PU CET UG 2015 Question Paper Maths

CET-2015 Sr. No.: 1138517

Booklet Series Code : A
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O.M.R. Answer Sheet Serial No.
Signature of the Candidate: .__ .,...- _
S rbject : MATHEMATICS
T me: 70 minutes Number of Questions : 60 Maximum Marks: 120
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Mathematic
1. Let A and B be two sets containing 3 and 4 elements respectively. The number of functions
from A to B is :
(A), 12 (B) 81
(C) 64 (D) 24
2. Let f: (2,3) -+ (0, 1) be defined by f(x) = x - [x], where [.] denotes the greatest integer value
function, then f-l(x) equals:
(A) x-2 ,(B) x + 1
(C) x-I (D) x + 2
3. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set
A = {3, 6, 9, 12}. The relation R is :
(A) an equivalence relation (B) reflexive and symmetric
(C) reflexive and transitive (D) only reflexive
4. Let f(x) = xl-2x-3, g(x) = f(lxl). The number of solutions ofg(x) = 0 ls/are :
(A) 2 (B) 3
(C) 4 (D) 0
5. In a right angle triangle ABC, with right angle at C, the value of tan A + tan B is :
(A) a + b (B) c2/ab
(C) a2/bc (D) b2/ac
6. Which one of the following is true?
(A) tan 1 = tan' 1 (B) tan 1 > tan:' 1
(C) tan 1 < tarr+l (D) tan 1 • tan" 1 '= 1

n -I 2k ' n -I k
7. Given that L cos ~ = 0, the value of L cos1 ---.! is :
k=O. n k=1 n

(A) 0 (B) 1

1 1
(C) 2 (n - 2) (D) 2 (n -1)

8. If sin x + sin1x + sin'x = 1 then cos'x - 4 cos'x + 8 cos'x equals:
(A) 1 (B) 2
(C) 3 (D) 4

MathematicsIBFH-30854-A 3 [Turnover
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9. Let S(k) =,1 + 3 + 5 + .....+ (2k - 1) = 3 + k1. Then which of the following is true?

(A) S(l) is correct

(B) S(k) => S(k + 1)

(C) S(k) i=> S(k + I)

(0) Principle of Mathematical Induction can be used to prove the formula for S(k)

10. If 1, w, w1, ..•, wn-I are the nth roots of unity then (2 -w)(2 _w1) •.... (2 _wn-I) equals:

(A) 2n - 1 (B) 2n

(C) 0 (0) -1

11. If n > 1 and if z" = (z +)n then:

I 1
(A) Rez =- (B) Rez = --
2 2

1 1
(C) Imz=- (0) Imz =--
2 2

12. If a. ~ (I + !)' then for DEN, which one of the following is not true?

(A) an ~ 2

(C) an < 4

13. The remainder when 21015is divided by 17 is :

(A) 1 (B) 2

(C) 8 (0) 9
14. The sum to n terms of the series

1 3 7 15
-+-+-+-+ .....
2- 4 8 16

is equal to:

(A) 2n-n-l (B) 1- 2-n

(C) 2-n + n - 1 (0) 2n-l

MathematicsIBFH-30854-A 4
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15. If a, b, c are digits then the rational number represented by O:c a b a b ab ..... is :

cab 99c + ab
(A) 990 (B)
990

99c + lOa+b 99c + 10a+b
(C)
99
(D)
990

16. Iffis a function satisfying

f(x + y) = f(x) . fey) for all ~, YEN,

n
such that f(l) = 3 and I f(x) = 120 then value ofn is :
x =I

(A) 4 (B) 5

(C) 6 (D) 7

17. If a(!
b
+ !),
c
b(!
c
+ !),
a
c(! + !)
ab·
are in AP then a, b, c are in :

(A) AP (B) GP

(C) HP (D) nothing can be said

18. If the straight lines

ax+may+l=O

bx+(m+l)by+l=O

c x + (m + 2) c y + 1 = 0, m ':f! 0

are concurrent, then a, b, c are in :

(A) AP only for m = I (B) AP for all m

(C) GP for all m (D) HP for all m

19. From the pointA(0,3) on the circle X2+4x + (y_3)2 =0, a chord AB is drawn and extended to
a point M such that AM = 2.AB. Then the locus of M is a :

(A) Straightline (B) Circle

(C) Parabola (D) Hyperbola

MathematicslBFH-30854-A 5 [Turn over
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20. The radius of the circle having the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 as tangents is :

1
(A) 1 (B) 2

2 3
(C) 3 (D) 4

21. The product of the lengths of the perpendiculars drawn from two foci of the hyperbola
xl yl
2"- 1 = 1 to any tangent to this hyperbola is :
a b
(A) a2
(C) b2

22. If A and B are the points (3, 4, 5) and (-1, 3,-7) respectively then theset of points Psuch that
PAl + PBl = Kl, where K is a constant lie on a proper sphere if:

(A) !C < 161
2

2

(C) K2 = 161 (D) K = 1
2

23. Which of the following functions is an eve~ function?

a" + a-x
= a +1
X

(A) f'(x) = (B) f(x)
aX _ a-x aX -1

aX -1
(C) f'(x) = x . (D) i(x) = IOg2 (x + ~x2 + 1 )
a" + 1

sin [x] .
24. If f(x) = for [x] :f: O. Then hm f(x) equals:
[x] 1--.0_

(A) 1
(C) sin 1
(B) °
(D) no number Le. does not exist .

