List of top Mathematics Questions asked in MHT CET

The value of $\lim_{x \to 0} \frac{\cos(mx) - \cos(nx)}{x^2}$ is

Area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is

A rectangle of maximum area is inscribed in an ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$, then its dimensions are

The Cartesian equation of a line is $3x + 1 = 6y - 2 = 1 - z$, then its vector equation is

Solution of the differential equation $y' = \frac{x^2+y^2}{xy}$, where $y(1) = -2$ is given by

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{bmatrix}$, then the value of the determinant of $A^{-1}$ is

The value of $\int e^x \left(\frac{x - 1}{x^2}\right) dx =$

The position vector of the point of intersection of the medians of a triangle, whose vertices are $A(1, 2, 3)$, $B(1, 0, 3)$ and $C(4, 1, -3)$ is

The value of $\int_{-\pi}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx =$

The general solution of $\sin^{-1}\left(\frac{dy}{dx}\right) = x + y$ is

$\tan 3A \cdot \tan 2A \cdot \tan A =$

In $\triangle ABC$, with usual notations, $2ab \sin \frac{1}{2}(A+B-C) =$

If the slope of one of the lines $ax^2 + 2hxy + by^2 = 0$ is twice that of the other, then $h^2 : ab$ is

If statements $p$ and $q$ are true and $r$ and $s$ are false, then truth values of $\sim ( p \rightarrow q ) \leftrightarrow ( r \wedge s )$ and $( \sim p \rightarrow q ) \wedge ( r \leftrightarrow s )$ are respectively

Let $$\begin{array}{ll} f(x) = |x| + 3, & \text{if } x \le -3 \\ f(x) = -2x, & \text{if } -3 < x < 3 \\ f(x) = 6x - 2, & \text{if } x \ge 3 \end{array}$$ then

The equation of a circle that passes through the origin and cut off intercepts $-2$ and $3$ on the X-axis and Y-axis respectively is

The particular solution of the differential equation $y(1+\log x) = \left(\log x^x\right)\frac{dy}{dx}$, when $y(e) = e^2$ is

If $y^2 = ax^2 + bx + c$, where $a, b, c$ are constants, then $y^3 \frac{d^2y}{dx^2}$ is equal to

Let $a : \sim(p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false, then the truth values of $a$ and $b$ are respectively

If $$\int_{0}^{a} \sqrt{\frac{a-x}{x}} \, dx = \frac{k}{2}$$ then $k =$

If $f(x) = [8x] - 3$, where $[x]$ is the greatest integer function of $x$, then $f(\pi) =$ (where $\pi = 3.14$)

The slant height of a right circular cone is $\sqrt{3}\text{ cm}$. The height of the cone for maximum volume is

$$\int \cos^{-1} x \, dx =$$

$$\int \frac{1}{\cos x + \sqrt{3}\sin x} \, dx =$$

If $\omega$ is the complex cube root of unity, then $(3 + 5\omega + 3\omega^2)^2 + (3 + 3\omega + 5\omega^2)^2 =$