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Physics - 3 — MH-CET Full Length Paper MCQs with Solutions

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Sample questions with solutions

Q1 — easy
The torque acting on a body rotating with constant angular momentum $L$ is:
A. $L \omega$
B. $\frac{dL}{dt} = 0$  ✓ Correct
C. $I \omega^2$
D. $\frac{1}{2}I\omega$
Solution: Torque $\tau = dL/dt$. If angular momentum $L$ is constant, $\tau = 0$
Q2 — easy
An open water tank has a small orifice located $5\text{ m}$ below the free surface of water. Taking $g = 10\text{ m/s}^2$, the velocity of efflux through the orifice is:
A. $5\text{ m/s}$
B. $10\text{ m/s}$  ✓ Correct
C. $15\text{ m/s}$
D. $20\text{ m/s}$
Solution: Torricelli's law: $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 5} = 10\text{ m/s}$
Q3 — easy
A small spherical ball of radius $r$ falling in a viscous liquid of coefficient of viscosity $\eta$ with velocity $v$ experiences a retarding viscous drag force equal to:
A. $6\pi\eta r v$  ✓ Correct
B. $6\pi\eta r^2 v$
C. $\frac{6\pi\eta v}{r}$
D. $4\pi\eta r v^2$
Solution: Stokes' law: the retarding viscous force on a sphere is $F_v = 6\pi\eta r v$
Q4 — easy
The angle of contact between pure water and clean glass is:
A. $0^\circ$  ✓ Correct
B. $90^\circ$
C. $135^\circ$
D. $180^\circ$
Solution: Pure water completely wets clean glass; hence the angle of contact is zero
Q5 — easy
If the temperature of an ideal black body is doubled from $300\text{ K}$ to $600\text{ K}$, the rate of radiant heat emission per unit area increases by a factor of:
A. 2
B. 4
C. 8
D. 16  ✓ Correct
Solution: Stefan-Boltzmann law: $E = \sigma T^4$. When $T$ doubles, power increases by $2^4 = 16$
Q6 — easy
The distance between two consecutive antinodes in a stationary wave of wavelength $\lambda$ is:
A. $\lambda$
B. $\lambda / 2$  ✓ Correct
C. $\lambda / 4$
D. $2\lambda$
Solution: Distance between successive antinodes (or nodes) in a stationary wave is $\lambda/2$
Q7 — easy
When an open organ pipe is sounded in its fundamental mode, the nature of stationary waves formed inside contains:
A. One node and two antinodes  ✓ Correct
B. Two nodes and one antinode
C. One node and one antinode
D. Two nodes and two antinodes
Solution: Open pipe: both ends are antinodes; the fundamental has two antinodes and one node between them
Q8 — easy
A completely unpolarized beam of light of intensity $I_0$ passes through an ideal Polaroid sheet. The intensity of the transmitted beam is:
A. $I_0$
B. $I_0 / 2$  ✓ Correct
C. $I_0 / 4$
D. Zero
Solution: Unpolarized light through an ideal Polaroid: transmitted intensity = $I_0/2$
Q9 — easy
The electrostatic potential energy stored in an electric dipole of moment $\vec{p}$ placed in a uniform electric field $\vec{E}$ at an angle $\theta$ is:
A. $-pE\cos\theta$  ✓ Correct
B. $+pE\sin\theta$
C. $-pE\sin\theta$
D. $+pE\cos\theta$
Solution: Potential energy of dipole in external field: $U = -\vec{p}\cdot\vec{E} = -pE\cos\theta$
Q10 — easy
Three capacitors of values $2\mu\text{F}$, $3\mu\text{F}$, and $6\mu\text{F}$ are joined in series across a $100\text{ V}$ supply. The equivalent capacitance of the network is:
A. $11\mu\text{F}$
B. $1\mu\text{F}$  ✓ Correct
