List of top Mathematics Questions

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

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

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

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

The probability that the same number appear on throwing three dice simultaneously, is

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is

If a=\(\log _{2} 3, b=\log _{2} 5, c=\log _{7} 2,\) then \(\log _{140} 63\) in terms of a, b, c is

If $(\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots . .(\cos n \theta+i \sin n \theta)=1$, then the value of $\theta$ is, $m \in N$

The length of the common chord of the ellipse $\frac{(x+1)^{2}}{9}+\frac{(y-2)^{2}}{4}=1$ and the circle $x-1^{2}+y-2^{2}=1$ is

For the hyperbola $\frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1$, which of the following remains constant when $\alpha$ varies

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

If $\sin^{-1} \, x + \sin^{-1} \, y = \frac{\pi}{2},$ then $\frac{dy}{dx} $ is equal to

If $ P\left(A\right)=\frac{1}{12}, P\left(B\right)=\frac{5}{12},$ and $P\left(B|A\right) =\frac{1}{15}$ then $p\left(A\cup B\right)$ is equal to

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

If (x +y )sin u = $x^2y^2$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $

The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to

If the normal at $(ap^2, 2ap)$ on the parabola $y^2 = 4ax,$ meets the parabola again at $(aq^2, 2aq)$, then