List of top Questions asked in MHT CET

A projectile is thrown with an initial velocity $(a \hat{i}+b \hat{j}) \text{ m/s}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, then
A uniform rope of length $12\text{ m}$ and mass $6\text{ kg}$ hangs vertically from a rigid support. A block of mass $2\text{ kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\text{ m}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is
For a two input AND gate, the four entries are shown in the truth table. Identify the correct ones out of these ($A$, $B = $ input, $Y = $ output)

Choose the correct answer from the options given below
For an ideal gas, $R = \frac{2}{3} C_v$. This suggests that the gas consists of molecules, which are ($R = $ universal gas constant)
A circuit containing resistance $R_1$, inductance $L_1$ and capacitance $C_1$ connected in series resonates at the same frequency $f_0$ as another circuit containing $R_2$, $L_2$ and $C_2$ in series. If two circuits are connected in series then the new frequency at resonance is
If the potential difference across a capacitor is increased from $5 \text{ V}$ to $15 \text{ V}$, then the ratio of final energy to initial energy stored in the capacitor is
A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is
An object executes SHM along $x$-axis with amplitude $0.06 \text{ m}$. At certain distance $x$ metre from mean position, it has kinetic energy $10 \text{ J}$ and potential energy $8 \text{ J}$. The distance $x$ will be
Three charges $-q$, $Q$ and $-q$ are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero then the ratio $\frac{Q}{q}$ is
In photoelectric effect, the photo current
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)
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 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
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 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
For all real $x$, the minimum value of the function $f(x) = \frac{1 - x + x^2}{1 + x + x^2}$ 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
The area of the triangle ABC is $10\sqrt{3}\ \text{cm}^2$, angle B is $60^\circ$ and its perimeter is $20\ \text{cm}$, then $\ell(\text{AC}) =$
Evaluate the indefinite integral $$\int \frac{dx}{\cos x \sqrt{\cos 2x}}$$
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 $h^2 : ab =$
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