List of top Mathematics Questions

$\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is

The Cartesian equation of the line passing through the points A(2, 2, 1) and B(1, 3, 0) is

$\int \sec^4 x \cdot \tan^4 x dx = \frac{\tan^m x}{m} + \frac{\tan^n x}{n} + c$ (where $c$ is constant of integration), then $m + n =$

The x-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $(1, 2)$ is :

p : It rains today
q : I am going to school
r : I will meet my friend
s : I will go to watch a movie.
Then symbolic form of the statement "If it does not rain today or I won't go to school, then I will meet my friend and I will go to watch a movie" is

The variance of the following probability distribution is,

If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio $2:1$, then $n =$

If $\omega$ is complex cube root of unity and $(1+\omega)^7=A+B\omega$, then values of $A$ and $B$ are, respectively

If $[\vec{a} \vec{b} \vec{c}]=4$, then the volume (in cubic units) of the parallelopiped with $\vec{a}+2\vec{b}, \vec{b}+2\vec{c}$ and $\vec{c}+2\vec{a}$ as coterminal edges, is

If $a = \lim_{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$ and $b = \lim_{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$, then

If $m$ is order and $n$ is degree of the differential equation $y = x\frac{dy}{dx} + \sqrt{a^2 \left(\frac{dy}{dx}\right)^2 - b^2}$, then the value of $m + n$ is

The surface area of a spherical balloon is increasing at the rate $2\ \text{cm}^2/\text{sec}$. Then rate of increase in the volume of the balloon is, when the radius of the balloon is $6\ \text{cm}$.

$\vec{a}, \vec{b}, \vec{c}$ are vectors such that $|\vec{a}| = 5, |\vec{b}| = 4, |\vec{c}| = 3$ and each is perpendicular to the sum of the other two, then $|\vec{a} + \vec{b} + \vec{c}|^2 = $

Evaluate: $\sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3})$

The p.m.f. of a random variable $X$ is $P(X = x) = \frac{1}{2^5} \binom{5}{x}, x = 0, 1, 2, 3, 4, 5$, then

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $x_0$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $Kx_0$, then K =

If $\int_0^{\frac{\pi}{2}} \frac{dx}{5+4\sin x} = A \tan^{-1} B$, then A + B =

If $X \sim B(4, p)$ and $P(X = 0) = \frac{16}{81}$, then $P(X = 4) =$

If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle, then the radius of the circle is

If $h(x)=\sqrt{4 f(x)+3 g(x)}$, $f(1)=4$, $g(1)=3$, $f^{\prime}(1)=3$, $g^{\prime}(1)=4$, then $h^{\prime}(1)=$

If $x = a \cos \theta$, $y = b \sin \theta$, then $\left[\frac{d^2 y}{d x^2}\right] = $

If the line $\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$ lies in the plane $3x-14y+6z+49=0$, then the value of $m$ is

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$, where $-1 \leq x \leq 1$, then $x =$

If $x \in \left(0, \frac{\pi}{2}\right)$ and $x$ satisfies the equation $\sin x \cos x = \frac{1}{4}$, then the values of $x$ are

$\int \frac{x+\sin x}{1+\cos x} d x=$