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