CUET PG PYQs for Limits and derivations with Solutions: Practice CUET PG Previous Year Questions

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Limits and derivations is an important topic in the Mathematics section in CUET PG exam. Practising this topic will increase your score overall and make your conceptual grip on CUET PG exam stronger.

This article gives you a full set of CUET PG PYQs for Limits and derivations with explanations for effective preparation. Practice of CUET PG Mathematics PYQs including Limits and derivations questions regularly will improve accuracy, speed, and confidence in the CUET PG 2026 exam.

CUET PG PYQs for Limits and derivations with Solutions

1.
Which one of the following is not correct?
- The set of limit points of a bounded sequence is bounded.
- A bounded sequence with a unique limit point is convergent.
- The limit points of the sequence ⟨2+(-1)ⁿ⟩ are 1 and 2.
- The limit points of the sequence ⟨(-1)ⁿ⟩ are -1 and 1.
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2.
Match List-I and List-II
LIST I LIST II
A. \(\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}\) I. e^-1/6
B. \(\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2\) II. e
C. \(\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}\) III. e²
D. \(\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}\) IV. ½

Choose the correct answer from the options given below:

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A)-(1), (B)-(II), (C)-(III), (D)-(IV)
(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

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3.
The function f(z) defined by \(f(z)= \begin{cases} \frac{Re(z)}{z} & z\neq0\\ 0 & z=0 \end{cases}\)then which one of the following is true?
- \(\lim\limits_{z\rightarrow0}f(z)\)exists
- f(z) is continuous at z=0
- f(z) is differentiable everywhere
- f(z) is not continuous at z=0
View Solution
4.
Given below are two statements:
Statement I: The sum of the series 2{7^-1+3^-17^-3 +5^-1.7^-5 +....} is log_e(\(\frac{4}{3}\)).
Statement II: The value of e always lies between 2 and 3.
In the light of the above Statements, choose the most appropriate answer from the options given below :
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but statement II is false
- Statement I is false but statement II is true
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LIST I		LIST II
A.	\(\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}\)	I.	e^-1/6
B.	\(\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2\)	II.	e
C.	\(\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}\)	III.	e²
D.	\(\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}\)	IV.	½

CUET PG PYQs for Limits and derivations with Solutions

1.Which one of the following is not correct?

3.The function f(z) defined by \(f(z)= \begin{cases} \frac{Re(z)}{z} & z\neq0\\ 0 & z=0 \end{cases}\)then which one of the following is true?

4.Given below are two statements:Statement I: The sum of the series 2{7-1+3-17-3 +5-1.7-5 +....} is loge(\(\frac{4}{3}\)).Statement II: The value of e always lies between 2 and 3.In the light of the above Statements, choose the most appropriate answer from the options given below :

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1.
Which one of the following is not correct?

3.
The function f(z) defined by \(f(z)= \begin{cases} \frac{Re(z)}{z} & z\neq0\\ 0 & z=0 \end{cases}\)then which one of the following is true?

4.
Given below are two statements:
Statement I: The sum of the series 2{7^-1+3^-17^-3 +5^-1.7^-5 +....} is log_e(\(\frac{4}{3}\)).
Statement II: The value of e always lies between 2 and 3.
In the light of the above Statements, choose the most appropriate answer from the options given below :