List of top Mathematics Questions asked in MHT CET

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

The area of the region bounded by the curve \( y = 4x^3 - 6x^2 + 4x + 1 \) and the lines \( x = 1, x = 5 \) and the X axis is

If \[ \sin \theta = \frac{-12}{13}, \quad \cos \phi = \frac{-4}{5}, \quad \text{and} \quad \theta, \phi \text{ lie in the third quadrant, then } \tan(\theta - \phi) = \]

The length of the latus rectum of the parabola whose focus is at \( (1,-2) \) and directrix is the line \( x + y + 3 = 0 \) is

Solution of the differential equation \[ \frac{dy}{dx} + 2y = e^{-x} \text{ is:} \]

If \[ \tan^{-1} x + \tan^{-1} y = c \text{ is the general solution of the differential equation} \]

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

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

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

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

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 $\tan x=$

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

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

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

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

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

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290K and the metal temperature drops from 370K to 330K in 10 minutes, then the time required to drop the temperature up to 295K is

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

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