List of top Mathematics Questions asked in MHT CET

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 $\tan x=$

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

Evaluate the integral \[ \int \frac{\sin 2x}{\sin^2 x \cos^2 x}\, dx \]

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

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

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 \(k+2=\)

If two angles of \( \triangle ABC \) are \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \), then the ratio of the smallest and greatest side is

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 \( k = \)

If the acute angle between the lines \[ x^2-4xy+y^2=0 \] is \(\tan^{-1}(k)\), then \(k=\)

Evaluate: \[ \cos x \cos 7x - \cos 5x \cos 13x \]

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

If the angle between the lines given by the equation \[ x^2 - 3xy + Ay^2 + 3x - 5y + 2 = 0, \quad \lambda \geq 0, \quad \text{is} \, \tan^{-1} \left( \frac{1}{3} \right), \, \text{then} \, \lambda = \]

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 value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{5} \right) + \tan^{-1} \left( \frac{1}{7} \right) + \tan^{-1} \left( \frac{1}{8} \right) \] is

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

The radius of the circle passing through the points \[ (5, 7), \quad (2, -2), \quad (-2, 0) \] is

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

If the vectors \( i + j + k \), \( i - j + k \) and \( 2i + 3j + mk \) are coplanar, then \( m = \)

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