List of top Mathematics Questions asked in MHT CET

If \( y = e^{4x}\cos 5x \), then find \( \dfrac{d^2y}{dx^2} \) at \( x = 0 \).

If \( x = a(1 - \cos\theta) \), \( y = a(\theta - \sin\theta) \), then \( \frac{d^2y}{dx^2} = \)

If \( a \), \( b \), \( c \) are non-negative distinct numbers and \( ai + aj + ck \), \( i + j + k \), and \( ci + cj + bk \) are coplanar vectors, then

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

Evaluate \[ \sec 2\theta - \tan 2\theta = \]

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 \( \sin x + \sin^2 x = 1 \), then \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) is

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

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

If \[ f(x)=\frac{(e^{2x}-1)\sin x^\circ}{x^2}, \quad x\neq0 \] is continuous at \(x=0\), then \(f(0)=\)

If \( P(\theta) \) lies on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and \( S \) and \( S' \) are foci of the hyperbola, then \( SP \cdot SP' = \)

The function \[ f(x) = \frac{x + 1}{9x + x^3} \] is

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

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

The area bounded by the circle \(x^2 + y^2 = 16\) and the lines \(x = 0\) and \(x = 2\) is

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

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

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

If $x^2+y^2=t+\dfrac{1}{t}$ and $x^4+y^4=t^2+\dfrac{1}{t^2}$, then $\dfrac{dy}{dx}=$