www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

Padasalai.Net’s Special – Centum Coaching Team

Question Paper 2017-2018

XII MATHEMATICS - 4

Marks: 200 Time: 3 hours

Part I Choose The Best Answer 40 x 1 = 40

1. If A and B are any two matrices such that AB = 0 and A is non-singular, then

a) B = 0 b) B is singular c) B is non-singular d) B = A

2. If cbeae yx ; dqepe yx andqp

ba1 ;

qd

bc2 ;

dp

ca3 then the value of ( x, y ) is

a)

1

3

1

2 ,

b)

1

3

1

2 log,log

c)

2

1

3

1 log,log

d)

3

1

2

1 log,log

3. Inverse of

25

13

is , a)

35

12

b)

31

52

c)

35

13 d)

21

53

4. If pand q

and qp

are vectors of magnitude then the magnitude of qp

is

a) 2 b) 3 c) 2 d) 1

5. The value of ikkjji

,, is equal to a) 0 b) 1 c) 2 d) 4

6. The equation of the plane passing through the point (2, 1, -1) and the line of intersection of

the planes 0)3( kjir

and 0)k2j(r

is,

a) x+4y-z=0 b) x+9y+11z=0 c) 2 x+y-z+5=0 d) 2x-y+z=0

7. The following two lines 1

z

1

1y

2

1x

and 2

1z

5

1y

3

2x

are,

a) parallel b) intersecting c) skew d) perpendicular

8. The vector dcba

is

a) perpendicular to a

, b, c

and d

b) parallel to the vectors ba

and dc

c) parallel to the line of intersection of the plane containing a

and b

and the plane

containing c

and d

d) perpendicular to the line of intersection of the plane containing a

and b

and the

plane containing c

and d

9. If )4()5( nim is the complex conjugate of )23()32( nim then (n,m) are

a)

8,

2

1

b)

8,

2

1

c)

8,

2

1

d)

8,

2

1

10. The points 4321 ,,, zzzz in the complex plane are the vertices of a parallelogram taken in order

if and only if

a) 3241 zzzz b) 4231 zzzz

c) 4321 zzzz d) 4321 zzzz

11. If is the nth root of unity then

a) ..................1 5342 b) 0n c) 1n d) 1 n

12. The line 2x + 3y + 9 = 0 touches the parabola x8y2 at the point.

a)(0,-3) b) (2,4) c)

2

9,6

d)

6,

2

9

13. The radius of the director circle of the conic 144y16x9 22 is

a) 7 b) 4 c) 3 d) 5.

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

14. The product of the perpendiculars drawn the point (8,0) on the hyperbola 136

y

64

x 22

to its

asymptotes is a) 576

25

b) 25

576

c) 25

6

d) 6

25

15. A spherical snowball is melting in such a way that its volume is decreasing at a rate of

.min/1 3cm The rate at which the diameter is decreasing when the diameter is 10 cms is

a) min/

50

1cm

b) min/

50

1cm

c) min/

75

11cm

d) min/

75

2cm

16. For the curve x = et cos t ; y = et sin t the tangent line is parallel to the x axis when t is

equal to

a) – 4 b) 4 c) 0 d) 2

17. The curve y = -e-x is…

a) concave upward for x > 0 b) concave downward for x > 0

c) everywhere concave upward. d) everywhere concave downward.

18. The curve 9y² = x² (4-x²) is symmetrical about.

a) y axis. b) x axis. c) y = x d) both the axes.

19. The value of

4/

0

3 xdx2cos

is

a) 2 / 3 b) 1/ 3 c) 0 d) 32

20. The volume, when the curve y = 2x3 from x = 0 to x = 4 is rotated about x axis is .

a) 100 b) 9

100 c)

3

100 d) 100 / 3

21. The curved surface area of a sphere of radius 5, intercepted between two parallel planes of

distance 2 and 4 from the centre is.

a) 20 b) 40 c) 10 d) 30

22. Integrating factor of 2x

2y.

xlogx

1

dx

dy is

a) ex. b) log x. c) 1/ x d) e-x.

23. The complementary function of (D² + 1 ) y = e2x is.

a) (Ax+B)ex. b) A cos x + B sin x . c) (Ax+B)e2x. d) (Ax+B)e-x.

24. The integrating factor of the differential equation xcosxtanydx

dy is

a) sec x . b) cos x. c) etanx. d)cot x.

