PU CET UG 2026 Question Paper Maths

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PU CET UG 2026
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PU CET UG 2026 Question Paper Maths

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co m .
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em las

as ag [CET-UG-26- MATH] - A

1. Let E = {1, 2, 3, 4} and F = {1, 2}. Then the number of onto functions from E to F is
(A) 14 (B) 16 (C) 12 (D) 8

3 1  sin 
2. If cot θ = in the third quadrant, then the value of
4 1  sin 
1 1
m
(A) (B) 3 (C) (D) 9

c o
3 9
m .
co b em
a
.
n
3. In the binomial expression (a - b) , n ≥ 5, the sum of the fifth and sixth terms is zero. then is

e m l a s
equal to
l a s a g
n  5ag
6 5 1 1
(A) (B) (C) n  4 (D) n  5
n4 5 6
    
4. If a and b are two perpendicular unit vectors, then a × ( a × b ) is equal to
   
(A)  a (B) a (C) b (D)  b
 
5. The absolute maximum value of f ( x )  sin 2 x  cos 2 x, x  0,  is
 2
(B) 2 2 2
m
(A) 0 (C) 2 (D)

. co
6. Find the equation of the line which passes through the point of intersection of the line

em
2x - 3y = 0 and 4x - 5y = 2 and which is perpendicular to the line x + 2y + 1 = 0.
(A) 2x - y - 4 = 0 (B) 2x - y + 4 = 0
l a s
(C) 2x - 3y + 5 = 0 (D) 2x - 3y - 5 = 0

7. In △ABC, 2ac sin
A BC
is equal to a g
2
(A) a2 + b2 - c2 (B) c2 + a2 - b2 (C) b2 - c2 - a2 (D) c2 - a2 - b2
5 4 1  2 
8. If   X    , where X is a 2 × 2 matrix, then X =
1 1 1 3 
 3 14   3  14    3 14    3  14 
(A)   (B)   (C)   (D)  
17 
m
  4 17    4 17   4  17   4

m c. o
c. o m
9. R is a relation over the set of integers and it is given by (x, y) ∈ R ⇔ |x - y| ≤ 1. Then R is a

s e
em
(A) Reflexive and transitive (B) Symmetric and transitive

s
(C) Reflexive and symmetric
g l a
(D) An equivalence relation

gla a
a
10. If the system of equations x - ky - z = 0, kx - y - z = 0 and x + y - z = 0 has a non-zero solution then
the possible values of k are
(A) -1, 2 (B) 1, 2 (C) 0, 1 (D) -1, 1
tan x  sin x
11. Evaluate lim
x 0 x3
1 1 1
(A) 0 (B) (C) (D)
2 4 8

m . c
c. o m
(1)

m s e
se
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[CET-UG-26- MATH] - A

dy
12. Find , when log(xy) = x2 + y2
dx
2 x  1y
2
2 x  1y
2
2 x  1y
2
2 x  1y
2

x1  2 y  x1  2 y  x1  2 y  x1  2 y 
(A) 2 (B) 2 (C) 2 (D) 2

13. A particle moves along a line according to the law s = t3-6t2+9t+3. Find the velocity of the particle
at the instant where its acceleration is zero.
(A) 3 unit/sec (B) 5 unit/sec (C) -3 unit/sec (D) -5 unit/sec

14. Find the equation of normal to the curve y = x + sin x cos x at x =
2
   
(A) x  0 (B) x  0 (C) y  0 (D) y  0
2 2 2 2
 x 1  1  x  1  
15. Solve the equation tan 1    tan    for x.
 x2  x2 4
1
(A) x = 2 and x   (B) x  2 and x   2
2
1 1 1
(C) x  and x   (D) x   2 and x 
2 2 2
  7  7 
16. Let f(x) = [x] and g(x) = |x|, evaluate gof      fog   
  3  3 
(A) -5 (B) -3 (C) -1 (D) 1
17. If f : R × R → R such that f(x + iy) = + x 2  y 2 . then f is
(A) many-one and into (B) one-one and onto
(C) many-one and onto (D) one-one and into
18. Find the equation of the normal to the curve 2x2 - y2 = 14 which is parallel to 3y + x = 4
(A) 3x + 9y = ±2 (B) 3x + 9y = ±17
(C) x + 3y = ±6 (D) x + 3y = ±9
19. If z is a nonreal complex number then which of the following may not be real?
(C)  z  z 
2
(A) z  z (B) z 2  z 2 (D) z 3  z 3
 
