List of top Mathematics Questions asked in MHT CET

The circumcenter of the triangle formed by lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is ______.

The area of smaller part between the circle $x^2 + y^2 = 4$ and the line $x = 1$ is ______ sq. units.

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

The least distance of the point A(10, 7) from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is length of seg AM. If MM' is the diameter of the circle, then the lengths of AM and AM' are respectively ______, ______ units.

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 ______.

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

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

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 ______.

In a triangle ABC, with usual notations, if $a = 5$, $b = 7$, $\sin A = \frac{3}{4}$, then total number of triangles possible are ______.

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 ______.

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 ______.

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

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be vectors of magnitude 2, 3 and 4 respectively. If $\vec{a} \cdot (\vec{b} + \vec{c}) = 0$, $\vec{b} \cdot (\vec{c} + \vec{a}) = 0$ and $\vec{c} \cdot (\vec{a} + \vec{b}) = 0$, then the magnitude of $\vec{a} + \vec{b} + \vec{c}$ is ______.

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 ______.

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 ______.

The modulus of the square root of the complex number $6 + 8i$ (where $i = \sqrt{-1}$) is ______.

If $\tan(\pi \cos \theta) = \cot(\pi \sin \theta)$, then $\sin\left(\frac{\pi}{4} + \theta\right) = $ ______.

If $\int \frac{(x^4+1)}{x(x^2+1)^2} \, dx = A \log |x| + \frac{B}{1+x^2} + c$, then $A - B$ is ______.

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

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 ______.

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 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 ______.

Let $\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}$, $\vec{b} = 3\hat{i} - \hat{j} + \beta\hat{k}$ and $\vec{c} = \hat{i} + 2\hat{j} - 2\hat{k}$ where $\alpha, \beta \in \mathbb{R}$, be three vectors. If the projection of $\vec{a}$ on $\vec{c}$ is $\frac{10}{3}$ and $\vec{b} \times \vec{c} = -6\hat{i} + 10\hat{j} + 7\hat{k}$, then the value of $(\alpha + \beta)$ is ______.

If \(A = \left[ \begin{array}{cc} 1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1 \end{array} \right]\) then \(A^{-1} =\)

The distance between the lines represented by \[ 16x^2 + 9y^2 + 48x - 24xy - 36y + 35 = 0 \] is ......... units