PU CET UG 2025 Question Paper Maths

1. Let 𝑓 𝑥 + =𝑥 + , (𝑥 ≠ 0), then 𝑓(𝑥) is equal to
(A) 𝑥 (B) 𝑥 − 1
(C) 𝑥 − 2 (D) 𝑥 + 1
2. The range of the function 𝑓(𝑥) = 𝑥 +
(A) [1, ∞) (B) [2, ∞)
(C) ,∞ (D) None of these
3. If 𝑓 is an even function defined on the interval [−5, 5], then the real values of x
satisfying the equation 𝑓 (𝑥 ) = 𝑓 are
±√ ±√ ±√ ±√
(A) , (B) ,
±√ ±√
(C) (D)

4. If tan 2 and tan 3 be two angles of a triangle, then the third angle is
(A) 75 (B) 60
(C) 30 (D) 45
5. The value of 3 tan + 2 tan + sin is
(A) (B)
(C) 𝜋 (D) zero
6. If A and B are two matrices such that 𝐴𝐵 = 𝐵 and 𝐵𝐴 = 𝐴, then 𝐴 + 𝐵 =
(A) 2𝐴𝐵 (B) 2𝐵𝐴
(C) 𝐴 + 𝐵 (D) 𝐴𝐵
7. Let A, B be two square matrices such that 𝐴 + 𝐵 = 𝐴𝐵, then
(A) 𝐴𝐵 = 𝐵𝐴 (B) 𝐴𝐵 = −𝐵𝐴
(C) 𝐴𝐵 + 2𝐵𝐴 = 0 (D) 𝐴 = 𝐵
√
8. If 𝑦 = tan , then =

(A) (B)
( )

(C) (D)
( ) ( )

9. The second derivate of a sin 𝑡 w.r.t. 𝑎 cos 𝑡 at 𝑡 = is

(A)
√ (B) 2

(C) (D) 1

10. The set of all points where the function
0, 𝑥=0
𝑓 (𝑥 ) = 𝑥
, 𝑥≠0
1+𝑒
is differentiable in
(A) (0, ∞) (B) (−∞, ∞ ) − {0}
(C) (−∞, 0) (D) (−∞, ∞ )

(1)

11. The angle between the curves 𝑦 = sin 𝑥, 𝑦 = cos 𝑥 is

(A) (B) tan √2
(C) tan 2√2 (D)

12. If 𝑎𝑥 + ≥ 𝑐 for all +ve x, where 𝑎, 𝑏 > 0, then
(A) 27𝑎𝑏 ≥ 4𝑐 (B) 27𝑎𝑏 < 4𝑐
(C) 4𝑎𝑏 ≥ 27𝑐 (D) 4𝑎𝑏 < 27𝑐
13. The two curves 𝑦 = 4𝑥 𝑎𝑛𝑑 𝑥 + 𝑦 − 6𝑥 + 1 = 0 at the point (1, 2)
(A) Intersect orthogonally (B) Intersect at angle
(C) Touch each other (D) None of these

14. ∫ =
(A) log 1 + cot +𝑐 (B) log 1 − cot +𝑐
(C) log 1 + tan +𝑐 (D) log 1 − tan +𝑐

15. ∫ =
(A) 1 (B) 2
(C) -1 (D) 0
16. The area of the region bounded by the curve 𝑦 = 2𝑦 − 𝑥 and the y-axis is
(A) sq. units (B) sq. units
(C) sq. units (D) sq. units

17. The area bounded by the curves 𝑦 = 𝑥 and 𝑦 = 𝑥 is
(A) 1 sq. units (B) sq. units
(C) 2 sq. units (D) 0 sq. units

18. The solution of = is

(A) 𝑦 = 𝐶𝑒 (B) 𝑦 = 𝐶𝑒
(D) None of these
(C) 𝑦 = 𝐶𝑒
19. Solution of 𝑥 = 𝑦 + 𝑥𝑦 + 𝑥 + 1 is
(A) 𝑦 + 1 = 𝐴𝑒 (B) 𝑦 + 1 = 𝐴𝑥𝑒
(C) 𝑥𝑒 = 𝐶 (D) 𝑦 + 𝑥𝑒 = 𝐶
20. The solution of (𝑦 log 𝑥 − 1)𝑦𝑑𝑥 = 𝑥 𝑑𝑦 is
(A) 𝑦(log(𝑒𝑥) + 𝑐𝑥) = 2 (B) 𝑦 = log(𝑒𝑥) + 𝑐𝑥
(C) 𝑦 = log(𝑒𝑥 ) − 𝑐𝑥 (D) None of these
21. If 𝑎⃗ + 𝑏⃗ = 𝑎⃗ − 𝑏⃗ , then angle between 𝑎⃗ and 𝑏⃗ is (𝑎⃗, 𝑏⃗ ≠ 0)
(A) (B)