25. Which of the following is a contradiction ?

a) p v q. b) p ^ q c) p v ~p. d) p ^ ~p

26. The order of –i in the multiplicative group of 4th roots of unity

a)4 b) 3 c) 2 d) 1

27. Which of the following are statements ?

i) May God bless you ii) Rose is a flower

iii) Milk is white. iv) 1 is a prime number.

a) (i), (ii), (iii) b) (i), (ii),(iv) c) (i), (iii), (iv) d) (ii), (iii), (iv)

28. Given E(X +c) = 8 and E (X –c) = 12 then the value of c is.

a) -2 b) 4 c) -4 d) 2.

29. If in a Poisson distribution P(X=0) = k then the variance is.

a) log 1/ k b) log k. c) e d) 1 / k

30. The marks secured by 400 students in a Mathematics test were normally distributed with

mean 65. If 120 students got more marks above 85, the number of students securing

marks between 45 and 65 is.

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

a) 120 b) 20 c) 80 d) 160

31. In the system of 3 linear equations with three unknowns, if 0 and all 2 x 2 minors of

0 and atleast one 2 x 2 minor of x or y or z is non-zero then the system is

a) consistent b) inconsistent

c) consistent and the system reduces to two equations

d) consistent and the system reduces to a single equation

32. The angle between the vectors kji 623 and kji 84 is

a)

63

34cos 1

b)

63

34sin 1

c)

63

34sin 1

d)

63

34cos 1

33. The modulus values of and

a) 5,5 b) 15,52 c) 13,22 d) -4, 1

34. The point of contact of the tangent cmxy and the ellipse 12

2

2

2

b

y

a

x is

a)

c

ma

c

b 22

,

b)

c

b

c

ma 22

,

c)

c

b

c

ma 22

,

d)

c

b

c

ma 22

,

35. If the temperature C of the certain metal rod of “ l “ meters is given by 20000004.000005.01 l then the rate of change of l in m / C ° when the

temperature is 100°C is

a) Cm00013.0 b)

Cm00023.0 c)

Cm00026.0 d)

Cm00033.0

36. The curve 222 1 xxy is defined only for

a) 22 xandx b) 11 xandx c) 11 xandx d) 11 xandx

37. If n is odd then

2

0

sin

dxxn is

a)

2 4

1 3 5 2

n n n

n n n

b)

1 3 5 1

2 4 2 2

n n n

n n n

c)

2 4 31

1 3 5 2

n n n

n n n

d)

1 3 5 21

2 4 3

n n n

n n n

38. The order and degree of the differential equation 72

2

3

3

y

dx

dy

dx

yd

dx

ydare

a) 3 , 1 b) 1 , 3 c) 3 , 5 d) 2 , 3

39. If p is true and q is false then which of the following statements is not true ?

a) qp is false b)

qp is true c)

qp is false d)

qp is true

40. Which of the following is not true regarding the normal distribution?

a) skewness is zero b) Mean = median = mode

c) the Points of inflection are at X d) maximum height of the curve is 2

1

Part II Answer Any 10 Of The Following Questions 10 X 6 = 60 Q.no 55 is compulsory

41. Find the rank of the matrix

2751

5121

1513

i22 i32

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

42. Find the adjoint of the matrix

53

21A and verify the result

.A A )A adj ( )A adj (A

43. a) Find the angles which the vector kji 2 makes with the coordinate axes.

b) If A (-1,4,3) is one end of a diameter AB of the sphere 015223222 zyxzyx , then

find the coordinates of B

44. a) If 0.,0.,0. cxbxax and 0x then show that cba ,, are coplanar

b) For any vector r prove that kkrjjriirr

45. a) Simplify :

612

57

5sin5cos4sin4cos

3sin3cos2sin2cos

ii

ii

b ) If iziz 23,2 21 and iz2

3

2

13

find the conjugate of (i) 21 zz (ii) 43z

46. Find the equation of the asymptotes to the hyperbola 02423108 22 yxyxyx

47. a) Prove that xe is strictly increasing function on R.

b) Find the critical numbers of xx 453

48. If zyxu tantantanlog , prove that 22sin

x

ux

49. Find the volume of the solid generated when the region enclosed by 2, yxy and 0x

is revolved about the y – axis.

50. Solve: xeyDD 22 1213

51. Prove that identity element of a group is unique. 52. a) Prove that inverse element of an element of a group is unique.

b) State and prove reversal law on inverse of a group.

53. A game is played with a single fair die. A player wins Rs. 20 if a 2 turns up, Rs. 40 if a turns up, loses Rs. 30 if a 6 turns up. While he neither wins nor loses if any other face turns up. Find the expected sum of money he can win.

54. Let X be a binomially distributed variable with mean 2 and standard deviation .3

2Find

the corresponding probability function.