25. The set of all points where the function f(x) = x Ix I is differentiable is :
(A) (-00, 00) (B) (-00, 0) U (0, 00)
,(C) (0,00) (D) [0,00)

MathematicsIBFH-30854-A 6
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26. Let fbe a function satisfying

X
f ( -2-
+ Y) = f(x) +2 f(y) ' for all real x and y.
Iff'(O) exists and equal-land f(O) = 1, then f(2) equals:

(A) 0 (B) -I
(C) (D) 3/2
27. Which ofthe following statements is true?
(A) p v - (p /\ q) is a tautology (B) - (p /\ q) = - P /\ - q
(C) Ifp ~ q is true, then p is true (D) p~q =q ~p
28. The mean deviation from mean of the observations a, a + d, a + 2d, ... a + t nd is :

n(n + l)d2 (B) n(n + l)d
2
(A) 3
2

n(n + l)d2 (D) n(n + 1)1dl
(C) a + --'---'---
2 2n + 1

29. Nine digit numbers are formed using 1, 2, 3, ..., 9 without repetition. The probability that the
number is divisible by 4 is :

(A) 217 (B) 3/8
(C) 1/9 (D) 2/9

•
30. A n e 11Ipse 0 ft··· 2..fi..ISmseri ·b ed i10 a circ
eccen rtctty -- . lee and
an aa noi
pom t WIithi10 th·e circ
. I·e ISCh osen a t
. 3
random. The probability that this point lies outside the ellipse is :

1 4
(A) 9 (B) 9

1 2
(C) 3 (D) 3

31. The relation R defined on the set of rea Is by (a, b) e R if and only i( 1 + ab >- 0 is :
(A) Reflexive but not symmetric . (B) Symmetric but not reflexive
(C) Symmetric but not transitive and reflexive (D) Reflexive, symmetric but not transitive

MathematicsIBFH-30854-A 7 [Turnover
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32. If f: [0, 1) -+ IR is defined by the rule

if x is a rational number
f(x) = {x
I-x if x is an irrational number

then:

(A) .f 0 f'(x) = x for all x E [0, 1] (B) fo f(x) = l--:-x for all x E [0,1]

(C) f 0 f'(x) = 1 for all x E [0, 1] (D) fof(x)=OforalIxE[O,I]

33. If f: R -+ IR is given by f(x) = 3x - 5 then f-I(x) :

I x+5
(A) is given by 3x - 5 (B) is given by -3 -

(C) does not exist as f is not one-one (D) does not exist as f is not onto

34. If sin' x + sin-I(1 - x) = COS-IX,then x equals:

(A) 1, -~ (B) 1, °
(C) 0,112 (D) 1, 1/2

t -I x -I X - Y
35. an - - tan -- equals:
y x+y

(A) 'Tt/2 (B) 'Tt/3
(C) 'Tt/4 (0) 'Tt/6

36. If A = [~ =:} [= _:]
B= aod (A + B)'=-[A' + B'] then a, bare:

(A) 1,-4 (B) -1,4

(C) -1,-4 (D) 1,4

37. Let A = ( : -~ -IJo . The only correct statement about the matrix A is :
. -1. 0 o .
(A) A2 = I (B) A=-I

(C) A-I does not exist (D) A is the zero matrix

MathematicsIBFH-30854-A 8
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38. If a" a2, ••• , an' ... are in GP., then the value of the determinant

log an log an + t log an + 2
log an + 3 log an + 4 log an + S is :
log an + 6 log an + 7 log an +'8

(A) -2 (8) 1
(C) 2 (0) 0

1
1 1
39. If D = 1 1 + X 1 for x :#: 0, Y :#: 0 then D is :
1 I" I+y

(A) divisible by x but not by y (8) divisible by y but not by x
(C) divisible by neither x nor y (0) divisible by both x and y

sin 0
4-8. Let A =l-s:n -1
0 1
-sin 0
Si~ 0
1
J where 0 S 9 S 27t. Then
.
:

(A) detA=O (8) detA E (2, (0)
(C) detA E [2.4] (0) det A E (2,4)

41. If a' + b2 + c2 =-2 and

. 1+ a2x (1 + b2)x (1 + c2)x "
f(x) = (1 + a2)x 1 + b2x (1 + c2)x
(1 +a2)x (1 + b2)x 1+ c2x

then f(x) is a polynomial of degree:

(A) 1 (8) 2
(C) 0 (0) 3

42. Suppose f(x) is differentiable at x = 1 and hm f(1 + h) = 5. Then f'(l) equals:
"" h~O h

(A) 5 (8) 3
(C) 4 (0) 6

MathematicslBFH- 30854-A 9 [Turnover
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43. Let fbe differentiable for all x. Iff(l) = -2 and f''(x) ~ 2 for x e (1,6], then:
(A) f(6) < 8 (8) f(6) < 5

(C) f(6) ~ 8 (0) f(6) = 5

44. Iffis a real valued differentiable function satisfying I f(x) - f(y) I ~ (x - y) for all real x and y
2

and f(O) = 0 then f(l) equals:

(A) -I (8)

(C) 2 (0) 0
45. Letf: R~R bea function defined by f(x) = min {(x + 1), I x] + I}. Then which of the following
is true?