20. The unit vector perpendicular to both the vectors a  iˆ  ˆj  kˆ and b  2iˆ  ˆj  3kˆ and making an
acute angle with the vector k̂ is

(A)
1
26

4iˆ  ˆj  3kˆ  (B)
1
26

4iˆ  ˆj  3kˆ 
(C) 
1
26

4iˆ  ˆj  3kˆ  (D) 
1
26

4iˆ  ˆj  3kˆ 

(2)

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co m .
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as ag [CET-UG-26- MATH] - A

 3 5
21. Evaluate cos sin 1  sin 1 
 5 13 
63 33 13 27
(A) (B) (C) (D)
65 65 65 65
22. If 2n+1Pn-1 : 2n-1Pn = 7 : 22, find n

m
co
(A) 6 (B) 8 (C) 10 (D) 12

. om
c (B) 19
23. Compute the area bounded by the lines y = 4x + 5, y = 5 - x and 4y - x = 5
e m .
15
e m 39 43
l a s
s g
(A) (C) (D)
a
oflthe function f(x) = |x - 1| + |x - 2|, - 1 ≤ x ≤ 3, is a
2 2 2 2
24. The range g
(A) [1, 3]a (B) [1, 4] (C) [3, 5] (D) [1, 5]
 5x  2  4 x  4 x2

25. For what value of k, the function f ( x )   x2 , is continuous at x = 2?
 x2
k;
1 1 1 1
(A) (B) (C) (D)

m
5 3 4 3 3 3 2 3

. co
26. The arithmetic mean and the geometric mean between two positive numbers a and b, where

em
s (B) m  m  n : m  m  n
a > b are in the ratio m : n. Then the ratio of numbers a and b is
(A) m  m 2  n 2 : m  m 2  n 2
l a
g (D) m  m  n : m  m  n
2 2 2 2

(C) m  m 2  n 2 : m  m 2  n 2 a 2 2 2 2

27. If f(x) = (x2 - x + 2)(x2 - 4) then the set {x : f(x) > 0, x ∈ R} is equal to
(A) (-∞, -2) (B) (2, ∞) (C) (-2, 2) (D) (-∞, -2)  (2, ∞)
        
28. Let a  iˆ  ˆj  kˆ , c  ˆj  kˆ. If b is a vector satisfying a × b = c and a · b = 3, then b is


1 ˆ
5i  2 ˆj  2kˆ  (B) 3iˆ  ˆj  kˆ 
1 ˆ
5i  2 ˆj  2kˆ  (D) 3iˆ  ˆj  kˆ
m
(A) (C)

c. o
3 3

m
c. o m
29. For what values of λ, the line 3x - 4y = λ touches the circle x2 + y2 - 4x - 8y - 5 = 0

s e
em30. Calculate Cov(x, y) if  x = 100,  y = 140,  (x - 10)(y - 15) = 60 and an = 10.
(A) 15 and 35 (B) -35 and 15 (C) -30 and 15 (D) -30 and 5

s g l
gla i i
a (D) 0.4
i i

a (A) 6 (B) 13 (C) 3.5

31. Four persons are chosen from a group consisting of 2 men, 3 women and 4 children. Then the
chance that at most two of them will be children.
1 1 5 5
(A) (B) (C) (D)
6 21 6 21

m . c
c. o m
(3)

m s e
se
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[CET-UG-26- MATH] - A