C. $0.5\mu\text{F}$
D. $2\mu\text{F}$
Solution: $1/C_{eq} = 1/2 + 1/3 + 1/6 = (3+2+1)/6 = 1 \implies C_{eq} = 1\mu\text{F}$
Q11 — easy
The SI unit of magnetic dipole moment is:
A. A m
B. A m$^2$  ✓ Correct
C. A/m
D. J T
Solution: Magnetic moment $M = I \times A$, units = ampere times meter squared = A m$^2$
Q12 — easy
Lenz's law of electromagnetic induction is a direct consequence of the law of conservation of:
A. Electric charge
B. Momentum
C. Energy  ✓ Correct
D. Angular momentum
Solution: Lenz's law ensures mechanical work done against induced forces converts to electrical energy, obeying energy conservation
Q13 — easy
The total energy of an electron revolving in the second excited state ($n = 3$) of a hydrogen atom is:
A. $-13.6\text{ eV}$
B. $-3.4\text{ eV}$
C. $-1.51\text{ eV}$  ✓ Correct
D. $-0.85\text{ eV}$
Solution: $E_n = -13.6/n^2\text{ eV}$. For $n = 3$: $E_3 = -13.6/9 \approx -1.51\text{ eV}$
Q14 — easy
A light-emitting diode (LED) emits light when it is operated in:
A. Forward bias mode  ✓ Correct
B. Reverse bias mode
C. Breakdown region
D. Unbiased condition
Solution: An LED generates photons via spontaneous electron-hole recombination in forward bias
Q15 — easy
The dynamic resistance of a forward-biased semiconductor junction diode is defined as:
A. $V/I$
B. $\Delta V/\Delta I$  ✓ Correct
C. $I/V$
D. $\Delta I/\Delta V$
Solution: Dynamic (AC) resistance: $r_d = \Delta V/\Delta I$
Q16 — easy
For a transistor in common-emitter configuration, the relation connecting the current amplification factors $\alpha$ and $\beta$ is:
A. $\beta = \frac{\alpha}{1 - \alpha}$  ✓ Correct
B. $\alpha = \frac{\beta}{1 - \beta}$
C. $\beta = \frac{1 + \alpha}{\alpha}$
D. $\alpha \beta = 1$
Solution: $\beta = \alpha/(1 - \alpha)$
Q17 — easy
The efficiency of a Carnot engine operating between temperatures $T_H = 600\text{ K}$ and $T_C = 300\text{ K}$ is:
A. 25%
B. 33.3%
C. 50%  ✓ Correct
D. 75%
Solution: $\eta = 1 - T_C/T_H = 1 - 300/600 = 0.50 = 50\%$
Q18 — easy
A parallel-plate capacitor of plate area $A$ and separation $d$ is charged to a potential difference $V$. The energy density (energy per unit volume) in the electric field between plates is:
A. $\frac{1}{2}\varepsilon_0 E^2$  ✓ Correct
B. $\varepsilon_0 E^2$
C. $\frac{1}{2}\frac{E^2}{\varepsilon_0}$
D. $\frac{1}{2}\varepsilon_0 V^2$
Solution: Energy density of electrostatic field: $u = \frac{1}{2}\varepsilon_0 E^2$
Q19 — easy
The force experienced by a straight wire of length $L$ carrying current $I$ oriented parallel to a uniform magnetic field $\vec{B}$ is:
A. $ILB$
B. $2ILB$
C. Zero  ✓ Correct
D. $\frac{1}{2}ILB$
Solution: $F = IL \times B \sin\theta$. When parallel, $\theta = 0 \implies F = 0$
Q20 — easy
The decay constant ($\lambda$) and half-life ($T_{1/2}$) of a radioactive element are connected by:
A. $T_{1/2} = \frac{0.693}{\lambda}$  ✓ Correct
B. $T_{1/2} = 0.693\lambda$
C. $T_{1/2} = \frac{\lambda}{0.693}$
D. $T_{1/2} = \frac{1}{\lambda}$
Solution: $T_{1/2} = \ln 2 / \lambda \approx 0.693/\lambda$
Q21 — easy
The angle between two vectors $\vec{P} = \hat{i} + \hat{j}$ and $\vec{Q} = \hat{j} + \hat{k}$ is:
A. 30 degrees
B. 45 degrees
C. 60 degrees  ✓ Correct
D. 90 degrees
