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CET 2016
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CET-2015 MATHEMATICS
IMPORTANT INSTRUCTIONS TO CANDIDATES
1. This question booklet contains 60 questions and each question will have one statement and four
distracters. (Four different options / choices. )
2. After the 3rd Bell is rung at 10.40 a.m., remove the paper scal on the right hand side of this
question booklet and a complete test booklet. Read each item and start answering on the OMR
answer sheet.
3. During the subsequent 70 minutes :
Read each question carefully.
Choose the correct answer from out of the four available distracters (options / choices) given
under each question / statement.
Completely darken / shade the relevant circle with a Blue or Black ink ball point pen against the
question number on the OMR answer sheet.
4. Please note that even a minute unitened ink dot on the OMR answer sheet will also be
recognised and recorded by the scanner. Therefore, avoid multiple markings of any kind on the
OMR anser sheet.
5. Uns the space provided on each page of the question booklet for Rough Work. Do not use the
OMR answer sheet for the same.
6. After the last bell is rung at 11.50 a.m., stop writing on the OMR answer sheet and affix your Left
hand thumb impression on the OMR answer sheet as per the intstructions.
7. Hand over the OMR answer sheet to the room invigilator as it is.
8. After separating the top sheet (Our Copy), the invigilator will return the bottom sheet replica
(Candidate’s copy) to you to carry home for self-evaluation.
9. Preserve the replica of the OMR answer sheet for a minimum period of One year.
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1. f(x)= 2
1- tan 11
2
x
x
and g(x) = ).443( 2xx
find domain of (f + g)
(1)
1,
2
1
(2)
1,
2
1
(3)
2
3,
2
1
(4) (-1,1)
2. Write the set builder form A = {-1, 1}
(1) A = {x : x is a real number}
(2) A = {x : x is an integer}
(3) A = {x : x is a root of equation x2 = 1}
(4) A = {x :x is a root of the equation x2 + 1 = 0}
3. If the operation is defined by a b = a2 + b2 for all real numbers ‘a’ and ‘b’, then (2
3) 4=
(1) 181
(2) 182
(3) 184
(4) 185
4. If Z =
,)68(
)43(32
23
i
ii
then |Z| is equal to
(1) 0
(2) 1
(3) 2
(4) 3
5. If and are the roots of x2 – ax + b
2 = 0, the
2 +
2 is equal to __________
(1) a2 – 2b
2
(2) 2a2 – b
2
(3) a2 – b
2
(4) a2 + b
2
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6. if the 2nd
and 5th
terms of G.P are 24 and 3 respectively, then the sum of 1st six term is
_______
(1) 2
189
(2) 5
189
(3) 2
179
(4) 189
2
7. The middle term of expansion of
10
10
10
x
x
(1) 7C5
(2) 8C5
(3) 9C5
(4) 10C5
8. If ,02
x2c
y x2b
y x2a
33
22
11
abc
y
then the area of the triangle whose vertices are
a
y
a
x 11 , .
