List of top Mathematics Questions

Rain is falling vertically downwards with a velocity of $4\, km / h$. A man walks in the rain with a velocity of $3 \,km / h$. The raindrops will fall on the man with a velocity of

The value of $\cos \frac{\pi}{15}\, \cos \frac{2\pi}{15}\, \cos \frac{4\pi}{15}\, \cos \frac{8\pi}{15} $ is

The order and degree of the following differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5/2} = \frac{d^{3}y}{dx^{3}}$ are respectively

The differential equation of the family of circles passing through the fixed points $(a, 0)$ and $(-a, 0)$ is

The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is

The value of $\displaystyle\lim_{n\to\infty}\left(\frac{1}{n+1} +\frac{1}{n+2}+... +\frac{1}{6n}\right)$ is

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vector $\widehat{a},\widehat{b},\widehat{c}$ such that $\widehat{a}.\widehat{b}=\widehat{b}.\widehat{c}=\widehat{c}.\widehat{a}=\frac{1}{2}.$Then, the volume of the parallelopiped is

Let $S_n= \displaystyle \sum_{k=0}^n \frac{n}{n^2+kn+k^2} \, and \, T_n= \displaystyle \sum_{k=0}^{n-1} \frac{1}{n^2+kn+k^2} , \, for \, $ $n = 1 ,2 ,3 $,... Then,

If $0 < x < 1$, then $\sqrt{1+x^2}[\{x cos(cot^{-1}x)$ $+sin(cot^{-1}x)\}^2-1]^{1/2}$ is equal to

Let $g(x) = \frac{(x -1)^n}{\log \cos^m (x -1)} ; 0 < x < 2 , m $ and $n$ are integers, m $\neq$ 0, n > 0 , and let $p$ be the left hand derivative of $|x - 1|$ at $x = 1$. If $\displaystyle \lim_{x \to 1^{+}} \, g(x) = p $ , then

The area of the region between the curves $ y= \sqrt \frac{1 + sin x}{cos x} $ and $ y= \sqrt \frac{1 - sin x}{cos x} $ and bounded by the lines $x = 0$ and $ x = \frac{\pi}{4} $ is

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes, then the number of outcomes that $B$ must have, so that $A$ and $B$ are independent, is

Let a and b be non-zero and real numbers. Then, the equation $ (ax^2 + by^2 + c) \, ( x^2 - 5xy + 6y^2) = 0 $ represents

Consider a branch of the hyperbola $x^2 - 2y^2 - 2\sqrt2x - 4\sqrt2y - 6 = 0$ with vertex at the point A. Let B be one of the end points of its latusrectum. If C is the focus of the hyperbola nearest to the point A, then the area of the $\Delta ABC$ is

$ \frac{x-y}{x}+\frac{1}{2}{{\left( \frac{x-y}{x} \right)}^{2}}+\frac{1}{3}{{\left( \frac{x-y}{x} \right)}^{3}}+.... $ =

The displacement of particle is given by $x=a_{0}+\frac{a_{1} t}{2}-\frac{a_{2} t^{2}}{3}$ What is its acceleration?

If g (x) is a polynomial satisfying g (x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g (2) = 5 then $\underset{\text{x $\rightarrow$ 3}}{{Lt }}$ g(x)is

$(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to

If 11,109,999 is divided by 1111, then what is the remainder?

The length of a ladder is exactly equal to the height of the wall it is leaning against.If the lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall the upper end of the ladder coincides with the top of the wall.Then the height of the wall is

$\frac {3x^2+1}{x^2-6x+8}$ is equal to

The value of the $ \int_{{}}^{{}}{\frac{\sin x+\cos x}{3+\sin 2x}}dx $ is

The equation of the circle concentric to the circle $ 2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0 $ and having area double the area of this circle, is

The imaginary part of $\frac{\left(1+i\right)^{2}}{i\left(2i-1\right)} $ is