CET 2016 - tnl-uploads.s3-ap-southeast-1.amazonaws.com · CET 2016 Byju’s Classes| 6.5 lakh + likes on . India’s most liked Educational Company | Contact: 9900012400 6. if the

CET 2016

Byju’s Classes| 6.5 lakh + likes on . India’s most liked Educational Company | Contact: 9900012400

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.

CET 2016


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

CET 2016


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 ________

CET 2016


(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

CET 2016


,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

CET 2016


(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 …….

CET 2016


(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

CET 2016


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

CET 2016


(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

CET 2016


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

CET 2016


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

Documents

CET 2016 - tnl-uploads.s3-ap-southeast-1.amazonaws.com · CET 2016 Byju’s Classes| 6.5 lakh + likes on . India’s most liked Educational Company | Contact: 9900012400 6. if the