Question 1
Which of the following statements is strictly correct according to NCERT regarding an n-type semiconductor? [cite: 1]
✅ Correct Answer: The dopant atom usually has 5 valence electrons.
Explanation: To create an n-type semiconductor, a pentavalent impurity (having 5 valence electrons) like Phosphorus or Arsenic is added to pure Silicon or Germanium[cite: 10]. The 5th electron becomes a free charge carrier. The semiconductor crystal as a whole remains electrically neutral[cite: 11]. Common Mistake: Students often choose B, thinking "n-type" implies a net negative charge, forgetting that the atom itself was neutral before bonding[cite: 13].
Question 2
According to NCERT, which electromagnetic waves are produced by bombarding a metal target with high-energy electrons? [cite: 14]
✅ Correct Answer: X-rays
Explanation: X-rays are commonly produced by the sudden deceleration of high-speed electrons when they hit a heavy metal target (like tungsten)[cite: 23]. Gamma rays, on the other hand, originate from radioactive nuclear decay[cite: 24].
Question 3
As per NCERT, the magnetic susceptibility of a paramagnetic substance is: [cite: 27]
✅ Correct Answer: Small and positive
Explanation: Paramagnetic substances are weakly attracted by external magnetic fields, meaning their magnetic susceptibility ($\chi$) is positive but very small ($\chi > 0$ and close to 0)[cite: 36]. Diamagnetic is small and negative, while ferromagnetic is very large and positive[cite: 37].
Question 4
According to NCERT, for an incompressible fluid in steady, non-viscous flow, the principle that dictates an increase in flow speed at a constriction in a pipe is: [cite: 40]
✅ Correct Answer: Equation of Continuity
Explanation: The Equation of Continuity states that $A_1 v_1 = A_2 v_2$[cite: 49]. When a pipe constricts (Area $A$ decreases), the velocity ($v$) must increase to keep the mass flow rate constant[cite: 49]. While Bernoulli's explains the pressure drop, the speed increase is derived from the Equation of Continuity[cite: 51].
Question 5
A particle moves under the influence of a conservative force. If the kinetic energy of the particle increases as it moves, what happens to its potential energy and the work done by the conservative force? [cite: 52, 53]
✅ Correct Answer: Potential energy decreases, work done is positive
Explanation: By the Work-Energy theorem, an increase in kinetic energy means total work done is positive[cite: 62]. For a conservative force, Work done = $-\Delta U$. Thus, positive work means the change in potential energy is negative (potential energy decreases)[cite: 63].
Question 6
In a standard P-V diagram, two expansion curves pass through the same initial point - one represents an isothermal process and the other an adiabatic process. Which of the following is true? [cite: 66, 67]
✅ Correct Answer: The adiabatic curve is steeper than the isothermal curve.
Explanation: The slope of an isothermal curve on a P-V diagram is $-P/V$, while the slope of an adiabatic curve is $-\gamma(P/V)$[cite: 76]. Since $\gamma > 1$ for all ideal gases, the adiabatic curve is $\gamma$ times steeper than the isothermal curve[cite: 77].
Question 7
If the phase difference between two interfering light waves originating from two slits changes rapidly and randomly with time, the resulting interference pattern on the screen will be: [cite: 80]
✅ Correct Answer: Uniformly illuminated with no distinct fringes
Explanation: For a sustained interference pattern, the sources must be coherent (constant phase difference)[cite: 89]. If the phase difference fluctuates rapidly, the maxima and minima shift so fast that our eyes average them out, resulting in uniform general illumination of intensity $I_1+I_2$[cite: 90].
Question 8
In a photoelectric effect experiment, if the intensity of the incident monochromatic light is doubled while keeping its frequency constant (and above the threshold frequency), what happens to the stopping potential? [cite: 93]
✅ Correct Answer: It remains unchanged
Explanation: Stopping potential depends only on the maximum kinetic energy of the emitted photoelectrons, which is determined by the frequency of the incident light[cite: 102]. Changing intensity only changes the number of photons (and thus the saturation current), not their individual energy[cite: 103].
