CUET · MATHS · PYQ PAPER 2025

Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously, and it takes 12 minutes more to fill the cistern due to leakage. If the cistern is full, what will be the time taken by the leakage to empty it?

A 84 hours
B 72 hours
C 108 hours
D 120 hours

Verified Solution

Answer & Solution

Correct Answer

(D) 120 hours

Step-by-step Solution

Detailed explanation

\(R_{pipes} = \frac{1}{8} + \frac{1}{12} = \frac{3+2}{24} = \frac{5}{24}\) cistern/hour \(T_{no\_leak} = \frac{1}{R_{pipes}} = \frac{24}{5}\) hours \( = 4.8\) hours Extra time \( = 12\) minutes \( = \frac{12}{60} = 0.2\) hours \(T_{with\_leak} = 4.8 + 0.2 = 5\) hours…

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

The projection of the vector \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) on the vector \(2 \hat{i}+6 \hat{j}+3 \hat{k}\) is:

CUET 2025 Medium

Match List-I with List-II

List-I	List-II
(A) If A is a non singular matrix of order n, then \(\| A (\operatorname{adjA})\|\) is equal to	(I) \(\|A\|^{n-1}\)
(B) If A is a non singular matrix of order n, then \|adj(adj A)\| is equal to	(II) \(\|A\|^{n-2} A\)
(C) If A is a non singular matrix of order n, then \(\operatorname{adj}(\operatorname{adj} A )\) is equal to	(III) \(\|A\|^n\)
(D) if A is a non singular matrix of order n, then \(\|(\operatorname{adj} A)\|\) is equal to	(IV) \(\|A\|^{(n-1)^2}\)

Choose the correct answer from the options given below :

CUET 2025 Easy

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List-I	List-II
(A) If A is a non singular matrix of order n, then \(\| A (\operatorname{adjA})\|\) is equal to	(I) \(\|A\|^{n-1}\)
(B) If A is a non singular matrix of order n, then \|adj(adj A)\| is equal to	(II) \(\|A\|^{n-2} A\)
(C) If A is a non singular matrix of order n, then \(\operatorname{adj}(\operatorname{adj} A )\) is equal to	(III) \(\|A\|^n\)
(D) if A is a non singular matrix of order n, then \(\|(\operatorname{adj} A)\|\) is equal to	(IV) \(\|A\|^{(n-1)^2}\)

LIST I (Causal Agent)	LIST II (Disease)
(A) Salmonella typhi	(I) Typhoid
(B) Streptococcus pneumoniae	(II) Pneumonia
(C) Rhino Viruses	(III) Common cold
(D) Plasmodium	(IV) Malaria