CUET-PG SERIES Mathematics
Differential Equations
33 previous year questions.
Volume: 33 Ques
Yield: High
High-Yield Trend
18
2025 15
2023 Chapter Questions 33 MCQs
01
PYQ 2023
medium
mathematics ID: cuet-pg-
Which of the following functions is differentiable at x = 0?
1
cos (|x|) +|x|
2
cos (|x|) -|x|
3
sin (|x|) +|x|
4
sin (|x|) -|x|
02
PYQ 2023
medium
mathematics ID: cuet-pg-
If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈]0, 1[
1
2f' (c) = g' (c)
2
2f' (c) = 3g' (c)
3
f' (c) = g' (c)
4
f' (c) = 2g' (c)
03
PYQ 2023
easy
mathematics ID: cuet-pg-
Find out the degree of the differential equation
1
2
2
1
3
0
4
Not defined
04
PYQ 2023
medium
mathematics ID: cuet-pg-
If f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]2+[g(x)]2 and h(5)=11, then h(10) =
1
22
2
11
3
15
4
21
05
PYQ 2023
medium
mathematics ID: cuet-pg-
The integrating factor of the differential equation is
1
2
3
4
06
PYQ 2023
medium
mathematics ID: cuet-pg-
If the solution of is , then value of is
1
5
2
10
3
15
4
20
07
PYQ 2023
medium
mathematics ID: cuet-pg-
If , then particular integral (P.I) of the given differential equation is
1
2
3
4
08
PYQ 2023
medium
mathematics ID: cuet-pg-
If , then the value of is
1
2
3
4
09
PYQ 2023
medium
mathematics ID: cuet-pg-
With the help of suitable transform of the independent variable, the differential equation
reduces to the form:
reduces to the form:
1
2
3
4
10
PYQ 2023
medium
mathematics ID: cuet-pg-
Match List I with List II
| Homogeneous function | Degree | ||
| A. | I. | 3 | |
| B. | II. | ||
| C. | III. | 1 | |
| D. | IV. |
Choose the correct answer from the options given below:
1
A II, B IV, CI, D III
2
A IV, B II, C I, D III
3
A III, B I, C II, D IV
4
A I, B III, C IV, D II
11
PYQ 2023
medium
mathematics ID: cuet-pg-
If and then, m is equal to
1
2
2
4
3
-2
4
1
12
PYQ 2023
medium
mathematics ID: cuet-pg-
Match List I with List II
Choose the correct answer from the options given below:
| List I Differential Equation | List II Particular Integral (P.I) | ||
| A. | (D2+6D+9)y=e3x | I. | |
| B. | (D2-6D+9)y=3 | II. | |
| C. | (D2+4)y=cos3x | III. | |
| D. | (D2+9)y= cos3x | IV. | |
1
A-IV, B-III, C-II, D-I
2
A-III, B-II, C-I, D-IV
3
A-II, B-I, C-III, D-IV
4
A-I, B-IV, C-II, D-III
13
PYQ 2023
medium
mathematics ID: cuet-pg-
Given below are two statements :
Statement I: Mdx+Ndy = 0 is said to be an exact differential equation if it satisfies the following condition
Statement II: If Mdx + Ndy = 0 is not an exact differential equation and , then
In the light of the above statements, choose the correct answer from the options given below :
Statement I: Mdx+Ndy = 0 is said to be an exact differential equation if it satisfies the following condition
Statement II: If Mdx + Ndy = 0 is not an exact differential equation and , then
In the light of the above statements, choose the correct answer from the options given below :
1
Both Statement I and Statement II are true
2
Both Statement I and Statement II are false
3
Statement I is true but Statement II is false
4
Statement I is false but Statement II is true
14
PYQ 2023
medium
mathematics ID: cuet-pg-
Match List I with List II
Choose the correct answer from the options given below:
| List I Differential Equation | List II I.F. | ||
| A. | y'+y=sinx | I. | x |
| B. | y'-y=x2 | II. | |
| C. | III. | ex | |
| D. | IV. | e-x | |
1
A-I, B-II, C-III, D - IV
2
A-II, B-III, C-IV, D-I
3
A-III, B-IV, C-I, D-II
4
A-IV, B-I, C-II, D-III
15
PYQ 2023
medium
mathematics ID: cuet-pg-
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A given family of curves is said to be 'self- orthogonal' if the family of orthogonal trajectory is the same as the given family of curves.
