List of top Mathematics Questions asked in MHT CET

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 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 ______.

In a triangle ABC, with usual notations, if $a = 5$, $b = 7$, $\sin A = \frac{3}{4}$, then total number of triangles possible 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 $f(x) = \sqrt{1 + \cos^2(x^2)}$, then $f'(\frac{\sqrt{\pi}}{2})$ is ______.

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

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

If $[x]^2 - 5[x] + 6 = 0$, where $[.]$ denotes the greatest integer function, then ______.

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

If the truth value of the expression $[(p \vee q) \wedge (q \to r) \wedge (\sim r)] \to (p \wedge q)$ is False, then truth values of p, q, r are respectively ______.

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

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

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 ______.

In a triangle ABC, with usual notations, $\cot\left(\frac{A+B}{2}\right) \cdot \tan\left(\frac{A-B}{2}\right) = $ ______.

In a triangle ABC, with usual notations, $(a + b + c)(a + b - c) = 3ab$, then $\angle C = $ ______.

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 ______.

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})| = $ ______.

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 ______.

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

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

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

If $\vec{a} = \lambda x \hat{i} + y \hat{j} + 4z \hat{k}$, $\vec{b} = x \hat{i} + y \hat{j} + 3y \hat{k}$, and $\vec{c} = -2 \hat{i} - 2z \hat{j} - (\lambda + 1) \hat{k}$ such that $\vec{a} + \vec{b} - \vec{c} = \vec{0}$, then the value of $\lambda$ 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 ______.

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