(C) (D)

(2)

22. If G is the centroid of a triangle ABC, then 𝐺𝐴 + 𝐺𝐵 + 𝐺𝐶 =
(A) 0⃗ (B) 3𝐺𝐴⃗
(C) 3𝐺𝐵⃗ (D) 3𝐺𝐶⃗
23. If 𝜃 is the angle between 𝚤⃗ + 𝚥⃗ + 𝑘⃗ and 2𝚤⃗ − 𝚥⃗ + 2𝑘⃗ , then sin 𝜃 =
(A) (B)
√

√ √
(C) (D)

24. The equation of the plane containing the two lines
= = and = = is
(A) 8𝑥 + 𝑦 − 5𝑧 − 7 = 0 (B) 8𝑥 + 𝑦 + 5𝑧 − 7 = 0
(C) 8𝑥 − 𝑦 − 5𝑧 − 7 = 0 (D) 8𝑥 − 𝑦 − 5𝑧 + 7 = 0
25. The area of the triangle whose vertices are (1, 2, 3), (2, 5, −1) and (−1, 1, 2) is
(A) 150 sq. units (B) 145 sq. units
√ (D) sq. units
(C) sq. units
26. The projection of a line segment on the co-ordinate axes are 12, 4, 3 respectively.
The length of the line segment is
(A) 13 (B) 15
(C) 16 (D) 19
27. The objective function of a L.P.P. is
(A) A constraint (B) A function to be optimized
(C) A relation between the variables (D) None of these
28. The minimum value of 𝑃 = 3𝑥 + 𝑦 subject to 2𝑥 + 3𝑦 ≤ 6, 𝑥 + 𝑦 ≥ 1, 𝑥 ≥ 0,
𝑦 ≥ 0 is
(A) ½ (B) 0
(C) 1 (D) 2
29. Which of the following statements is correct?
(A) Every L.P.P admits an optimal (B) A L.P.P. admits a unique solution
solution
(C) If a L.P.P. admits two optimal (D) A L.P.P. admits two optimal
solutions, then it has an infinite solutions
number of optimal solutions

30. If A and B are two independent events such that
𝑃(𝐴̅ ∩ 𝐵 ) = 𝑎𝑛𝑑 𝑃(𝐴 ∩ 𝐵 ) = , then 𝑃(𝐵) =
(A) or (B) or
(C) ¼ or ¾ (D) or 1

31. In a binomial distribution, mean=5 and variance=4, then the number of trials is
(A) 4 (B) 5
(C) 16 (D) 25

(3)

32. 3 distinct integers are selected at random from 1, 2, 3, … … . , 20. The probability
that the sum is divisible by 5 is
(A) 49/285 (B) 29/285
(C) 11/285 (D) 9/285
33. A card is drawn from a well shuffled pack of 52 cards. The probability that the
card is black or a club, is
(A) 1/3 (B) ¼
(C) ½ (D) 1/6
34. The number of values of k for which the linear equations
4𝑥 + 𝑘𝑦 + 2𝑧 = 0
𝑘𝑥 + 4𝑦 + 𝑧 = 0
2𝑥 + 2𝑦 + 𝑧 = 0
posses a non-zero solution is :
(A) 3 (B) 2
(C) 1 (D) 0
35. The coefficient of 𝑥 in the expression of (1 − 𝑥 − 𝑥 + 𝑥 ) is :
(A) 144 (B) -132
(C) -144 (D) 132
36. Let 𝑎 ≠ 𝑎 ≠ 0, 𝑓(𝑥 ) = 𝑎𝑥 + 𝑏𝑥 + 𝑐, 𝑔(𝑥 ) = 𝑎 𝑥 + 𝑏 𝑥 + 𝑐 and 𝑝(𝑥 ) =
𝑓 (𝑥 ) − 𝑔(𝑥). If 𝑝(𝑥) = 0 only for 𝑥 = −1 𝑎𝑛𝑑 𝑝(−2) = 2, then the value of
𝑝(2) is :
(A) 3 (B) 6
(C) 9 (D) 18
𝜔 0
37. If 𝜔 ≠ 1 is the complex cube root of unity and matrix 𝐻 = , then 𝐻 is
0 𝜔
equal to :
(A) H (B) 0
(C) –H (D) 𝐻
38. Let 𝛼, 𝛽 be the roots of 𝑥 − 6𝑥 − 2 = 0, with 𝛼 > 𝛽. If 𝑎 = 𝛼 − 𝛽 for 𝑛 ≥ 1,
then the value of is
(A) 1 (B) 2
(C) 3 (D) 4
39. The circle passing through the point (-1,0) and touching the y-axis at (0,2) also
passes through the point
(A) − , 0 (B) − , 2
(C) − , (D) (−4, 0)
40. A value of b for which the equations
𝑥 + 𝑏𝑥 − 1 = 0
𝑥 +𝑥+𝑏 =0
have one root in common is
(A) -√2 (B) – 𝑖√3
(C) 𝑖√5 (D) √2