Solution: $\cos\theta = \frac{\vec{P}\cdot\vec{Q}}{|P||Q|} = \frac{0+1+0}{\sqrt{2}\sqrt{2}} = 1/2 \implies \theta = 60^\circ$
Q22 — easy
The acceleration due to gravity at a depth $d$ below the surface of the Earth of radius $R$ is given by:
A. $g(1 - d/R)$  ✓ Correct
B. $g(1 - 2d/R)$
C. $g(1 - d^2/R^2)$
D. $g/(1 + d/R)^2$
Solution: $g_d = g(1 - d/R)$
Q23 — easy
How much heat is required to convert $10\text{ g}$ of ice at $0^\circ\text{C}$ completely into water at $0^\circ\text{C}$? (Latent heat of fusion $L_f = 80\text{ cal/g}$):
A. $80\text{ cal}$
B. $800\text{ cal}$  ✓ Correct
C. $4184\text{ cal}$
D. $8000\text{ cal}$
Solution: $Q = mL_f = 10 \times 80 = 800\text{ cal}$
Q24 — easy
Two sound waves of frequencies $340\text{ Hz}$ and $344\text{ Hz}$ propagate in air. The time interval between two successive maximum beat intensities is:
A. $0.25\text{ s}$  ✓ Correct
B. $0.5\text{ s}$
C. $4\text{ s}$
D. $0.125\text{ s}$
Solution: Beat frequency = $|340 - 344| = 4\text{ Hz}$. Time interval = $1/4 = 0.25\text{ s}$
Q25 — easy
A ray of light traveling in water ($\mu = 4/3$) strikes the water-air interface. The critical angle for total internal reflection is:
A. $\sin^{-1}(3/4)$  ✓ Correct
B. $\sin^{-1}(4/3)$
C. $\sin^{-1}(1/2)$
D. $\sin^{-1}(2/3)$
Solution: $\sin\theta_c = 1/\mu = 3/4 \implies \theta_c = \sin^{-1}(3/4)$
Q26 — easy
A p-type semiconductor material is electrically:
A. Positively charged
B. Negatively charged
C. Neutral  ✓ Correct
D. Positively or negatively charged depending on dopant level
Solution: A doped semiconductor (p-type or n-type) remains electrically neutral as total proton charge balances total electron charge
Q27 — hard
A solid sphere and a hollow sphere of identical mass and radius roll down the same inclined plane without slipping from rest. The ratio of their linear accelerations $a_{\text{solid}} / a_{\text{hollow}}$ is:
A. 25 : 21  ✓ Correct
B. 21 : 25
C. 15 : 14
D. 14 : 15
Solution: Solid sphere: $k^2/R^2 = 2/5 \implies a_1 = \frac{5}{7}g\sin\theta$. Hollow sphere: $k^2/R^2 = 2/3 \implies a_2 = \frac{3}{5}g\sin\theta$. Ratio = 25:21
Q28 — hard
In an electrical LC circuit with inductance $L = 20\text{ mH}$ and capacitance $C = 5\mu\text{F}$, the natural resonant angular frequency of electrical oscillations is:
A. $1000\text{ rad/s}$
B. $3162\text{ rad/s}$  ✓ Correct
C. $5000\text{ rad/s}$
D. $10^4\text{ rad/s}$
Solution: $\omega_0 = 1/\sqrt{LC} = 1/\sqrt{20 \times 10^{-3} \times 5 \times 10^{-6}} = 1/\sqrt{10^{-7}} \approx 3162\text{ rad/s}$
Q29 — hard
Two soap bubbles of radii $3\text{ cm}$ and $4\text{ cm}$ are formed inside a vacuum chamber and coalesce isothermally. The radius of the combined bubble is:
A. $5\text{ cm}$  ✓ Correct
B. $7\text{ cm}$
C. $3.5\text{ cm}$
D. $2.4\text{ cm}$
Solution: Isothermal coalescence in vacuum: $R = \sqrt{r_1^2 + r_2^2} = \sqrt{9 + 16} = 5\text{ cm}$
Q30 — medium
In a conical pendulum, a bob of mass $m$ revolves in a horizontal circle of radius $r$ at a constant speed $v$. If the string makes an angle $\theta$ with the vertical, the tension $T$ in the string is given by:
A. $mg \cos\theta$
B. $\frac{mg}{\cos\theta}$  ✓ Correct
C. $mg \tan\theta$
D. $\frac{mg}{\sin\theta}$
Solution: Resolving tension vertically: $T\cos\theta = mg \implies T = \frac{mg}{\cos\theta}$