Question 9
Assertion: The electric field inside a solid isolated conducting sphere is always zero under electrostatic conditions.
Reason: Charges always reside completely on the outer surface of a conductor to minimize electrostatic potential energy. [cite: 106, 107]
✅ Correct Answer: Both Assertion and Reason are correct and Reason is the correct explanation.
Explanation: In a conductor, free electrons move until the internal electric field is zero[cite: 116]. To achieve this state of minimum potential energy, all excess charge distributes itself entirely on the outer surface, causing internal fields to cancel out perfectly[cite: 117].
Question 10
Assertion: The resistivity of a typical semiconductor decreases with an increase in temperature.
Reason: The relaxation time of electrons in a semiconductor increases with temperature. [cite: 120, 121]
✅ Correct Answer: Assertion is correct but Reason is incorrect.
Explanation: The assertion is true; semiconductor resistivity drops with heating. However, the reason is false[cite: 130]. Relaxation time actually decreases with temperature due to increased lattice vibrations[cite: 131]. Resistivity drops purely because the number density ($n$) of charge carriers increases exponentially, overpowering the decrease in relaxation time[cite: 132].
Question 11
Consider the following two statements:
Statement I: The escape velocity from the surface of a planet depends directly on the mass of the escaping body.
Statement II: The orbital velocity of a satellite revolving very close to the surface of a planet is independent of the mass of the satellite. [cite: 136, 137]
✅ Correct Answer: Statement I is incorrect but Statement II is correct.
Explanation: Escape velocity $v_e = \sqrt{2GM/R}$ and orbital velocity $v_O = \sqrt{GM/R}$[cite: 146]. In both formulas, $M$ is the mass of the planet, not the object[cite: 146]. Therefore, neither velocity depends on the mass of the satellite/body itself[cite: 147].
Question 12
Consider the following two statements:
Statement I: In a series LCR circuit, the total impedance is maximum at the resonant frequency.
Statement II: The power factor of a series LCR circuit at resonance is unity. [cite: 151, 152]
✅ Correct Answer: Statement I is incorrect but Statement II is correct.
Explanation: At resonance, inductive reactance ($X_L$) equals capacitive reactance ($X_C$), causing them to cancel out[cite: 161]. The impedance $Z=R$, which is the minimum possible impedance, making Statement I false[cite: 162]. Since the circuit is purely resistive at this point, phase angle $\phi = 0^\circ$, so power factor $\cos(\phi) = 1$ (unity), making Statement II true[cite: 163].
Question 13
A particle is projected from the ground with kinetic energy $E$ at an angle of $60^\circ$ with the horizontal. What will be its kinetic energy at the highest point of its trajectory? [cite: 166, 167]
✅ Correct Answer: $E/4$
Explanation: At the highest point, the vertical component of velocity is zero[cite: 176]. The particle only has the horizontal component, $u_x = u \cos(60^\circ) = u/2$[cite: 177]. Since velocity is halved, the kinetic energy, which is proportional to $v^2$, becomes $(1/2)^2 = 1/4$ of the initial energy[cite: 177].
Question 14
A prism made of a material with refractive index $\sqrt{2}$ has a refracting angle of $60^\circ$. What is the angle of minimum deviation for this prism? [cite: 180]
✅ Correct Answer: $30^\circ$
Explanation: Using the prism formula: $\mu = \frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$[cite: 189]. Substitute $\mu = \sqrt{2}$ and $A = 60^\circ$[cite: 190].
$\sqrt{2} = \frac{\sin((60^\circ + \delta_m)/2)}{\sin(30^\circ)}$ [cite: 191]
$\sqrt{2} \times 0.5 = \sin((60^\circ + \delta_m)/2)$ [cite: 192]
$1/\sqrt{2} = \sin((60^\circ + \delta_m)/2)$ [cite: 193]
$\implies (60^\circ + \delta_m)/2 = 45^\circ \implies 60^\circ + \delta_m = 90^\circ \implies \delta_m = 30^\circ$[cite: 194].