(4)

41. If 𝑓 ∶ 𝑅 → 𝑅 is a function defined by 𝑓(𝑥) = [𝑥] cos 𝜋, where [𝑥] denotes
the greatest integer function, then f is :
(A) Discontinuous only at x=0. (B) Discontinuous only at non-zero
integral values of x.
(C) Continuous only at x=0. (D) Continuous for every real x.
42. If the line 2𝑥 + 𝑦 = 𝑘 passes through the point which divides the line segment
joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals :
(A) 5 (B) 6
(C) 11/5 (D) 29/5
43. Let P and Q be 3 × 3 matrices with 𝑃 ≠ 𝑄. If 𝑃 = 𝑄 𝑎𝑛𝑑 𝑃 𝑄 = 𝑄 𝑃, then the
determinant of (𝑃 + 𝑄 )is equal to :
(A) 1 (B) 0
(C) -1 (D) -2
44. The function 𝑓 ∶ [0, 3] → [1, 29], defined by 𝑓 (𝑥) = 2𝑥 − 15𝑥 + 36𝑥 + 1, is
(A) One-one and onto (B) Onto but not one-one
(C) One-one but not onto (D) Neither one-one nor onto
45. The slope of the normal to the curve 𝑦 = 2𝑥 + 3 sin 𝑥 𝑎𝑡 𝑥 = 0 is
(A) 3 (B) 1/3
(C) -3 (D) -1/3
46. The rectangle of maximum area that can be inscribed in a circle of radius 𝑎 is a
square of side :
(A) √2𝑎 (B)
√
(C) 2√2𝑎 (D)
√

47. For all real values of x, the minimum value of is
(A) 0 (B) 1
(C) 3 (D) 1/3
48. If 𝐴 = {1, 2, 3, 4, 5}, then the number of proper subsets of A is
(A) 120 (B) 30
(C) 31 (D) 32
49. If R is a relation on a finite set A having n elements, then the number of relations
on A is
(A) 2 (B) 2
(C) 𝑛 (D) 𝑛
50. The range of the function 𝑓(𝑥) = | | is
(A) 𝑅 − {0} (B) 𝑅— {−1, 1}
(C) {−1, 1} (D) 𝑅 − {1}
51. If tan 𝜃 + sec 𝜃 = 𝑒 , then cos 𝜃 equals
(A) (B)
(C) (D)

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52. The smallest positive angle which satisfies the equation
2 sin 𝜃 + √3 cos 𝜃 + 1 = 0 is
(A) (B)
(C) (D)

53. The least positive integer n such that is a positive integer, is
(A) 16 (B) 8
(C) 4 (D) 2
54. The amplitude of is equal to
(A) 1 (B)
(C) − (D) 𝜋

55. In the expansion of 2𝑥 − , the term without x is
(A) 7920 (B) -7920
(C) 495 (D) -495
56. If the first, second and last term of an A.P. are a, b and 2a respectively, then its
sum is
(A) ( )
(B)
(C) (D)
( )

57. If second term of a G.P. is 2 and sum of its infinite terms is 8, then its first term is
(A) ¼ (B) ½
(C) 2 (D) 4
58. The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (-2, 6). The
third vertex is
(A) (0, 0) (B) (4, 7)
(C) (7, 4) (D) (7, 7)
59. The circle 𝑥 + 𝑦 + 2𝑔𝑥 + 2𝑓𝑦 + 𝑐 = 0 does not intersect x-axis, if
(A) 𝑔 > 𝑐 (B) 𝑔 < 𝑐
(C) 𝑔 > 2𝑐 (D) 𝑔 < 𝑐
60. In a three dimensional space the equation 𝑥 − 5𝑥 + 6 = 0 represents
(A) Points (B) Planes
(C) curves (D) pair of straight lines
x-x-x
[ROUGH WORK]

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[ROUGH WORK]

(7)

[ROUGH WORK]

(8)

[ROUGH WORK]

(9)

[ROUGH WORK]

(10)