List of top Mathematics Questions asked in MHT CET

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 differential equation which represents the family of curves $y = c_1 e^{c_2 x}$, where $c_1, c_2$ are arbitrary constants 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 general solution of the differential equation $\frac{dy}{dx} = \cot x \cdot \cot y$ is ______.

The angle between the tangents drawn from the point (1, 4) to the parabola $y^2 = 4x$, is ______.

The equation of the directrix of the parabola $y^2 + 4y + 4x + 2 = 0$ is ______.

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three coplanar vectors such that $|\vec{a}| = 1$, $|\vec{b}| = 2$, $\vec{b} \cdot \vec{c} = 8$, the angle between $\vec{b}$ and $\vec{c}$ is $45^\circ$, then $|\vec{a} \times (\vec{b} \times \vec{c})| = $ ______.

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 $\sin^{-1}(4x) + \sin^{-1}(4\sqrt{3}x) = -\frac{\pi}{2}$, then the value of $x$ is ______.

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

The line MN whose equation is $x - y - 2 = 0$ cuts the X-axis at M and coordinates of N are (4, 2). The line MN is rotated about M through $45^{\circ}$ in anticlockwise direction. The equation of the line MN in the new position is ______.

The solution for minimizing the function $z = x + y$ under an L.P.P. with constraints $x + y \ge 2$, $x + 2y \le 8$, $y \le 3$, $x, y \ge 0$ is ______.

If $f(x) = \frac{\cos ax - \cos bx}{\cos cx - \cos bx}$ for $x \ne 0$ and $f(0) = -1$ is continuous at $x = 0$, then $a^2, b^2, c^2$ are in ______.

The probability that a person is not a sportsperson is $1/6$. Then the probability that out of 6 members of the family, 5 are sportspersons is ______.

A manufacturer sells $x$ items at a price of ₹$(6 - \frac{x}{40})$ each. The cost price of $x$ items is ₹$(\frac{x}{5} + 193)$. The maximum profit in ₹ is ______.

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

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) = $ ______.

A triangle ABC is formed by A(1, -1, 0), B(3, 5, 3), C(-11, -5, 6). The equation of the internal angle bisector of angle A is ______.

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 ______.

If $f(x) = \sqrt{1 + \cos^2(x^2)}$, then $f'(\frac{\sqrt{\pi}}{2})$ is ______.

If the foot of the perpendicular drawn from the origin to a plane is P(-1, -1, 2), then the equation of the plane is ______.

The angle between lines whose direction cosines satisfy the equation $l + m + n = 0$ and $l^2 - m^2 - n^2 = 0$, is ______.

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

$\int_0^1 \tan^{-1} x \, dx = $ ______.

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.