CUET · PHYSICS · PYQ PAPER 2025

Two nuclei have mass numbers 125 and 27, respectively. The mass density ratio of their nuclei will be

A \(5: 3\)
B 125:27
C V125 : V27
D 1:1

Verified Solution

Answer & Solution

Correct Answer

(D) 1:1

Step-by-step Solution

Detailed explanation

\(\rho = \frac{M}{V}\) \(M \approx A m_p\) \(V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi (R_0 A^{1/3})^3 = \frac{4}{3}\pi R_0^3 A\) \(\rho = \frac{A m_p}{\frac{4}{3}\pi R_0^3 A} = \frac{m_p}{\frac{4}{3}\pi R_0^3}\) \(\rho_1 : \rho_2 = 1:1\)

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.

Same subject

Explore more questions on app

From CUET

In the reaction \(\left( CH _3\right)_3 C - O - CH _3+ HI \rightarrow\) Products, \(CH _3 OH\) and \(\left( CH _3\right)_3 CCl\) are the products and not \(CH _3 I\) and \(\left( CH _3\right)_3 COH\). It is because:
(A) In step 2 of the reaction, the departure of leaving group ( \(HO - CH _3\) ) creates less stable carbocation.
(B) In step 2 of the reaction, the departure of leaving group ( \(HO - CH _3\) ) creates more stable carbocation.
(C) The reaction follows an SN1 mechanism.
(D) The reaction follows SN2 mechanism.
Choose the correct answer from the options given below :

CUET 2024 Hard

Match List-l with List-ll

List-l (Genetic disorder)	List-II (Cause)
(A) Thalassemia	(I) 45+XΟ
(B) Sickle-cell anemia	(II) Formation of abnormal hemoglobin
(C) Klinefelter's syndrome	(III) Substitution of glutamic acid by valine
(D) Turner's syndrome	(IV) 47, XXY

Choose the correct answer from the options given below:

CUET 2025 Easy

Explore more questions on app

List-I	List-II
(A) Adenine	(I) Purine
(B) Thymine	(II) Pyrimidine
(C) Uracil	(III) DNA
(D) Deoxyribose	(IV) RNA