Question 15
A block of mass $M$ is pulled along a smooth horizontal surface by a thick rope of mass $m$. If a horizontal force $F$ is applied at the free end of the rope, the tension at the midpoint of the rope is: [cite: 197, 198]
✅ Correct Answer: $\frac{F(M + m/2)}{M + m}$
Explanation: First, find common acceleration: $a = \frac{F}{M+m}$[cite: 208]. To find tension at the midpoint, consider the mass being pulled by that point[cite: 209]. The midpoint pulls the block $M$ plus half the rope $m/2$[cite: 210].
$T = (\text{Mass being pulled}) \times a = (M+m/2) \times \frac{F}{M+m}$[cite: 211].
Question 16
In electromagnetism, the quantity $\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ has the exact same dimensional formula as: [cite: 214]
✅ Correct Answer: Velocity
Explanation: According to Maxwell's equations, the speed of light in a vacuum ($c$) is given by $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$[cite: 223]. Therefore, this term has the dimensions of speed/velocity, which is $[L T^{-1}]$[cite: 224].
Question 17
An electron and a proton are accelerated from rest through the exact same potential difference $V$. What is the ratio of their de Broglie wavelengths ($\lambda_e / \lambda_p$)? [cite: 227]
✅ Correct Answer: $\sqrt{m_p/m_e}$
Explanation: De Broglie wavelength $\lambda = \frac{h}{\sqrt{2mK}}$[cite: 236]. Since both are accelerated through the same potential $V$, their kinetic energy $K = qV$ is the same (both have charge magnitude $e$)[cite: 236]. Therefore, $\lambda \propto 1/\sqrt{m}$[cite: 237]. This gives $\lambda_e / \lambda_p = \sqrt{m_p/m_e}$[cite: 237].
Question 18
A solid sphere and a solid cylinder, both having the same mass and the same radius, are released simultaneously to roll down a rough inclined plane without slipping. Which one will reach the bottom first? [cite: 240, 241]
✅ Correct Answer: Solid sphere
Explanation: Acceleration of a rolling body is $a = \frac{g \sin\theta}{1 + k^2/R^2}$[cite: 250]. The body with the smaller $k^2/R^2$ ratio has higher acceleration[cite: 251].
For a solid sphere, $k^2/R^2 = 2/5 = 0.4$[cite: 252].
For a solid cylinder, $k^2/R^2 = 1/2 = 0.5$[cite: 253].
Since the sphere has a smaller ratio, it accelerates faster and reaches the bottom first[cite: 254].
Question 19
A simple pendulum has a time period $T$ in a vacuum. The bob has a density $\sigma$. If the pendulum is completely immersed in a non-viscous liquid of density $\rho$ (where $\rho < \sigma$), what is its new time period $T'$? [cite: 257, 258]
✅ Correct Answer: $T' = T \sqrt{\frac{\sigma}{\sigma - \rho}}$
Explanation: In liquid, the effective gravity $g'$ decreases due to buoyancy[cite: 267]. Net downward force = $mg - \text{Buoyant force} = V\sigma g - V\rho g$[cite: 268]. Effective gravity $g' = g (1-\rho/\sigma) = g \frac{\sigma - \rho}{\sigma}$[cite: 269]. Since $T = 2\pi\sqrt{L/g}$, $T \propto 1/\sqrt{g}$[cite: 269]. Substituting $g'$ gives $T' = T \sqrt{\frac{\sigma}{\sigma - \rho}}$[cite: 270].
Question 20
TRAP QUESTION: A parallel plate capacitor is fully charged using a battery. The battery is then disconnected. A dielectric slab (with dielectric constant $K>1$) is now slowly inserted between the plates. What happens to the potential difference across the plates and the energy stored in the capacitor? [cite: 273, 274, 275]
✅ Correct Answer: Both decrease
Explanation: Since the battery is disconnected, the charge $Q$ is trapped and remains constant[cite: 284]. When the dielectric is inserted, the capacitance $C$ increases to $KC$[cite: 285]. Potential difference $V = Q/C$. Since $C$ increases and $Q$ is constant, $V$ decreases[cite: 286]. Energy stored $U = Q^2/2C$. Since $C$ increases in the denominator, $U$ must also decrease[cite: 287].
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