List of top Questions asked in MHT CET- 2020

Simplify the expression \( \sin \left( \frac{\pi}{3} + x \right) - \cos \left( \frac{\pi}{6} + x \right) \)

The integral \[ \int_0^a \frac{x}{\sqrt{a - x}} \, dx = \]

If one of the lines given by \( kx^2 + xy - y^2 = 0 \) bisects the angle between the co-ordinate axes, then values of \( k \) are:

If \( Z = 7x + y \) subject to \[ 5x + y \geq 5, \quad x + y \geq 3, \quad x \geq 0, \quad y \geq 0, \quad \text{then the minimum value of } Z \text{ is} \]

The displacement of a particle at time \(t\) is \[ s = t^3 - 4t^2 - 5t \] Then the velocity of the particle at \(t = 2\) sec is

Which of the following functions is not a p.d.f. of a continuous random variable \( X \)? \[ F_1 \text{ given by} \quad f(x) = e^{-x} \quad \text{if} \quad x \geq 0, \quad f(x) = 0 \quad \text{otherwise}, \] \[ F_2 \text{ given by} \quad f(x) = \frac{1}{4} x^{-1/2} \quad \text{if} \quad 0 \leq x \leq 4, \quad f(x) = 0 \quad \text{otherwise}, \] \[ F_3 \text{ given by} \quad f(x) = 6x(1 - x) \quad \text{if} \quad 0 \leq x \leq 1, \quad f(x) = 0 \quad \text{otherwise}, \] \[ F_4 \text{ given by} \quad f(x) = \frac{x}{2} \quad \text{if} \quad -2 \leq x \leq 2, \quad f(x) = 0 \quad \text{otherwise}, \]

The area of the region bounded by the parabola \[ y^2 = 8x \quad \text{and its latus rectum is} \]

If \[ A=\begin{bmatrix} 1 & 2 & i\\ 1 & 1 & 1\\ 1 & 1 & 0 \end{bmatrix}, \] then \( [\operatorname{adj}(\operatorname{adj}A)]^{-1} \) is

Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin^{\frac{2}{3}} x}{\sin^{\frac{2}{3}} x + \cos^{\frac{2}{3}} x}\, dx \]

If the line \( \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \) is parallel to the plane \( \vec{r} = (3i - 2j - mk) = 5 \), then the value of \( m \) is

If the origin is the centroid of the triangle whose vertices are \( A(2, p, -3) \), \( B(q, -2, 5) \) and \( C(-5, 1, r) \), then

If the direction cosines of a line are \( \frac{1}{c}, \frac{1}{c}, \frac{1}{c} \), then

The eccentricity of the ellipse \[ y^2 + 4x^2 - 12x + 6y + 14 = 0 \] is

The area of the region bounded by the parabola $x^2=16y$, the lines $y=1$, $y=4$ and the $y$-axis lying in the first quadrant is

For the probability distribution of \( X \) given below, the variance of \( X \) is

Evaluate \( \int \frac{\cos \sqrt{x}}{\sqrt{x}} \, dx \)

In a certain culture of bacteria, the rate of increase is proportional to the number present. It is found that the number doubles in 4 hours. Then the number of times the bacteria are increased in 12 hours is

If \( P(A) = \frac{2}{5}, \, P(B) = \frac{1}{4}, \, P(A \cup B) = \frac{1}{2}, \) then \( P(A' \cup B') = \)

The probability that a person who undergoes a certain operation will survive is 0.2. If 5 patients undergo similar operations, find the probability that exactly four will survive.

If \[ A = \{2, 4\}, \quad B = \{3, 4, 5\}, \quad \text{then} \quad (A \cap B) \times (A \cup B) = \]

If the points $A(2,1,-1)$, $B(0,-1,0)$, $C(4,0,4)$ and $D(2,0,x)$ are coplanar, then $x=$

Evaluate \( \displaystyle \int_{-\pi}^{\pi} \frac{2x}{1+\cos^2 x}\,dx \)

If one of the lines given by the equation \( x^2 + kxy + 2y^2 = 0 \) is \( x + 2y = 0 \), then the value of \( k \) is

If \( x^2 + y^2 = 1 \), then find \( \dfrac{d^2x}{dy^2} \).

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sin x \cos x}{1 + \sin^4 x} \, dx = \]