List of top Questions asked in MHT CET- 2021

A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is

de-Broglie wavelength associated with an electron accelerated through a potential difference $V$ is $\lambda$. When the accelerating potential is increased to $4V$, the de-Broglie wavelength

Two positive ions, each carrying a charge $q$ are separated by a distance $d$. If $F$ is the force of repulsion between the ions, the number of electrons missing from each ion will be ($\varepsilon_0$ = permittivity of free space, $e$ = charge on an electron)

A metre scale is supported on a wedge at its centre of gravity. A body of weight $w$ is suspended from the $20 \text{ cm}$ mark and another weight of $25 \text{ gram}$ is suspended from the $74 \text{ cm}$ mark to balance it and the metre scale remains perfectly horizontal. Neglecting the weight of the metre scale, the weight of the body is

A bob of simple pendulum of mass $m$ performs SHM with amplitude $A$ and period $T$. Kinetic energy of pendulum at displacement $x = \frac{A}{2}$ will be

When the temperature of a semiconductor is increased, its resistance and electric conductivity respectively

Two circular loops P and Q are made from a uniform wire. The radii of P and Q are $R_1$ and $R_2$ respectively. The moments of inertia about their own central axis are $I_P$ and $I_Q$ respectively. If $\frac{I_P}{I_Q} = \frac{1}{8}$ then the ratio $\frac{R_2}{R_1}$ is

A glass rod of radius $r_1$ is inserted symmetrically into a vertical capillary tube of radius $r_2$ ($r_1 < r_2$) such that their lower ends are at the same level. The arrangement is dipped in water. The height to which water will rise into the tube will be ($\rho$ = density of water, $T$ = surface tension in water, $g$ = acceleration due to gravity)

An electron in a circular orbit of radius $0.05 \text{ nm}$ performs $10^{14}$ revolutions/second. What is the magnetic moment due to the rotation of electron? ($e = 1.6 \times 10^{-19} \text{ C}$)

If the function defined by $f(x) = K(x - x^2)$ if $0 < x < 1$ and $f(x) = 0$ otherwise, is the probability density function (p.d.f.) of a random variable X, then the value of $P\left(X < \frac{1}{2}\right)$ is

The moment of inertia of a body about the given axis, rotating with angular velocity $1 \text{ rad/s}$ is numerically equal to 'P' times its rotational kinetic energy. The value of 'P' is

For all real $x$, the minimum value of the function $f(x) = \frac{1 - x + x^2}{1 + x + x^2}$ is

If the slopes of the lines given by the equation $ax^2 + 2hxy + by^2 = 0$ are in the ratio $5 : 3$, then the ratio $h^2 : ab =$

Evaluate the indefinite integral $$\int \frac{dx}{\cos x \sqrt{\cos 2x}}$$

The derivative of the function $\cot^{-1}\left[(\cos 2x)^{1/3}\right]$ at $x = \frac{\pi}{6}$ is

With usual notations in $\triangle \text{ABC}$, if $\frac{\sin \text{A}}{\sin \text{C}} = \frac{\sin(\text{A} - \text{B})}{\sin(\text{B} - \text{C})}$, then $a^2, b^2, c^2$ are in

The domain of the function $\log_{10}(x^2 - 5x + 6)$ is

If $\vec{a} = 2\hat{\text{i}} - \hat{\text{j}} + \hat{\text{k}}$, $\vec{b} = \hat{\text{i}} + 2\hat{\text{j}} - 3\hat{\text{k}}$ and $\vec{c} = 3\hat{\text{i}} + \lambda\hat{\text{j}} + 5\hat{\text{k}}$ are coplanar, then $\lambda$ is the root of the equation

The general solution of the differential equation $\cos(x + y) \frac{dy}{dx} = 1$ is

The equation of the tangent to the curve $y = \sqrt{2} \sin\left(2x + \frac{\pi}{4}\right)$ at $x = \frac{\pi}{4}$ is

If $\int \frac{\sqrt{x}}{x(x+1)} \, dx = k \tan^{-1} m + c$ (where $c$ is a constant of integration), then

Let two cards be drawn at random from a pack of 52 playing cards. Let X be the number of aces obtained. Then the value of E(X) is

Evaluate the definite integral $$\int_{1}^{3} \left[ \tan^{-1}\left(\frac{x}{x^2-1}\right) + \tan^{-1}\left(\frac{x^2-1}{x}\right) \right] dx$$

The order and degree of the differential equation $$\frac{d^2y}{dx^2} = \sqrt{\frac{dy}{dx}}$$ are respectively

A fair coin is tossed 100 times. The probability of getting a head for an even number of times is