CUET Sample Paper for Maths

CUET UG
ENTRANCE
SAMPLE PAPER
2023
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QUESTION PAPERS • YEAR 2023 •
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2023 JUNE
MAY 2023

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CUET 2023 Overview

CUET is a Common entrance exam. The full form of CUET is Common University Entrance Test. It
is organized by National Testing Agency at a National level. It is organized by National Testing
Agency as a National level exam in India for admission in All Central Universities, and State, Deemed,
Private Universities accepting CUET scores.

Highlights of the examination are as follows.

Aspects Details

Name of Exam CUET 2023

Full Form of CUET Common University Entrance Test

Organizing Body NTA

Full Form of NTA National Testing Agency

Type of Exam Common Entrance Exam

Level of Exam National

Region India

Official Website cuet.samarth.ac.in

Courses Where BA, BCA, B.Sc, B.Com, BJMC, B.Pharm, D.Pharm, B.Tech, B.Voc, BVA,
Admission is Through BFA, BPA, BSW, Integrated MA Integrated B.Ed, Integrated M.Sc,
CUET Integrated B.Tech-M.Tech, Integrated MPA, BA LLB, BBA LLB, Diploma,
Shastri,

Colleges Where All Central Universities, and State, Deemed, Private Universities acepting
Admission is Through CUET scores
CUET

Minimum Educational Class 12th
Qualification

Mode of Exam Computer Based Test-CBT

Type of Questions Objective type with Multiple Choice Questions

Marking Scheme +5, -1

CUET 2023 Exam Pattern

The exam pattern is as follows

▪ Mode of Exam – The exam is a Computer Based Test-CBT.
▪ Question type – The questions are Objective type with Multiple Choice Questions.
▪ Number of Subjects – A candidate can choose upto 10 Subjects for giving the Exam.
▪ Language of Question Paper – The question paper is in 13 languages (Assamese, Bengali,
English, Gujarati, Hindi, Kannada, Malayalam, Marathi, Punjabi, Odia, Tamil, Telugu, and
Urdu).

Marking Scheme –
▪ Candidates get +5 marks for correct answer.
▪ And negative marks is -1 for incorrect answers

List of Languages/ Domain Specific Subjects /General Test offered under CUET (UG)-2023

---

Maths

Q.No. 1 ∫

(B) csc(b − a) log

(C) csc(b − a) log

(D) sin(b − a) log

(C) equivalence

(D) None of these

(D) 1
dx

∣
sin(x−a) sin(x−b)

(A) sin(b − a) log
sin(x−b)

sin(x−a)

sin(x−a)

sin(x−b)

sin(x−b)

sin(x−a)

sin(x−a)

sin(x−b)
Sample Paper

+ C

+ C

+ C

+ C

is equal to


Q.No. 2 Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a
is congruent to b ∀ a, b ∈ T. Then R is

(A) reflexive but not symmetric

(B) transitive but not symmetric

Q.No. 3 The magnitude of the vector 6^i + 2^j + 3k

(A) 5

(B) 7

(C) 12
^ is

Q.No. 4 If P(A) = 0.4, P(B) = 0.8 and P(B | A) = 0.6, then P(A ∪ B) is equal to

(A) 0.24

(B) 0.3

(C) 0.48

(D) 0.96

Q.No. 5 Distance of the point (α,β,γ) from y-axis is

(A) β

(B) |β|

(C) |β| + |v|

(D) √α + y 2 2

Q.No. 6 If f (x) = x sin
2 1

x
, where x ≠ 0 then the value of the function f at x = 0, so that the function is
continuous at x = 0, is
(A) 0

(B) -1

(C) 1

(D) None of these

^ and →
→ = 2^i + λ^j + k
Q.No. 7 Find the value of λ such that the vectors a b =^
i + 2^ ^ are orthogonal
j + 3k

(A) 0

(B) 1

(C) 3

2

(D) − 5

2

Q.No. 8 The feasible solution for a LPP is shown in Figure. Let Z = 3x – 4y be the objective function.
Minimum of Z occurs at

