CUET · PHYSICS · PYQ PAPER 2023

Identify X in the following nuclear reaction:
\( {}_{6}^{12}C + {}_{1}^{1}H \rightarrow X \)

A \( {}_{7}^{13}N \)
B \( {}_{5}^{10}B \)
C \( {}_{6}^{12}C \)
D \( {}_{7}^{14}N \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( {}_{7}^{13}N \)

Step-by-step Solution

Detailed explanation

Conservation of atomic number (Z): \( 6 + 1 = Z_X \Rightarrow Z_X = 7 \) Conservation of mass number (A): \( 12 + 1 = A_X \Rightarrow A_X = 13 \) \( X = {}_{7}^{13}N \)

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) The degree of differential equation \(\frac{d^3 y}{d x^3}=e^{\frac{d y}{d x}}\)	(I) 2
(B) The order of differential equation \(\left(\frac{d y}{d x}\right)^2+\frac{d^3 y}{d x^3}=0\)	(II) 4
(C) The sum of order and degree of differential equation \(\frac{d}{d x}\left(\frac{d^2 y}{d x^2}\right)+\left(\frac{d y}{d x}\right)^5=x\)	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

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Identify X in the following nuclear reaction:\( {}_{6}^{12}C + {}_{1}^{1}H \rightarrow X \)

Step-by-step Solution

Identify X in the following nuclear reaction:
\( {}_{6}^{12}C + {}_{1}^{1}H \rightarrow X \)