List of top Mathematics Questions

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

The value of $c$ in Lagrange's theorem for the function $f(x) = \log (\sin \, x)$ in the interval $\left[ \frac{\pi}{6} , \frac{5 \pi}{6} \right]$ is

The differential equation of the family of parabolas $y^2 = 4ax$, where $a$ is parameter, is

If $\tan(x + y) = 33$ and $x = \tan^{-1} \, 3,$ then $y$ is

The maximum area in square units of an isosceles triangle inscribed in an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with its vertex at one end of the major axis is

The direction ratios of the line which is perpendicular to the lines $\frac{ x - 7}{2} = \frac{y +17}{-3}= \frac{z - 6}{1} $ and $\frac{ x + 5}{1} = \frac{y +3}{2}= \frac{z - 4}{-2} $ are

A line making angles $45^\circ$. and $60^\circ$ with the positive directions of the axis of $x$ and $y$, makes with the positive direction of $z$-axis, an angle of