List of top Mathematics Questions asked in MHT CET

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

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

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

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

$\vec{a}, \vec{b}, \vec{c}$ 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 = $

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 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

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

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 $6\ \text{cm}$.

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

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

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

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 $h^{\prime}(1)=$

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

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

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

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

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is

The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

If $\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$, then $f(x)=$

The value of $\sin 18^{\circ}$ is