CUET · MATHS · PYQ PAPER 2023

Consider sets A and B, each having 4 elements. If \(f : A \to B\) be a function, then number of functions from A to B are:

A 216
B 256
C 64
D 16

Verified Solution

Answer & Solution

Correct Answer

(B) 256

Step-by-step Solution

Detailed explanation

Number of elements in A = \(|A| = 4\) Number of elements in B = \(|B| = 4\) Number of functions from A to B = \(|B|^{|A|}\) \(= 4^4\) \(= 256\)

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

If A and B are two events such that \(P(B) = \frac{3}{5}\), \(P(A|B) = \frac{1}{2}\) and \(P(A \cup B) = \frac{4}{5}\), then P(A) is equal to:

CUET 2023 Medium

Match List I with List II

LIST I	LIST II
A. \(\int \sin x \cos x d x\)	I. \(\log _e\left(1+\sin ^2 x\right)+C\)
B. \(\int \frac{d x}{\sin ^2 x \cos ^2 x}\)	II. \(\tan \frac{x}{2}+C\)
C. \(\int \frac{\sin 2 x}{1+\sin ^2 x} d x\)	III. \(-\frac{1}{4} \cos 2 x+C\)
D. \(\int(1-\cos x)\operatorname{cosec}^2 x d x\)	IV. \(\tan x-\cot x+C\)

CUET 2023 Hard

Match List-l with List-ll

List-l Differential Equation	List-ll Integrating Factor
(A) \(y d x+\left(x-y^3\right) d y=0\)	(I) \(e^{-x}\)
(B) \(x \frac{d y}{d x}+y=x^2\)	(II) \(\frac{1}{x}\)
(C) \(\frac{d y}{d x}-y=e^x\)	(III) \(y\)
(D) \(x d y-y d x=x^3 d x\)	(IV) \(x\)

Choose the correct answer from the options given below :

CUET 2025 Hard

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