5
32. Evaluate  f ( x ) dx, when f(x) = |x - 2| + |x - 3| + |x - 4|
2

31 9 19 11
(A) (B) (C) (D)
2 2 2 2
33. The equation zz + (4 - 3i)z + (4 + 3i) z + 5 = 0 represents a circle whose radius is
5 3
(A) 2 5 (B) 5 (C) (D)
2 2
n! n!
34. If and are in the ratio 2 : 1, find the value of n
2!n  2! 4!n  4!
(A) 11 (B) 9 (C) 7 (D) 5
35. Find the general solution of (1 + x)(1 + y2)dx + (1 + y)(1 + x2)dy = 0.
1
 
(A) tan y  log 1  y 2 1  x 2  tan 1 x  C
1
 1
1
(B) tan y  log
 
1 y2
 tan1 x  C
2 2  
1 x 2

1
  
(C) tan 1 y  log 1  y 2 1  x 2  tan 1 x  C
11
(D) tan y  log
1  y   tan x  C
2
1

2 2 1  x  2

1 1
36. If the mth term of an A.P. is and the nth term be , then the mnth term is
n m
(A) m - n (B) 1 (C) mn (D) 1 + mn
37. Find the coefficient of correlation between x and y when n = 10,  x = 50, y = -30,
x 2 = 290, y 2 = 300, xy = -115.
(A) 0.54 (B) 0.91 (C) 0.38 (D) 0.77
38. The optimal feasible solution of linear programming problem, if it exists, will exist at least at one of
the following points of the feasible region.
(A) Interior point (B) Corner point
(C) Boundary point which is not a Corner Point (D) Exterior point
x 1
39. Integrate with respect to x
2  3x
10 2 10 2
(A)  2  3x  2  3x 3  C (B)  2  3x  2  3x 5  C
9 27 9 27
9 2 9 2
(C)  2  3x  2  3x 3  C (D)  2  3x  2  3x 5  C
10 27 10 27
40. One card is drawn at random from a well shuffled pack of 52 cards. Find the probability of drawing
either a red card or a queen
1 7 2 5
(A) (B) (C) (D)
26 13 13 26

(4)

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co m .
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as ag [CET-UG-26- MATH] - A

p q
41. Solve the equation   p  q , for x
px  1 qx  1
pq 1  pq 1  pq 2   2 p  q  1 
(A)  ,  (B)  ,  (C)  ,  (D)  , 
 pq p  q   2 pq p  q   pq p  q   pq p  q

m
42. Form the differential equation of the family of all circles passing through the origin and having

om . co
their centers on y-axis.
 
.c   m
dy dy
e
(A) x 2  y 2  2 xy  0 (B) x 2  y 2  2 xy  0
m a s
 ase
dx dx

g l
  
a
dy dy
l
(C) x 2  y 2  2 xy 0 (D) x 2  y 2  2 xy 0

ag dx dx
43. If z = x + iy satisfies amp(z - 1) = amp(z + 3i), then the value of (x - 1) : y is equal to
(A) 2 : 1 (B) -2 : 1 (C) -1 : 3 (D) 1:3
44. Find the interval in which the function f(x) = x3 + 5x2 - 1 is strictly decreasing
 10   10   10   10 
(A)   ,1 (B)  0,  (C)   ,0  (D)   1, 
 3   3  3   3

m
45. Find the equation of the plane passing through the point (-1, -1, 2) and perpendicular to each of the

c. o
planes 3x + 2y - 3z = 1 and 5x - 4y + z = 5

m vectors  6iˆ  3 ˆj  2kˆ, 3iˆ  ˆj  4kˆ, 5iˆ  7 ˆj  3kˆ,
(A) 7x - 6y + 11z = 21 (B) 5x - 6y + z = 3 (C) 7x + 9y + z = -14 (D) 5x + 9y + 11z = 8