Reason R: For finding orthogonal trajectory, replace in
In the light of the above statements, choose the correct answer from the options given below:
Assertion A: A given family of curves is said to be 'self- orthogonal' if the family of orthogonal trajectory is the same as the given family of curves.
Reason R: For finding orthogonal trajectory, replace in
In the light of the above statements, choose the correct answer from the options given below:
1
Both A and R are true and R is the correct explanation of A
2
Both A and R are true but R is NOT the correct explanation of A
3
A is true but R is false
4
A is false but R is true
16
PYQ 2025
hard
mathematics ID: cuet-pg-
Match List-I with List-II and choose the correct option:
| LIST-I | LIST-II |
|---|---|
| (A) The solution of an ordinary differential equation of order 'n' has | (III) 'n' arbitrary constants |
| (B) The solution of a differential equation which contains no arbitrary constant is | (IV) particular solution |
| (C) The solution of a differential equation which is not obtained from the general solution is | (I) singular solution |
| (D) The solution of a differential equation containing as many arbitrary constants as the order of a differential equation is | (II) complete primitive |
Choose the correct answer from the options given below:
1
A - I, B - II, C - III, D - IV
2
A - I, B - III, C - II, D - IV
3
A - I, B - II, C - IV, D - III
4
A - III, B - IV, C - I, D - II
17
PYQ 2025
medium
mathematics ID: cuet-pg-
If the radius of curvature ( ) at (0, 1) of is , then is:
1
7
2
6
3
11
4
12
18
PYQ 2025
medium
mathematics ID: cuet-pg-
The function satisfies differential equation
1
2
3
4
19
PYQ 2025
medium
mathematics ID: cuet-pg-
Which of the following statements are true?
(A) For f(x) = |x|, for all x in [-1, 2]; Lagrange's mean value theorem is satisfied
(B) For f(x) = cosx, for all x in [0, /2]; Lagrange's mean value theorem is satisfied
(C) For f(x) = , for all x in [-1, 2]; Lagrange's mean value theorem is satisfied
(D) For f(x) = x(x-1)(x-2), for all x in [0, 1/2]; Lagrange's mean value theorem is satisfied
(E) For f(x) = , for all x in [-1, 1]; Lagrange's mean value theorem is satisfied
Choose the correct answer from the options given below:
(A) For f(x) = |x|, for all x in [-1, 2]; Lagrange's mean value theorem is satisfied
(B) For f(x) = cosx, for all x in [0, /2]; Lagrange's mean value theorem is satisfied
(C) For f(x) = , for all x in [-1, 2]; Lagrange's mean value theorem is satisfied
(D) For f(x) = x(x-1)(x-2), for all x in [0, 1/2]; Lagrange's mean value theorem is satisfied
(E) For f(x) = , for all x in [-1, 1]; Lagrange's mean value theorem is satisfied
Choose the correct answer from the options given below:
1
(A), (D) and (E) only
2
(A), (B) and (D) only
3
(B) and (D) only
4
(B), (D) and (E) only
20
PYQ 2025
medium
mathematics ID: cuet-pg-
Match List-I with List-II
Choose the correct answer from the options given below:
Choose the correct answer from the options given below:
1
(A) - (III), (B) - (II), (C) - (IV), (D) - (I)
2
(A) - (III), (B) - (II), (C) - (I), (D) - (IV)
3
(A) - (III), (B) - (I), (C) - (II), (D) - (IV)
4
(A) - (IV), (B) - (II), (C) - (I), (D) - (III)
21
PYQ 2025
medium
mathematics ID: cuet-pg-
Which one of the following statement is not correct?
