CUET · MATHS · PYQ PAPER 2025

In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4: 5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.

A 375 metres
B 125 metres
C 150 metres
D 300 metres

Verified Solution

Answer & Solution

Correct Answer

(B) 125 metres

Step-by-step Solution

Detailed explanation

Distance Meena needs to run to finish: \( 500 \text{ m} - 200 \text{ m} = 300 \text{ m} \) Distance Kamal runs in the same time: \( 300 \text{ m} \times \frac{5}{4} = 375 \text{ m} \) Distance by which Meena wins: \( 500 \text{ m} - 375 \text{ m} = 125 \text{ m} \)

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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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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LIST-I	LIST-I
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(C) \(\tan ^{-1} x\)	(III) \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
(D) \(\cot ^{-1} x\)	(IV) \([0, \pi]-\left\{\frac{\pi}{2}\right\}\)

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(D) It is set up for a particular upcoming expense.
Choose the correct answer from the options given below:

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List I	List II
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