s e
l a
46. Find the value of λ so that four points with position
g
ˆ ˆ ˆ
 13i  17 j  k , are coplanar.
(A) λ = -2 (B) λ = 2
a (C) λ = -1 (D) λ = 1
47. Find the square root of 6 + 8i
(A) 2  2 2i ,  2  2 2i (B) 2 2  2i ,  2 2  2i
(C) 7  i and  7  i (D) 3  3i and  3  3i
0 1 2
 
m
c. o
48. Find the inverse of the matrix  1 2 3 

m
c. o  1  1 1 
3 1 1
m
 

m (A) 1   8 6  2  s e
e la
 1 1 1 

s
1 

l a ag
(B)   8 6  2 

g
2 2
a  5 3 1   5 3 1 


 1 1 1   1 1 1 
1  1 
(C)   8 6  2  (D)   8 6  2 
2  2 
 5 3 1   5 3 2 
49. If sin θ + cosec θ = 2, then the value of sin8 θ + cosec8 θ is equal to
(A) 2 (B) 24 (C) 26 (D) 28

m . c
c. o m
(5)

m s e
se
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[CET-UG-26- MATH] - A

50. Find two positive numbers x and y such that x + y = 16 and x5y3 is maximum.
(A) 7, 9 (B) 8, 8 (C) 10, 6 (D) 12, 4
51. If | tan x| ≤ 1 and x ∈ [-π, π], then the solution set for x is
 3       3       3 
(A)   ,    ,    ,   (B)  ,    ,  
 4   4 4  4   4 4  4 
 3   3   3     
(C)   ,    ,   (D)   ,    , 
 4 4   4   4 4
52. The third term of a Geometric Progression is 4. The product of first five terms is
(A) 43 (B) 45 (C) 42 (D) 4
53. Find the orthocentre of the triangle whose angular points (or vertices) are (0, 0), (2, -1) and
(-1, 3).
(A) (-4, -3) (B) (4, 3) (C) (-3, -4) (D) (3, 4)
54. The value of (1 + i)3 + (1 - i)6 is
(A) i (B) 2(-1 + 5i) (C) 1 - 5i (D) 3 - 2i
55. Find the angle A of the triangle whose vertices are A(0, -1, -2), B(3, 1, 4) and C(5, 7, 1).
  
(A) (B) (C) (D) 
2 3 4
56. The coefficient of x15 in the product (1 - x)(1 - 2x)(1 - 22x)(1 - 23x)...(1 - 215x) is equal to
(A) 2105 - 2101 (B) 2120 - 2104 (C) 2121 - 2101 (D) 2105 - 2121

57. The number of values of x ∈ [0, 4π] satisfying 3cos x - sin x  2 is
(A) 2 (B) 0 (C) 4 (D) 8
 1 3  3  4i 
58. The modulus of     is
 1  2i 1  i  2  4i 
82 29 13 29
(A) (B) (C) (D)
4 4 5 17
sin x cos x cos x
 
59. The number of distinct real roots of cos x sin x cos x  0 in the interval   x  is
4 4
cos x cos x sin x
(A) 0 (B) 1 (C) 2 (D) 3
3 2
60. The minimum value of f(x) = x - 9x + 24x - 12 is
(A) -9 (B) -1 (C) 7 (D) 4
x-x-x

(6)

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co m .
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em las

as ag [CET-UG-26- MATH] - A

ROUGH WORK

m
om . co
.c e m
e m l a s
l a s a g
ag

m
. co
s em
g l a
a

m
m c. o
c. o s e m
s em la
gla ag
a

m . c
c. o m
(7)

m s e
se
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[CET-UG-26- MATH] - A

ROUGH WORK

(8)

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co m .
. e
em las

as ag [CET-UG-26- MATH] - A

ROUGH WORK

m
om . co
.c e m
e m l a s
l a s a g
ag

m
. co
s em
g l a
a

m
m c. o
c. o s e m
s em la
gla ag
a

m . c
c. o m
(9)

m s e
se
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[CET-UG-26- MATH] - A

ROUGH WORK

(10)

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