1
The functions and are linear dependent.
2
The functions and are linearly independent.
3
The functions 1, sinx and cosx are linearly dependent.
4
The functions x and are linearly independent.
22
PYQ 2025
medium
mathematics ID: cuet-pg-
The general solution of differential equation is:
1
2
3
4
23
PYQ 2025
medium
mathematics ID: cuet-pg-
Match List-I with List-II
Choose the correct answer from the options given below:
Choose the correct answer from the options given below:
1
(A) - (III), (B) - (IV), (C) - (I), (D) - (II)
2
(A) - (II), (B) - (III), (C) - (IV), (D) - (I)
3
(A) - (III), (B) - (I), (C) - (II), (D) - (IV)
4
(A) - (I), (B) - (III), (C) - (IV), (D) - (II)
24
PYQ 2025
medium
mathematics ID: cuet-pg-
The particular integral of differential equation is:
1
2
3
4
25
PYQ 2025
medium
mathematics ID: cuet-pg-
Match List-I with List-II and choose the correct option:
| LIST-I (Differential Equation) | LIST-II (Integrating Factor) |
|---|---|
| (A) | (IV) |
| (B) | (III) |
| (C) | (I) |
| (D) | (II) |
Choose the correct answer from the options given below:
1
A - I, B - II, C - IV, D - III
2
A - II, B - III, C - I, D - IV
3
A - I, B - II, C - III, D - IV
4
A - III, B - IV, C - I, D - II
26
PYQ 2025
medium
mathematics ID: cuet-pg-
Match List-I with List-II and choose the correct option:
| LIST-I (Differential) | LIST-II (Order/degree / nature) |
|---|---|
| (A) | (I) order = 2, degree = 2, non-linear |
| (B) | (III) order = 2, degree = 3, non-linear |
| (C) | (IV) order = 1, degree = 2, non-linear |
| (D) | (II) order = 1, degree = 1, linear |
Choose the correct answer from the options given below:
1
A - III, B - I, C - II, D - IV
2
A - I, B - III, C - II, D - IV
3
A - III, B - I, C - IV, D - II
4
A - III, B - IV, C - I, D - II
27
PYQ 2025
medium
mathematics ID: cuet-pg-
The solution of the differential equation is:
1
; where C is a constant
2
; where C is a constant
3
; where C is a constant
4
; where C is a constant
28
PYQ 2025
medium
mathematics ID: cuet-pg-
The solution of the differential equation is:
1
, where C is an arbitrary constant
2
, where C is an arbitrary constant
3
, where C is an arbitrary constant
4
, where C is an arbitrary constant
29
PYQ 2025
medium
mathematics ID: cuet-pg-
The solution of the differential equation , is
1
2
3
4
30
PYQ 2025
medium
mathematics ID: cuet-pg-
If and a particular integral (P.I.) of is , then is:
1
an increasing function on
2
a decreasing function on
3
a continuous function on
4
not differentiable function at
31
PYQ 2025
medium
mathematics ID: cuet-pg-
The orthogonal trajectory of the cardioid , where 'a' is an arbitrary constant is:
1
, where b is an arbitrary constant
2
, where b is an arbitrary constant
3
, where b is an arbitrary constant
4
, where b is an arbitrary constant
32
PYQ 2025
medium
mathematics ID: cuet-pg-
A complete solution of is , where and are constants, then the respective values of and are:
1
3, 3
2
3, 4
3
4, 3
4
4, 4
33
PYQ 2025
medium
mathematics ID: cuet-pg-
The solution of the differential equation , is
1
; where c is an arbitrary constant
2
; where c is an arbitrary constant
3
; where c is an arbitrary constant
4
; where c is an arbitrary constant
About Differential Equations - CUET-PG
Differential Equations is a vital chapter for CUET-PG aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Differential Equations PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Differential Equations carry the most weight. Then, tackle the questions iteratively to solidify your understanding.