(A) ttx) is differentiable everywhere (8) f(x) is not differentiable at x = 0

(C) f(x) ~ 1 for all real x (0) f(x) is not differentiable at x = 1

46. If f sm(x
. sin -x a) = A.x + B log sin (x - a) + C, then the value of (A, B) is :
(A) (- cos a, sin a) (8) (cos a, sin a)

(C) (- sin a, cos a) (0) (sin a, cos a)

47.
f cos xdx- sin x is equal to:
1
(A) -log
.fi tan (x2+g3X) +c

(C)
1
-log
.fi tan (x
---
2
3X)
8-
+c :

3
48. The value of fll - x2j dx is:
-2

(A) 1/3 (8) 14/3

(C) 7/3 (0) 28/3

_Mathematics/BFH-30854-A \0 ,
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If

49. J x f(sin x) dx is equal to :
o

1t

J f (sin
It

(A) 7t f f(cos x) dx (B) 7t x) dx
o o

1t/2 1t/2

(C) ; Jf(sin x) dx (0) 7t J f (cos x) dx
o o

50. The function f(x) = x + 2 has a local minimum at :
2 x

(A) x=2 (B) x =-2

(C) x=O (0) x= 1

51. The area enclosed between the curve y = loge (x + e) and the coordinate axes is :
(A) 3 (B) 2

(C) (0) 4

52. The differential equation for the family of circle Xl+ yl - 2ay = 0 where a is an arbitray
constant is :
(A) (x2 + y2)y'= 2xy (B) 2(x2 + y2)y'= xy

(C) (X2_y2)y'=2xy (0) 2(X2_y2)y'=XY

•..53. If a, b, c are distinct non negative numbers and the vectors a i+ a j + C k , i+ k and
cl +cj + bk lie in a plane, then c is:
(A) The Geometric Mean of a and b (B) The Arithmetic Meanofaand b

(C) Equal to zero' (0) The Harmonic Mean of a and b

54. If a, b, c are non Coplanarvecton and A.is a real number, then

II (a + b), II b, le j = [a, b + c, b ] for: '
(A) exactly one value ofA. (B) no value of A.in reals

(C) exactly three values oD. (0) exactly two values orA.

MathematicsIBFH-30854-A 11 [Turnover
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55. Distance between two planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is: .
(A) 2units (B) 4units

2
(C) 8units (0) J29 units
56. A line makes the same angle e, with each of x and z-axis. If the angle ~, which it makes with
y-axis is such that sin2~ = 3 sin2e, then cos2e equals:

(A) 2/5 (B) 1/5

(C) 3/5 (0) 2/3

3
57. The probability that A speaks truth is 4/5 while this probability for His 4 . The probability that

they contradict each other when asked to speak on a fact is :

(A) 4/5 (8) 1/5

(C) 7/20 (0) 3/20

58. The mean of the numbers obtained on throwing a die having written I on three faces, 2 on two
faces and 5 on onc face is :

(A) 1 (8) 2

(C) 5 (0) 8/3

59. The corner points of the feasible region determined by the following system of linear
inequalities: 2x + y S 10, x + 3y S 15, x, Y ~ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy,
p, q > O. The condition on p and q so that maximum of Z occurs at both (3, 4) and (0, 5) is :
(A) p = q (8) p = 2q

(C) p = Jq (0) q = 3p

60. The maximum value ofZ = 4x + 2ysubjected to the constraints 2x + 3y S 18, x + y ~ 10; where
x, y ~ 0 is :
(A) 36 (8) 40

(C) 20 (0) never attained

Mathematics/BFH-30854-A . 12
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Panjab University, Chandigarh
CET(UG)-2015
FINAL ANSWERS / KEY
Subject: MATHEMATICS
Booklet Series Code: A
1 2 3 4 5 6 7 8 9 10
C D C A B B C D B A

11 12 13 14 15 16 17 18 19 20
B D D C D A A D B D

21 22 23 24 25 26 27 28 29 30
C B C C A B A D D D

31 32 33 34 35 36 37 38 39 40
D A B C C A A D D C

41 42 43 44 45 46 47 48 49 50
B A C D A B A D D A

51 52 53 54 55 56 57 58 59 60
C C A B D C C B D D

Note: An 'X' in the key indicates that either the question is ambiguous or it has
printing mistake. All candidates will be given credit for this question.