Physics (Theory) • भौतिक विज्ञान (सैद्धांतिक)

Correct Option: (A) 15 minutes (10.15 a.m. to 10.30 a.m.)

Official Verbatim Rule (Note V):
"15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the candidates will read the question paper only and will not write any answer on the answer-book during this period."

Correct Option: (A) On the title page of the answer-book

Official Text (Note II):
"Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate."

Correct Option: (A) 33 Questions • 3 Hours • 70 Maximum Marks

• Time Allowed: 3 Hours (निर्धारित समय : 3 घण्टे)
• Maximum Marks: 70 (अधिकतम अंक : 70)
• Note (III): "Please check that this question paper contains 33 questions." (कृप्या जाँच कर लें कि इस प्रश्न-पत्र में 33 प्रश्न हैं ।)

Correct Option: (A) 27 printed pages

Official Text (Note I):
"Please check that this question paper contains 27 printed pages." (कृपया जाँच कर लें कि इस प्रश्न-पत्र में मुद्रित पृष्ठ 27 हैं ।)

Correct Option: (A) Write the Serial Number of the question at the given place

Official Text (Note IV):
"Please write down the Serial Number of the question in the answer-book at the given place before attempting it."

Correct Answer: (B) \(q E_0 x\)

Method 1: Work-Energy Theorem (Most Direct):
• The electrostatic force acting on the particle of charge \(q\) in electric field \(\vec{E} = E_0 \hat{i}\) is: • The work done \(W\) by this constant electric force during displacement \(x \hat{i}\) along the \(x\)-axis is: • According to the Work-Energy Theorem: • Since the particle starts from rest, initial kinetic energy \(K_i = 0\): Method 2: Equations of Kinematics:
• Acceleration of particle: \(a = \frac{F}{m} = \frac{q E_0}{m}\)
• Using third kinematic relation: \(v^2 - u^2 = 2 a x\). Since \(u = 0\): • Kinetic Energy:

Calculated Mathematical Value: \(2.5\text{ V}\)

Step 1: Determine Loop Geometry & Area:
• Side of square loop: \(a = 50\text{ cm} = 0.5\text{ m}\)
• Area of the loop: Step 2: Magnetic Flux Calculation:
• Magnetic field: \(B = 3.0\text{ T}\)
• Initially, \(\vec{B}\) is perpendicular to the plane of the loop \(\implies\) angle between \(\vec{B}\) and area normal vector \(\vec{A}\) is \(\theta_1 = 0^\circ\): • When rotated through \(90^\circ\), \(\vec{A}\) is perpendicular to \(\vec{B}\) (\(\theta_2 = 90^\circ\)): • Magnitude of change in flux: Step 3: Average Induced EMF (Faraday's Law):
• Time taken: \(\Delta t = 0.3\text{ s}\)

Correct Answer: (A) \(2.0 \times 10^8\text{ ms}^{-1}\)

Step 1: Compare with General Harmonic Wave Equation:
The standard equation of a travelling wave propagating in positive \(x\)-direction is: • Given equation: • By direct coefficient comparison: Step 2: Calculate Wave Velocity:
• The phase velocity of the electromagnetic wave is given by: Additional Concept: Refractive Index of Medium:
• Speed of light in vacuum \(c = 3 \times 10^8\text{ ms}^{-1}\)
• Refractive index \(n = \frac{c}{v} = \frac{3 \times 10^8}{2 \times 10^8} = 1.5\) (identifying the medium as optical glass).

Correct Answer: (B) \(-\frac{R}{\mu - 1}\)

Step 1: Focal length of thin plano-convex lens (\(f_1\)):
• \(R_1 = R\) (convex surface), \(R_2 = \infty\) (plane surface).
• Using Lens Maker's formula \(\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)\): Step 2: Focal length of thin equi-concave lens (\(f_2\)):
• \(R_1 = -R\), \(R_2 = +R\). Step 3: Combined Focal Length (\(F\)):
• For lenses in contact: \(\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}\) • The negative sign indicates that the combination acts as a diverging (concave) lens system.

Correct Answer: (A) \(2n\pi\)

Condition for Constructive Interference (Bright Spot / Maxima):
• In Young's double-slit experiment (YDSE), two coherent light waves interfere constructively to produce a maximum intensity (bright spot) when their path difference \(\Delta x\) is an integral multiple of wavelength \(\lambda\): • The relationship between phase difference \(\Delta \phi\) and path difference \(\Delta x\) is: • Note: For dark fringes (minima / destructive interference), the phase difference is \((2n + 1)\pi\) or \(2n\pi + \pi\) (Option D).

Correct Answer: (A) \(24,\ 150\text{ cm}\)

Given Parameters:
• Focal length of objective lens (\(f_o\)): \(144\text{ cm}\)
• Focal length of eyepiece lens (\(f_e\)): \(6.0\text{ cm}\)

1. Magnifying Power (\(m\)) in Normal Adjustment: 2. Length of Telescope Tube (\(L\)):

Correct Answer: (A) Twinkling of stars

Explanation of Optical Principles:
• Twinkling of stars: Caused by continuous atmospheric refraction through turbulent air layers of constantly varying temperature and optical density. It does not involve total internal reflection.
• Brilliance of diamonds: High refractive index (\(n \approx 2.42\)) gives a very small critical angle (\(i_c \approx 24.4^\circ\)). Multiple successive total internal reflections inside properly faceted diamond faces trap and bounce light.
• Optical fibre: Relies on repeated total internal reflection at the core-cladding boundary (\(n_1 > n_2\)) with almost zero transmission loss.
• Reflecting prism: Isosceles right-angled prisms turn light beams by \(90^\circ\) or \(180^\circ\) using total internal reflection (critical angle for crown glass is \(\sim 42^\circ\), and incidence angle is \(45^\circ > 42^\circ\)).