(A) (0, 0)

(B) (0, 8)

(C) (5, 0)

(D) (4, 10)

Q.No. 9 The area of the quadrilateral ABCD, where A(0,4,1), B (2, 3, –1), C(4, 5, 0) and D (2, 6, 2), is equal to

(A) 9 sq. units

(B) 18 sq. units
---

(C) 27 sq. units

(D) 81 sq. units

Q.No. 10 P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5,
then its y co-ordinate is

(A) 2

(B) 1

(C) -1

(D) -2

Q.No. 11 The corner points of the feasible region determined by the following system of linear constraints are
(0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z
occurs at both the points (15, 15) and (0, 20) is:

(A) p = q

(B) p = 2q

(C) q = 2p

(D) q = 3p

Q.No. 12 A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P (B ∩ A) equals
′

(A) 2

3

(B) 1

2

(C) 3

10

(D) 1

5

Q.No. 13 The area of the region bounded by the curve y = √16 − x and x -axis is
2

(A) 8 sq units

(B) 20πsq units

(C) 16π sq units

(D) 256π sq units

Q.No. 14 The value of cos −1
(cos
3π

2
) is equal to

(A) π

2

(B) 3π

2

(C) 5π

2

(D) 7π

2

Q.No. 15 The order of the differential equation of all circles of given radius 'a' is:

(A) 1
---

---

(B) 2

(C) 3

(D) 4

Q.No. 16 If

(A) 3

(B) ±3

(C) ±6

(D) 6

(A) one-one

(B) onto

(C) bijective

∣
2x

8

(D) f is not defined
5

x
=
6

7

(C) The two quantities are equal
−2

3
, then value of x is

Q.No. 17 Let f : R → R be defined by f (x) = 1

x
∀x ∈ R. Then f is

Q.No. 18 The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0,
40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in Column A and

Column B.

(A) The quantity in column A is greater

(B) The quantity in column B is greater

(D) The relationship can not be determined on the basis of the information supplied

Q.No. 19

(C) n =

(D) m = n =

(A) cosx

(B) tanx

(C) secx
If f (x) = {

(A) m = 1, n = 0

(B) m = nπ

2

mπ

2
+ 1

π

2
mx + 1

sin x + n,
, if x ≤

if x >
π

2
π

2
, is continuous at x =

Q.No. 20 Integrating factor of the differential equation cos x dy

dx
π

2
, then

+ y sin x = 1 is :

(D) sinx

Q.No. 21 Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle
2 2
x + y = 32 is

(A) 16π sq units

(B) 4π sq units

(C) 32π sq units

(D) 24 sq units

Q.No. 22 The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4), respectively is

(A) −^i + 12^j + 4k
^

(B) 5^i + 2^j − 4k
^

(C) −5^i + 2^j + 4k
^

(D) ^i + ^j + k
^

Q.No. 23 The angle between the vectors ^i − ^j and ^j − k
^
is

(A) π
3

(B) 2π

3

(C) −π

3

(D) 5π

6

Q.No. 24 A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the
ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the
ladder is decreasing when lower end of ladder is 2 metres from the wall is:

(A) 1

10
radian/sec

(B) 1

20
radian/sec

(C) 20 radian/sec

(D) 10 radian/sec

2x + y 4x 7 7y − 13
Q.No. 25 If [ ] = [ ], then the value of xandy is
5x − 7 4x y x + 6

(A) x=3, y=1

(B) x=2, y=3

(C) x=2, y=4

(D) x=3, y=3

Q.No. 26 Feasible region (shaded) for a LPP is shown in the Figure Minimum of Z = 4x + 3y occurs at the
point
---

---

(A) (0, 8)

(B) (2, 5)

(C) (4, 3)

