List of top Questions asked in MHT CET- 2020

A pipe open at both ends has length 1 m. The air column in the pipe cannot resonate for a frequency (Neglect end correction, speed of sound in air = 340 m/s)

The period of seconds pendulum on a planet, whose mass and radius are three times that of earth, is

If three vectors have equal magnitude i.e. $A = B = C$, then the angle between $\vec{A$ and $\vec{C}$ is $\alpha$. If $\vec{A} + \vec{B} + \vec{C} = 0$, then the angle between $\vec{A}$ and $\vec{C}$ is $\beta$, then $\dfrac{\alpha}{\beta}$ is}

If the Cartesian equation of the line is \[ x - 1 = 2y + 3 = 3 - z, \] then its vector equation is

The line through the points \( (1, 4), (-5, 1) \) intersects the line \( 4x + 3y - 5 = 0 \) in the point

Which of the following matrix is invertible?
\[ A_1 = \begin{pmatrix} 4 & 2 \\ 2 & 1 \end{pmatrix} \] \[ A_2 = \begin{pmatrix} -1 & -2 & 3 \\ 4 & 5 & 7 \\ 2 & 4 & -6 \end{pmatrix} \] \[ A_3 = \begin{pmatrix} 1 & 0 & 0 \\ 5 & 2 & 1 \\ 7 & 2 & 1 \end{pmatrix} \] \[ A_4 = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{pmatrix} \]

The parametric equations of the line passing through \( A(3, 4, -7) \), \( B(1, -1, 6) \) are

A bus is moving with a velocity of 5 m/s towards a wall. The driver blows the horn of frequency 165 Hz. If the speed of sound in air is 335 m/s, then after reflection of the sound wave, the number of beats per second heard by the passengers in the bus will be

A graph of magnetic flux ($\phi$) versus current ($I$) is shown for four inductors A, B, C and D. Larger value of self-inductance is for inductor

With usual notations, in \( \triangle ABC \), if \( a = 2 \), \( b = 3 \), \( c = 5 \) and \[ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = \frac{k}{7} + \frac{30}{30}, \] then \( k = \)

Evaluate the integral: \[ \int e^{\cos^{-1}x} \left[ x - \sqrt{1 - x^2} \right] \frac{dx}{\sqrt{1 - x^2}}. \]

If \[ |3x - 2| \leq \frac{1}{2}, \] then \( x \in \)

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

Evaluate the integral: \[ \int \frac{dx}{\cos x \sqrt{\cos 2x}}. \]

A random variable \( X \) takes the values 0, 1, 2. Its mean is 1.2. If \( P(X = 0) = 0.3 \), then \( P(X = 1) = \)

If the equation \[ x^2 - 3xy + y^2 + 3x - 5y + 2 = 0 \] represents a pair of lines, where \( \theta \) is the angle between them, then the value of \( \csc^2 \theta \) is

The rate of growth of bacteria is proportional to the number present. If initially there were 1000 bacteria and the number doubles in 1 hour, then the number of bacteria after \( 2\frac{1}{2} \) hours are (Given \( \sqrt{2} = 1.414 \))

The probability that a person wins a prize on a lottery ticket is \( \frac{1}{4} \). If he purchases 5 lottery tickets at random, then the probability that he wins at least one prize is

Evaluate the integral: \[ \int_{-5}^{5} \frac{e^x + e^{-x}}{e^x - e^{-x}} \, dx. \]

If \[ O = (0, 0, 0), \quad P = (1, \sqrt{2}, 1), \] then the acute angles made by the line OP with the \( XOY, \, YOZ, \, ZOX \text{ planes are, respectively,} \)

The equation of a plane containing the point \( (1, -1, 1) \) and parallel to the plane \[ 2x + 3y - 4z = 17 \text{ is} \]

The angle between the line \[ \frac{x - 1}{2} = \frac{y + 3}{1} = \frac{z + 7}{2} \] and the plane \[ \mathbf{r} \cdot (6\hat{i} - 2\hat{j} - 3\hat{k}) = 5 \] is

The Cartesian equation of the curve given by \[ x = 6 \cos \theta, \quad y = 6 \sin \theta \] is

The auxiliary equation of the lines passing through the origin and having slopes \[ \sqrt{3} + 1 \quad \text{and} \quad \sqrt{3} - 1 \quad \text{is} \]

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