List of top Questions asked in MHT CET

The solution of the differential equation \[ x^2 \frac{dy}{dx} = y^2 + xy \]

The differential equation of the family of lines having \(x\)-intercept \(a\) and \(y\)-intercept \(b\) is

The integrating factor of the differential equation $(1 + y + x^2y)\,dx + (x + x^3)\,dy = 0$ is

If \( p, q \) are true statements and \( r \) is a false statement, then which of the following statements is a true statement?

The maximum value of \( z = 3x + 5y \), subject to \( 3x + 2y \leq 18 \), \( x \leq 4 \), \( y \leq 6 \), \( x, y \geq 0 \) is

The order and degree of the differential equation \[ \left[ 1 + \left( \frac{dy}{dx} \right)^3 \right]^{\frac{3}{2}} = 7 \frac{d^2y}{dx^2} \] are respectively

If \( x = 3 \sin \theta \), \( y = 3 \cos \theta \cos \phi \), \( z = 3 \cos \theta \sin \phi \), then \( x^2 + y^2 + z^2 = \)

If the lines \[ \frac{1-x}{2} = \frac{y-8}{\lambda} = \frac{z-5}{2} \quad \text{and} \quad \frac{x-11}{5} = \frac{y-3}{3} = \frac{z-1}{1} \] are perpendicular, then \(\lambda =\)

If $3\sin^2x-8\sin x+4=0$, $x\in\left(\dfrac{\pi}{2},\pi\right)$, then $\tan x=$

In a single throw of three dice, the probability of getting a sum of at least 5 is

If the probability density function of a continuous random variable is \[ f(x) = \frac{x^3}{3} \quad \text{if} \quad -1<x<2, \quad f(x) = 0 \quad \text{otherwise}, \] then the cumulative distribution function of \( X \) is

With usual notations, in \( \triangle ABC \), if \( b\cos^2\frac{C}{2} + c\cos^2\frac{B}{2} = \frac{3a}{2} \), then

If \[ \cos x + \cos y = -\cos \alpha, \quad \sin x + \sin y = -\sin \alpha, \quad \text{then} \quad \cot \left( \frac{x + y}{2} \right) = \]

If the function \[ f(x)= \begin{cases} \dfrac{\log 10 + \log(0.1+2x)}{2x}, & x \neq 0 \\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then \(k+2=\)

The order and degree of the differential equation $\sqrt{1+\dfrac{1}{\left(\dfrac{dy}{dx}\right)^2}}=\left(\dfrac{d^2y}{dx^2}\right)^{\tfrac{3}{2}}$ are respectively

Evaluate \( \int \frac{dx}{\cos 2x + \sin^2 x} \)

If \(3\cos x \ne 2\sin x\), then the general solution of \[ \sin^2 x-\cos 2x=2-\sin 2x \] is

If \[ f(x) = \left[ \tan \left( \frac{\pi}{4} + x \right) \right]^{\frac{1}{x}} \quad \text{if} \quad x \neq 0 \] \[ f(x) = k \quad \text{if} \quad x = 0 \] is continuous at \( x = 0 \), then \( k = \)

The symbolic form of the following circuit is (where \( p, q \) represents switches \( s_1 \) and \( s_2 \) closed respectively)

The value of $\cos^{-1}\left(\cos\left(\frac{7\pi}{6}\right)\right)$ is

Simplify \( \sqrt{2} + \sqrt{2} + 2 \cos 4\theta = \)

A body cools according to Newton’s law from \(100^\circ\text{C}\) to \(60^\circ\text{C}\) in 20 minutes. The temperature of the surroundings being \(20^\circ\text{C}\), the temperature of the body after one hour is

The points of discontinuity of the function \[ f(x) = \begin{cases} \frac{1}{x - 1} & \text{if } 0 \leq x \leq 2 \\ \frac{x + 5}{x + 3} & \text{if } 2<x \leq 4 \end{cases} \] in its domain are

The integral \[ \int \cot x \cdot \log \left[ \log (\sin x) \right] \, dx = \]