c
y
c
x
b
y
b
x 3322 ,,, is
(1) 4
1abc
(2) 8
1abc
(3) 4
1
(4) 8
1
9. The shaded region shown in fig. is given by the inequation
(1) 14x + 5y 70 y 14 and x – y 5
(2) 14x + 5y 70 y 14 and x – y 5
(3) 14x + 5y 70 y 14 and x – y 5
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(4) 14x + 5y 70 y 14 and x – y 5
10. [(- p)^q] is logically equivalent to
(1) P v (q)
(2) P^(q)
(3) [p^(q)]
(4) (p v q)
11. The value of
Sin -1
3
22 + sin -1
3
1is equal to
(1) 6
(2) 2
(3) 4
(4) 3
2
12. If the eccentricity of the hyperbola 12
2
2
2
b
y
a
xis
4
5and 2x + 3y – 6 = 0 is a focal chord of
the hyperbola, then the length of transverse axis is equal to ____________
(1) 5
12
(2) 5
24
(3) 5
6
(4) 24
5
13. If bkjia
,22 and the angle between a
and b
is 6
, then the area of the triangle
formed by these two vectors as two sides is
(1) 2
15
(2) 15
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(3) 4
15
(4) 2
315
14. Let kjia 32
if b
is a vector such that a
, b
= b
and ba
= 7 , then b
=
___________
(1) 7
(2) 14
(3) 7
(4) 21
15. If direction cosines of a vector of magnitude 3 are 3
2,
3
9,
3
2 and a>0, then vector is ______
(1) 2i + j + 0k
(2) 21 – j + 2k
(3) i – 2j + 2k
(4) 8 + 2j + 2k
16. Equation of line passing through the point (2, 3, 1) and parallel to the line of intersection of
the plane x – y2 – z + 5 = 0 and x + y + 3 = 6 is
(1) 3
1
4
3
5
2
zyx
(2) 3
1
4
3
5
2
zyx
(3) 3
1
4
3
5
2
zyx
(4) 2
1
3
3
4
2
zyx
17. Foot of perpendicular drawn from the origin to the plane 2x – 3y + 4z = 29 is ____
(1) (5, -1,4)
(2) (2, - 3,4)
(3) (7, -1, 3)
(4) (5, -2, 3)
18. If two dice are thrown simultaneously, then the probability that the sum of the numbers
which come up on the dice to be more than 5 is ________
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(1) 36
5
(2) 6
1
(3) 18
5
(4) 18
13
19. If y = f(x2 + 2) and f
1(3) =5, then
dx
dy at x = 1 is _______
(1) 5
(2) 25
(3) 15
(4) 10
20. If x = a cos3,y=a sin
3, then
2
dx
dy is
(1) tan
(2) tan2
(3) sec2
(4) 1
21. Slope of Normal to the curve )0,1(1
2
2 atx
xy is
(1) 4
1
(2) 4
1
(3) 4
(4) -4
22.
4/34 12
1
xxdx is equal to __________
(1)
Cx
x
41
41
(2)
Cx
x
2
41
41
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(3)
Cx
x
2
1 41
4
(4)
Cx
x
43
41
23. If f: R R is defined by f(x) = ,12 x
xfind f(f(2))
(1) 29
10
(2) 29
1
(3) 10
29
(4) 29
24. Evaluate 75cos75sin
15sin15cos
(1) 1
(2) 0
(3) 2
(4) 3
25. A man takes a step forward with probability 0.4 and one step backward with probability
0.6. then the probability that at the end of eleven steps he is one step away from the
starting point is
(1) 53
11 48.0C
(2) 53
11 24.0C
(3) 36
11 12.0C
(4) 66
11 72.0C
26.
4/
0cos
cossinlog
dxx
xx
(1) 2log4
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(2) 2log2
(3) 2log8
(4) Log2
27. Area bounded by y = x3, y=8 and x=0 is ……..
(1) 2sq. units
(2) 14sq. units
(3) 12sq. units
(4) 6sq. units
28. Let ,,2 kjicandkjibkjia
a vector in the plane
a and
b whose
projection on
c is 3
1is ………
(1) 3i+j-3k
(2) 4i+j-4k
(3) I+j-2k
(4) 4i-j+4k
29. The mean deviation from the data 3,10,4,7,10,5:
(1) 3
(2) 2
(3) 3.75
(4) 2.57
30. The probability distribution of x is
x 0 1 2 3
P(x) 0.2 k k 2k
Find the value of k
(1) 0.2
(2) 0.3
(3) 0.4
(4) 0.1
31. If the function g(x) is defined by
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,52
.......198199200
)(2198199200
xxxxx
xg then g’(0) = …..
(1) 1
(2) 200
(3) 100
(4) 5
32. A box contains 6 red marbles numbers from 1 through 6 and 4 white marbles 15. Find the
probability that a marble drawn at random is white and odd numbered.
(1) 5
(2) 5
1
(3) 6
(4) 6
1
33.
is
x
x
x 20
cos1lim
(1) 2
(2) 3
(3) 2
1
(4) 3
1
34. f(x) =
52
583
xifk
xifxis continuous, find k.
