 :
The radius of a sphere is changing at the rate of $0.1 cm/sec$. The rate of its surface area when the radius is $200 cm$ is
Question 24 :
The coordinates of a moving point particle in a plane at time $t$ is given by $x=a\left( t+\sin { t } \right) $, $y=a\left( 1-\cos { t } \right) $. The magnitude of acceleration of the particle is
Question 25 :
The equation of a stationary wave is $y = 4\sin \frac{\pi x}{5} \cos (100 \pi t)$. The wave is formed using a string of length $20cm$. The second and 3rd antinodes are located at positions (in cm)
Question 26 :
A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre pr hour. Then the depth of the wheat is increasing at the rate of
Question 27 : <p>If the radius of a circle is increased by $10\% $ then what percent will increase the circumference of a circle?</p>
Question 28 :
Side of an equilateral triangle expands at the rate of $2 cm/sec$. The rate of increase of its area when each side is $10cm$ is
Question 36 :
$\displaystyle \int { \cfrac { x }{ 1+{ x }^{ 4 } }  } dx$ is equal to
Question 40 :
$\int { \dfrac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } dx } $ is equal to
Question 42 :
$\displaystyle \int { \frac { \sec { x }  }{ \sqrt { \sin { \left(2 x+\alpha  \right)  } +\sin { \alpha  }  }  } dx } =$
