List of top Questions asked in MHT CET- 2020

If the points \( A(5, k) \), \( B(-3, 1) \) and \( C(-7, -2) \) are collinear, then \( k = \)

If the A.M. and G.M. of the roots of a quadratic equation in \( x \) are \( p \) and \( q \) respectively, then its equation is

If $\vec a,\vec b,\vec c$ are nonzero vectors along the coterminous edges of a parallelepiped with volume $7$ cubic units, then the volume of the parallelepiped with $\vec a+\vec b,\ \vec b+\vec c,\ \vec c+\vec a$ as the coterminous edges is

Evaluate \( \int_0^{\frac{\pi}{2}} \sin^2 x \, dx \)

If \( A, B, C \) are angles of a triangle ABC, then \( \tan 2A + \tan 2B + \tan 2C = \)

If the body cools from \( 135^\circ C \) to \( 80^\circ C \) at room temperature of \( 25^\circ C \) in 60 minutes, then the temperature of the body after 2 hours is

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

If the length of perpendicular drawn from the point $(4,1)$ on the line $3x - 4y + k = 0$ is $2$ units, then the values of $k$ are

The equation of a line passing through the point of intersection of the lines \[ x + 2y + 8 = 0 \quad \text{and} \quad 3x - y + 4 = 0 \] and having x– and y–intercepts zero is

The domain of the function \( f(x) = \sqrt{x} \) is

If for an Arithmetic progression, 9 times the ninth term is equal to 13 times the thirteenth term, then the value of the twenty-second term is

For a sequence \( (t_n) \), if \( s_n = 7(3^n - 1) \), then \( t_n = \)

If for the harmonic progression, \( t_7 = \frac{1}{10}, \, t_{12} = \frac{1}{25}, \) then \( t_{20} = \)

The adjoint of the matrix \[ A = \begin{pmatrix} 2 & 3
-3 & 5 \end{pmatrix} \] is

Which of the following have the same value:
(a) \( \sin 120^\circ \)
(b) \( \cos 930^\circ \)
(c) \( \tan 840^\circ \)
(d) \( \cot(-1110^\circ) \)

If \( A \) and \( B \) are independent events such that odds in favour of \( A \) is 2:3 and odds against \( B \) is 4:5, then \( P(A \cap B) = \)

The entries in the last column of the truth table for \( \neg (p \wedge q) \) are

The equation of the plane passing through the points \( (2, 3, 1), (4, -5, 3) \) and parallel to the y-axis is

The probability that a bomb will miss the target is 0.2. Then the probability that out of 10 bombs dropped exactly 2 will hit the target is

The value of \( \sin^{-1} \left( -\frac{1}{2} \right) + \cos^{-1} \left( -\frac{\sqrt{3}}{2} \right) \) is

A ball falls in the downward direction from a height \( h \) with initial velocity \( V \). It collides with the ground, loses \( \frac{3}{4} \)th of energy and comes back to the same height. The initial velocity \( V \) is (g = acceleration due to gravity)

Which of the following elements is refined by zone refining?

In meter bridge experiment, null point was obtained at a distance \( f \) from left end. The values of resistances in the left and right gaps are doubled and then interchanged. The new position of null point is

Which one of the following shows interspecific competition?

______________ is obtained from fermented grains of mostly barley.