55. At what angle do the curves xay and xby intersect ba ? (or)

a) Graphically prove that 321321 zzzzzz

b) Find the least positive integer n such that 11

1

n

i

i

Part III Answer Any 10 Of The Following Questions 10 X 10 = 100

Q.no 70 is compulsory

56. A small seminar hall can hold 100 chairs. Three different colours ( red, blue and green) of

chairs are available. The cost of a red chair is Rs. 240, cost of blue chair is Rs. 260 and the

cost of a green chair is Rs. 300. The total cost of chair is Rs. 25,000. Find atleast 3

different solution of the number of chairs in each colour to be purchased.

57. Find the vector and Cartesian equations of the plane passing through the points (2,2,-1) ,

(3,4,2) and (7,0,6)

58. Verify dcbacdbadcba where kjia ; kib 2 ; kjic 2 ;

kjid 2

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

59. If P represents the variable complex number z. Find the locus of P, if 21

12Im

iz

z

60. The arch of a bridge is in the shape of a semi –ellipse having a horizontal span of 40ft and

16ft high at the centre. How high is the arch, 9ft from the right or left of the centre. 61. A comet is moving in a parabolic orbit around the sun which is at the focus of a parabola.

When the comet is 80 million kms from the sun, the line segment from the sun to the

comet makes an angle of 3

radians with the axis of the orbit. Find (i) the equation of the

comet’s orbit (ii) how close does the comet nearer to the sun?( Take the orbit as open rightward ).

62. Find the eccentricity, centre, foci, and vertices of the following hyperbola and draw the

diagram : 01643236169 22 yxyx

63. Show that of all the rectangles with a given area the one with smallest perimeter is a square.

64. Using Euler’s theorem, prove that uy

uy

x

ux tan

2

1

if

yx

yxu 1sin

65. Find the area of the region bounded by the parabola xy 42 and the line .42 yx

66. Find the surface area of the solid generated by revolving the arc of the parabola ,42 axy

bounded by its latus rectum about x - axis.

67. Solve : 011 dyyxedxe yxyx

given that ,1y where 0x

68. Prove that the set of four functions 4321 ,,, ffff on the set of non-zero complex numbers

0C defined by 0

11,, 4321 Cz

zzfand

zzfzzfzzf

forms an abelian group

with respect to the composition of functions. 69. The mean weight of 500 male students in a certain college in 151 pounds and the standard

deviation is 15 pounds. Assuming the weights are normally distributed, find how many students weigh (i) between 120 and 155 pounds (ii) more than 185 pounds.

70. Prove that the sum of the intercepts on the co-ordinate axes of any tangent to the curve

20,4sin,4cos

ayax

is equal to a. (or)

Solve:

xeydx

dy

dx

yd 3

2

2

223

when 0,2log yx and 0,0 yx

ALL THE BEST

CREATED BY,

S.SARAVANA KUMAR , TEACHER

MARY ANN MATRIC HIGHER SECONDARY SCHOOL

K.PUDUR, MADURAI -625007

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

ANSWER SHEETS SEND THIS ADDERESS

S.SARAVANA KUMAR

2/291, KULANTHAI YESU STREET BACK STREET, ANKAYAR KANNI COLONY

AATHIKULAM, K.PUDUR

MADURAI -625007

PHONE: 7092681321 (SCHOOL TIME PLEASE DON’T CALL)

8608033637

www.Padasalai.Net www.TrbTnpsc.com

Padasalai.Net’s Centum Coaching Team

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

?

1. Click Here & Enter Your Details (Students Only)

2.

,

.

3. A4 Size (Or) Legal Size .

“ ”

.

4. ” ”

,

.

5.

. .

6. (Return Cover)

.

7. 3

” ”

. Click Here for Complaint Box!

8. Slow Learners ,

,

,

, .

-

Mr. S.SARAVANA KUMAR, (Teacher), 2/291, KULANTHAI YESU STREET

BACK STREET, ANKAYAR KANNI COLONY, AATHIKULAM, K.PUDUR

MADURAI -625007 Cell: 7092681321, 8608033637

If any doubt, Please contact our Padasalai’s Centum Coaching Team Co-ordinator:

Mr. S. Ravi kumar, B.Sc., B.Ed., Headmaster., GHS, PasmarPenta,, Vellore Dt: CellNo: 9994453649

Useful Links:

1. All Other Subject Question Papers Download - Click Here

2. Centum Coaching Team Instructions - Click Here

3. Centum Coaching Team Teacher's Registration Form - Click Here

4. Centum Coaching Team Student's Registration Form - Click Here