List of top Mathematics Questions asked in MHT CET

The following is p.d.f. of continuous random variable X: $f(x) = \frac{x}{8}$ for $0 < x < 4$. Then $F(0.5)$, $F(1.7)$ and $F(5)$ is respectively ______.

If $y = \alpha \log x + \beta x^2 - x$ has extreme values at $x = -1$ and $x = 1$, then $\alpha$ and $\beta$ are respectively ______.

The cumulative distribution function of a discrete random variable X is given. Then $\frac{P(X \le 0)}{P(X > 0)} = $ ______.

The mirror image of the point $P(-1, 2, -4)$ in the plane $x - y - 2z + 1 = 0$ is ______.

$\int_{1/2}^{2} \frac{1}{x} \csc^{101} \left( x - \frac{1}{x} \right) dx = $ ______.

The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is ______.

$\lim_{x \to \infty} \frac{(2x+1)^{50} + (2x+2)^{50} + (2x+3)^{50} + \dots + (2x+100)^{50}}{(2x)^{50} + (10)^{50}} = $ ______.

A box contains 8 red and $x$ number of green balls. 3 balls are drawn at random, if the probability that 3 balls being red is $\frac{7}{15}$, then number of green balls is ______.

The equation of a curve passing through (1,0) and having slope of tangent at any point (x, y) of the curve as $\frac{y-1}{x^2+x}$ is ______.

The differential equation which represents the family of curves $y = c_1 e^{c_2 x}$, where $c_1, c_2$ are arbitrary constants is ______.

If $\int \frac{dx}{x^4 + 5x^2 + 4} = A \tan^{-1} x + B \tan^{-1} \frac{x}{2} + c$ where $c$ is a constant of integration, then ______.

Matrix A is non-singular matrix and $(A - 3I)(A - 5I) = 0$, then $\frac{15}{8} A^{-1} = \dots\dots$

If $f(x) = \frac{\sin^2 x}{1+\cot x} + \frac{\cos^2 x}{1+\tan x}$, then the value of $f'(\frac{\pi}{6})$ is equal to ______.

$\int \frac{\sqrt{\tan x}{\sin x \cdot \cos x} \, dx = $ ______.

If the plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{6} = 1$ cuts the co-ordinate axes at points A, B, C respectively, then area of the triangle ABC is ______.

The number of positive integral solutions of $\tan^{-1} x + \cos^{-1} \left( \frac{y}{\sqrt{1+y^2}} \right) = \sin^{-1} \left( \frac{3}{\sqrt{10}} \right)$ are ______.

If $y = \tan^{-1} \left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right)$, $0 \le x < \frac{\pi}{2}$, then $y' \left( \frac{\pi}{6} \right) = $ ______.

The volume of tetrahedron with co-terminus edges $\vec{a}$, $\vec{b}$, $\vec{c}$ is $\frac{64}{3}$ cubic units, then volume of parallelopiped considering co-terminus edges given by the vectors $\vec{a} + \vec{b}$, $\vec{b} + \vec{c}$, $\vec{c} + \vec{a}$ is ______ cubic units.

Consider statements $p$ : $S_1$ is closed; $q$ : $S_2$ is closed; $r$ : $S_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively ______.

The equation of the tangent to $y=be^{-x/a}$ at the point where it crosses the Y axis is}

The equation of the plane passing through (1,1,1) and through the line of intersection of $x+2y-z+1=0$ and $3x-y-4z+3=0$ is

If $y=\tan^{-1}(\frac{1}{1+x+x^{2}})+\tan^{-1}(\frac{1}{x^{2}+3x+3})+\tan^{-1}(\frac{1}{x^{2}+5x+7})$ then $y^{\prime}(0)$ is}

If $f(x)=3x^{2}+2xf^{\prime}(1)+f^{\prime\prime}(2)$, then $f(x)=..........$

If $0\le x\le\pi$ and $81^{\sin^{2}x}+81^{\cos^{2}x}=30$ Then $x$ takes the value}

The unit vectors perpendicular to the plane determined by the points $A(1,-1,2)$, $B(2,0,-1)$, $C(0,2,1)$ is