(D) (9, 0)

number is

(A) 4

(B) 5

(C) -4

(D) 9

(A) 1

(B) 7

(C) 1

7

(D) None of these

Q.No. 27 There are two values of a which makes determinant, Δ = 2

Q.No. 28 The distance of the plane r→ ⋅ ( 2^
7
i +
3 ^
7
j −

Q.No. 29 The area enclosed by the circle x + y = 2 is equal to

(A) 4π sq units

(B) 2√2π Sq units

(C) 4π sq units
2

(D) 2π sq units
2 2
6 ^
7
k) = 1

∣1

0
−2

a

4
5

−1

2a

from the origin is
, then sum of these
= 86

0 1
Q.No. 30 If A = [ ], then A
2
is equal to
1 0

0 1
(A) [
1 0
]
1 0
(B) [ ]
1 0

0 1
(C) [ ]
0 1

1 0
(D) [ ]
0 1

Q.No. 31 Which of the following is the principal value branch of cos −1
x ?

(A) [ −π

2
,
π

2
]

(B) (0, π)

(C) [0, π]

(D) (0, π) − { π

2
}

Q.No. 32 The set of points where the function f given by f (x) = |2x − 1| sin x is differentiable is

(A) R

(B) R − { 1

2
}

(C) (0, ∞)

(D) None of these

Q.No. 33 The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given
by

(A) (2, 0, 0)

(B) (0, 5, 0)

(C) (0, 0, 7)

(D) (0, 5, 7)

Q.No. 34 The sine of the angle between the straight line x−2

3
=
y−3

4
=
z−4

5
and the plane 2x – 2y + z = 5 is

(A) 10

6√ 5

(B) 4

5√ 2

(C) 2√ 3

5

(D) √2

10

Q.No. 35 If 3 tan −1
x + cot
−1
x = π, then x equals
---

---

(A) 0

(B) 1

(C) -1

(D) 1

2

Q.No. 36 The matrix P =

(A) square matrix

(B) diagonal matrix

(C) unit matrix

(D) None

√3
or −
√3

⎢⎥
⎡

⎣
0

0

4

0

4

0
4

0

0
⎤

⎦
is a

Q.No. 37 If the directions cosines of a line are k,k,k, then

(A) k>0

(B) 0

(C) k=1

(D) k = 1 1

Q.No. 38 Consider the following two binary relations on the set A ={a, b, c} :
R₁={(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R₂={(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}. Then :

(A) both R₁ and R₂ are not symmetric.

(B) R₁ is not symmetric but it is transitive.

(C) R₂ is symmetric but it is not transitive.

(D) both R₁ and R₂ are transitive.

Q.No. 39 The area of the region bounded by the circle x + y = 1 is

(A) 2π sq units

(B) π sq units

(C) 3π sq units

(D) 4π sq units

Q.No. 40 The degree of the differential equation [1 + (

(A) 4

(B) 3

2

(C) Not defined
2

dy

dx
2

2

) ]
3

2

=
2
d y

dx
2 is

(D) 2

Answer Sheet CUET 2023
Q.No Answer
Q.No. 1 (B)
Q.No. 2 (C)
Q.No. 3 (B)
Q.No. 4 (D)
Q.No. 5 (D)
Q.No. 6 (A)
Q.No. 7 (D)
Q.No. 8 (B)
Q.No. 9 (A)
Q.No. 10 (A)
Q.No. 11 (D)
Q.No. 12 (D)
Q.No. 13 (A)
Q.No. 14 (A)
Q.No. 15 (B)
Q.No. 16 (C)
Q.No. 17 (D)
Q.No. 18 (B)
Q.No. 19 (C)
Q.No. 20 (C)
Q.No. 21 (B)
Q.No. 22 (C)
Q.No. 23 (B)
Q.No. 24 (B)
Q.No. 25 (B)
Q.No. 26 (B)
Q.No. 27 (C)

Q.No. 28 (A)
Q.No. 29 (D)
Q.No. 30 (D)
Q.No. 31 (C)
Q.No. 32 (B)
Q.No. 33 (A)
Q.No. 34 (D)
---

Q.No. 35 (B)
Q.No. 36 (A)
Q.No. 37 (D)
Q.No. 38
(C)
Q.No. 39 (B)
Q.No. 40 (C)
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