List of top Questions asked in MHT CET- 2020

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

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

The bacteria increases at the rate proportional to the number of bacteria present. If the original number $N$ doubles in $4$ hours, then the number of bacteria in $12$ hours will be

Evaluate the following product: \[ \tan 1^\circ \times \tan 2^\circ \times \tan 3^\circ \times \cdots \times \tan 89^\circ \]

The shortest distance between the lines \( 1 + x = 2y = -12z \) and \( x = y + 2 = 6z - 6 \) is

If \( \tan \theta + \sin \theta = a \) and \( \tan \theta - \sin \theta = b \), then the values of \( \cot \theta \) and \( \csc \theta \) are respectively:

If \( \int_{0}^{1} (5x^2 - 3x + k) \, dx = 0 \), then \( k = \)

The eccentricity of the ellipse given by the equation \[ 9x^2 + 16y^2 = 144 \] 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

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

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

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

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

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

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

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

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

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

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 \( SP \cdot SP' = \)

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

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

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