List of top Questions asked in MHT CET- 2021

A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube = $1\text{ cm}$, $\eta = 1 \times 10^{-3}\text{ Ns/m}^2$, $R_n = 2500$ and density of water = $10^3\text{ kg/m}^3$]

The radii of curvature of both the surfaces of a convex lens of focal length $f$ and focal power $P$ are equal. One of the surfaces is made plane by grinding. The new focal length and focal power of the lens is respectively

A glass slab has refractive index $\mu$ with respect to air and the critical angle for a ray of light in going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, then the corresponding angle of refraction is

Two identical springs of constant $K$ are connected in series and parallel in shown in figure. A mass $M$ is suspended from them. The ratio of their frequencies is series to parallel combination will be

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?

If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height, then the satellite will

Two identical particles each of mass $m$ are separated by a distance $d$. The axis of rotation passes through the midpoint of $d$ and is perpendicular to the length $d$. If $K$ is the average rotational kinetic energy of the system, then the angular frequency is

The common region of the solutions of the inequations $x + 2y \ge 4$, $2x - y \le 6$ and $x, y > 0$ is

If $\int \frac{\cos x - \sin x}{8 - \sin 2x} \, dx = \frac{1}{p} \log \left[ \frac{3 + \sin x + \cos x}{3 - \sin x - \cos x} \right] + c$, then $p = $

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & a \\ 2 & 4 & 7 \end{bmatrix}$ and $B = \begin{bmatrix} 13 & 2 & b \\ -3 & -1 & 2 \\ -2 & 0 & 1 \end{bmatrix}$ where matrix $B$ is the inverse of matrix $A$, then the values of $a$ and $b$ are

For a $3 \times 3$ matrix $A$, if $A(\operatorname{adj}A) = \begin{bmatrix} -10 & 0 & 0 \\ 0 & -10 & 0 \\ 0 & 0 & -10 \end{bmatrix}$, then the value of the determinant of $A$ is

A die is thrown four times. The probability of getting a perfect square in at least one throw is

In any $\triangle ABC$, with usual notations, $c(a \cos B - b \cos A) = $

The differential equation of the family of parabolas with focus at the origin and the $X$-axis as its axis, is

If in a $\triangle ABC$, with usual notations, $a^2$, $b^2$, $c^2$ are in A.P., then $\frac{\sin 3B}{\sin B} = $

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

If $A = (-2, 2, 3)$, $B = (3, 2, 2)$, $C = (4, -3, 5)$, and $D = (7, -5, -1)$, then the projection of $\vec{AB}$ on $\vec{CD}$ is

If $A = \begin{bmatrix} 2 & -2 \\ 2 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$, then $(B^{-1}A^{-1})^{-1} = $

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

The probability distribution of a discrete random variable $X$ is given as

Find the value of $P(2 < X < 6)$.

The area bounded by the lines $y = x$, $x = -1$, $x = 2$ and the $X$-axis is

If $|\vec{a}| = 4$, $|\vec{b}| = 5$, then the values of $k$ for which $\vec{a} + k\vec{b}$ is perpendicular to $\vec{a} - k\vec{b}$ are

If $p$ : It is raining and $q$ : It is pleasant, then the symbolic form of "It is neither raining nor pleasant" is

If $\int \frac{dx}{32 - 2x^2} = A \log|4 - x| + B \log|4 + x| + c$, then the values of $A$ and $B$ are respectively

If $A$ and $B$ are the foot of the perpendicular drawn from the point $Q(a, b, c)$ to the planes $YZ$ and $ZX$ respectively, then the equation of the plane through the points $A$, $B$, and the origin $O$ is