List of top Mathematics Questions asked in MHT CET

The integral \[ \int_0^{\frac{\pi}{2}} \log \left( \frac{\sqrt{1 - \cos 2x}}{\sqrt{1 + \cos 2x}} \right) dx \] is

The differential equation of the circles having their centres on the line $y = 8$ and touching the $x$-axis is

The distance of the point $(1,2,-1)$ from the plane $x-2y+4z+10=0$ is

If \( \sin(x + y) + \cos(x + y) = \sin \left[ \cos^{-1} \left( \frac{1}{3} \right) \right] \), then \[ \frac{dy}{dx} = \]

The value of \( \int_{2}^{3} \frac{x}{x^2 - 1} \, dx \) is

The equation of a line passing through the point \( (2, 4, 6) \) and parallel to the line \[ 3x + 4 = 4y - 1 = 1 - 4z \] is

If \( A = \left[ \begin{array}{cc} 1 & -1 \\ 7 & 0 \end{array} \right] \), \( |A| = \left| \begin{array}{cc} 1 & 0 \\ 1 & 1 \end{array} \right| \), and \( A^2 = 8A + kI \), then the value of \( k \) is

Evaluate \[ \tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A = \]

If \( A=\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix} \) and \( B=\begin{bmatrix}2 & -3 \\-1 & 2\end{bmatrix} \), then \( (B^{-1}A^{-1})^{-1} \) is

If \( \mathbf{a} = 2\hat{i} - \hat{j} + \hat{k} \), \( \mathbf{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), and \( \mathbf{c} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) are coplanar, then \( \lambda \) is the root of the equation

In a box containing 100 bulbs, 10 are defective. The probability that out of 20 bulbs selected at random, none is defective is

Evaluate \( \sin 690^\circ \times \sec 240^\circ \)

If \( f(x) = \log(\sin x) \), \( x \in \left[ \frac{\pi}{6}, \frac{5\pi}{6} \right] \), then the value of \( c \) by applying L.M.V.T. is

If a function $f:\mathbb{R} \to \mathbb{R}$ is defined by $f(x) = \dfrac{4x}{5} + 3$, then $f^{-1}(x) =$

Evaluate \[ \int \frac{5^x}{\sqrt{5^{-2x}} - 5^{2x}}\,dx \]

Evaluate \( \int_{-2}^{1} \left[ x + 1 \right] \, dx \), where \( [x] \) is the greatest integer function not greater than \( x \)

If the line \( 6x - y - 4 = 0 \) touches the curve \( y^2 = ax^3 + b \) at the point (1, 2), then \( a + b = \)

Evaluate the integral: \[ \int_{-5}^{5} \frac{e^x + e^{-x}}{e^x - e^{-x}} \, dx. \]

If \[ f(x) = \begin{cases} 6\beta - 3x, & \text{if } -4 \leq x<-2,
4x + 1, & \text{if } -2 \leq x \leq 2, \end{cases} \] is continuous on \( [-4, 2] \), then \( \alpha + \beta = \)

The coordinates of the point where the line $\dfrac{x-1}{2}=\dfrac{y-2}{-3}=\dfrac{z+3}{4}$ meets the plane $2x+4y-z=1$ are

Evaluate \( \int_0^{\frac{\pi}{2}} \left( e^{\sin x} - e^{\cos x} \right) \, dx \)

If \( f(x) = 2x^2 + bx + c \), \( f(0) = 3 \) and \( f(2) = 1 \), then \( (f \circ f)(1) = \)

Evaluate $\displaystyle \int_{0}^{1} x(1-x)^5 \, dx$

If \[ \int \sqrt{x - 1} \left( \frac{x^2 + 1}{x^2} \right) dx = \frac{2}{3} (x - 1)^k + c, \quad \text{then the value of } k \text{ is} \]

For a sequence if \( S_n = \dfrac{5^n - 2^n}{2^n} \), then its fourth term is