List of top Questions asked in MHT CET- 2020

If $\displaystyle \int_{1}^{k} (3x^2 + 2x + 1)\,dx = 11$, then $k =$

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

The length of the perpendicular from the point \( P(a,b) \) to the line \( \dfrac{x}{a} + \dfrac{y}{b} = 1 \) is

The logical expression \( [p \wedge (q \vee r)] \vee [\neg r \wedge \neg q \wedge p] \) is equivalent to

Evaluate \[ \int \frac{\log x - 1}{1 + (\log x)^2} \, dx \]

Find the value of the following expression:
\[ 5^2 + 6^2 + 7^2 + \cdots + 20^2 = \]

The cumulative distribution function of a continuous random variable \( X \) is given by \( F(X = x) = \dfrac{\sqrt{x}}{2} \). Then \( P(X>1) \) is

The particular solution of the differential equation \[ \left( y + x \frac{dy}{dx} \right) \sin y = \cos x \quad \text{at} \quad x = 0 \, \text{is:} \]

A body is heated to $110^\circ$C and placed in air at $10^\circ$C. After $1$ hour its temperature is $60^\circ$C. The additional time required for it to cool to $30^\circ$C is

If the points \( (1, 1, \lambda) \) and \( (-3, 0, 1) \) are equidistant from the plane \( 3x + 4y - 12z + 13 = 0 \), then the integer value of \( \lambda \) 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 \(k+2=\)

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

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

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

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

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 $\tan x=$

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

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

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

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

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