CUET · PHYSICS · PYQ PAPER 2023

A telescope has an objective of focal length 50 cm and eyepiece of focal length 5 cm. The least distance of distinct vision is 25 cm. The telescope is focused for distant vision on a scale 200 cm away from the objective. Calculate the separation between objective and eyepiece :

A 70.8 cm
B 68.5 cm
C 58.3 cm
D 60.5 cm

Verified Solution

Answer & Solution

Correct Answer

(A) 70.8 cm

Step-by-step Solution

Detailed explanation

\( \frac{1}{v_o} = \frac{1}{f_o} + \frac{1}{u_o} = \frac{1}{50} + \frac{1}{-200} = \frac{4-1}{200} = \frac{3}{200} \) \( v_o = \frac{200}{3} \text{ cm} \) \( \frac{1}{u_e} = \frac{1}{v_e} - \frac{1}{f_e} = \frac{1}{-25} - \frac{1}{5} = \frac{-1-5}{25} = \frac{-6}{25} \)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Match List-I with List-II

List-I	List-II
(A) Gyromagnetic ratio	(I) \( 4 \times 10^{-5} \text{ T} \)
(B) Permeability of free space	(II) \( 9.27 \times 10^{-24} \text{ Am}^2 \)
(C) Earth's magnetic field at equator	(III) \( 8.8 \times 10^{10} \text{ C/kg} \)
(D) Bohr magneton	(IV) \( 12.56 \times 10^{-7} \text{ TmA}^{-1} \)

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List-l (Statement)	List-ll (Its value)
(A) Degree of the differential equation \(\frac{d^2 y}{d x^2}=e^{d y / d x}\) is	(I) 2
(B) Order of the differential equation \(\left(\frac{d y}{d x}\right)^2+\frac{d^3 y}{d x^3}=0\) is	(II) not defined
(C) Degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2-5 x^2=0\)	(III) 3
(D) If \(p\) is the order and \(q\) is the degree of the differential equation \(\frac{d y}{d x}+3 y=e^x\), then \(p+q\) is	(IV) 1

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