List of top Mathematics Questions

Let function $ f(x)={{(x-1)}^{2}}{{(x+1)}^{3}}. $ Then, which of the following is false?

In an isosceles right angled triangle $ABC$, a value of $ \tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right) $ is

The function is $ f(x)=\frac{1}{2-\cos \,3x},\,x\,\in \left[ 0,\frac{\pi }{3} \right], $ is

The last digit in the integer $ {{3}^{101}}+1 $ is

$ \underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin {{x}^{2}}}{1-\cos x} $ is

The derivative of $sin\, x$ with respect to $ cos\text{ }x $ is

If getting a number greater than $4$ is a success in a throw of a fair die, then the probability of at least $2$ successes in six throws of a fair die is

The number of integer value(s) of $k$ for which the expression $ {{x}^{2}}-2(4k-1)x+15{{k}^{2}} $ $ -2k-7>0 $ for every real number $x$ is/are

If the plane $ 2x-3y+6z-11=0 $ makes an angle $ \theta $ with the $x-axis$, then the value of $ \tan \theta $ is equal to

Let $A$ and $B$ be points $ (8,\,\,10) $ and $ (18,\,20), $ respectively. If the point $Q$ divides AB externally in the ratio $ 2:3 $ and $M$ is the $S$ mid-point of $AB$, then the length $MQ $ is equal to

If the image of the point $ (1,\,-2,3) $ in the plane $ 2x+3y-z=7 $ is the point $ (\alpha ,\beta ,\gamma ) $ then $ \alpha +\beta +\gamma $ is equal to

A balloon which always remains spherical is being inflated by pumping in $10$ cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15$ cms.

Slope of Normal to the curve $y=x^2 - \frac {1}{x^2}$ at $(-1,0)$ is

Equation of line passing through the point $(2, 3, 1) $and parallel to the line of intersection of the plane $x- 2y - z + 5 = 0$ and $x + y + 3z = 6$ is

Let $f: R \rightarrow R$ be a continuous function which satisfies $f(x)=\int\limits_{0}^{x} f(t) d t$. Then, the value of $f\left(\log _{e} 5\right)$ is

Area bounded by $y = x^3, y = 8$ and $x = 0 $ is

The area in square units bounded by the normal at $(1, 2)$ to the parabola $y^2 = 4x, x$-axis and the curve is given by

The angle between the curves $y^2 = 4ax$ and $ay = 2x^2$ is

The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y-8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is

A ladder $5\,m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2m/sec$. The speed at which its height on the wall decreases when the foot of the ladder is $4\, m$ away from the wall is

$\tan\left(\cos^{-1}\left( \frac{1}{5\sqrt{2}}\right)-\sin^{-1}\left(\frac{4}{\sqrt{17}}\right)\right)$ is