(1) 7
2
(2) 7
3
(3) 7
4
(4) 2
7
35. If f(x) = 2x2, find
48.3
)4()8,3(
ff
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(1) 1.56
(2) 156
(3) 15.6
(4) 0.156
36. If x=ct and .2, tatdx
dyfind
t
cy
(1) 4
1
(2) 4
(3) 4
1
(4) 0
37. A balloon which always remains spherical is being inflated by pumping in 10 cubic
centimeters of gas per second. Find the rate at which the radius of the balloon is
increasing when the radius in 15 cms.
(1) sec/90
1cm
(2) sec/9
1cm
(3) sec/30
1cm
(4) sec/1
cm
38. x
x
cos1
sin 2
(1) x+sinx+C
(2) x-sinx+C
(3) sinx+C
(4) cosx+C
39.
.........
cos1
sin1isdx
x
xe x
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(1) Cx
e x
2tan
(2) Cx
2tan
(3) Ce x
(4) Cxe x sin
40. If 1, w, w2 are three cube roots of unity, then .........11 22 iswwww
(1) 1
(2) 2
(3) 3
(4) 4
41. Solve for x
0,tan2
1
1
1tan 11
xxx
x
(1) 3
(2) 1
(3) -1
(4) 3
1
42. The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions
when …….
(1) 32 ba
(2) 103 ba
(3) 32 ab
(4) 103 ab
43. The value of tan(10) + tan(89
0) is …….
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(1) 01sin
1
(2) 02sin
2
(3) 01sin
2
(4) 02sin
1
44. If
1
123
2
x
CBx
x
A
xx
x , then cosec
-1
CBA
11 sec1
cot1
(1) 6
5
(2) 0
(3) 6
(4) 2
45. The remainder obtained when 1!+2!+3! ……+11! Is divided by 12 is …….
(1) 9
(2) 8
(3) 7
(4) 6
46. If ,cossin2 11 xxa then
(1) 22
(2) 2
3
2
(3) 0
(4) 20
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47. If A =
01
10, then A
2 equal to …….
(1)
01
10
(2)
01
01
(3)
10
01
(4)
10
10
48. The function f(x) = [x], where [x] denotes greatest integer function is continuous at
………
(1) 4
(2) – 2
(3) 1
(4) 1.5
49. If y = logdx
dythen
x
x,
1
12
2
is equal to …………
(1) 41
4
x
x
(2) 4
3
1
4
x
x
(3) 44
1
x
(4) 4
3
1
4
x
x
50. The two curves 23023 3223 yyxandxyx
(1) Touch each other
(2) Cut at right angle
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(3) Cut at angle 3
(4) Cut at angle 4
51. If x is real, then the minimum value of .....1782 isxx
(1) 1
(2) 2
(3) 3
(4) 4
52.
4/
4/2cos1
x
dx is equal to
(1) 2
(2) 1
(3) 4
(4) 0
53. The order of differential equation of all circles of given radius ‘a’ is …….
(1) 4
(2) 2
(3) 1
(4) 3
54. The solution of differential equation
22 xydx
dyx is ……..
(1) 2
2
4x
Cxy
(2) Cx
y 4
2
(3) 2
4
x
Cxy
(4) 2
4
4x
Cxy
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55. If sin x+siny = 2
1 and cosx+cosy = 1, then tan (x+y) = ……..
(1) 3
8
(2) 4
3
(3) 3
8
(4) 3
4
56. If A =
2
2and ,273 A then …….
(1) 1
(2) 2
(3) 7
(4) 5
57. If P = x
x
1
1 and Q = ,
11
11
11
x
x
x
then dx
dQ……….
(1) 3P+1
(2) 1-3P
(3) -3P
(4) 3P
58. A line passes through (2,2) and is perpendicular in the line 3x+y = 3 its y-intercepts is ---
---------
(1) 3
1
(2) 3
2
(3) 3
4
(4) 1
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59. Let f: R R be defined by f(x) = ,1
Rxx
then f is …………..
(1) one-one
(2) onto
(3) bijective
(4) f is not defined
60. the solution set of the in equation isx
xx0
4
762
(1) ( -7, 1)
(2) (-7, -4)
(3) 1,44,7
(4) 1,44,7