www.Padasalai.Net www.TrbTnpsc.com

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

PADASALAI.NET- CENTUM COACHING TEAM 2017-18

XII MATHEMATICS

Marks: 200 Time: 3 hours

Part I Choose The Best Answer 40 x 1 = 40

1. If A is a matrix of order 3, then det(kA) is,

a) )Adet(k3 b) )Adet(k2 c) )Adet(k d) det (A)

2. Inverse of

25

13

is , a)

35

12

b)

31

52

c)

35

13 d)

21

53

3. If the equations –2x+y+z=l ; x-2y+z=m ; x+y-2z=n such that l+m+n = 0, then the system has a)

non-zero unique solution b) trivial solution

c) infinitely many solutions d) no solution

4. The area of the parallelogram having a diagonal kji3

and a side k4j3i

is,

a) 310 b) 306 c) 302

3 d) 303

5. If

PR = kji2

,

QS = k2j3i

then the area of the quadrilateral PQRS is

a) 35 b) 310 c) 2

35 d)

2

3

6. If ac,cb,ba

= 8 then c,b,a

is

a) 4 b) 16 c) 32 d) -4

7. If the magnitude of moment about the point kj

of a force kjai

acting through the point ji

is

8 then the value of a is

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

8. 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

9. If ia 3 and iz 32 then the points on the Argand diagram representing azaz 3, and az are

a) vertices of a right angled triangle b) vertices of an equilateral triangle

c) vertices of an isosceles triangle d) collinear

10. If 122 yx then the value of iyx

iyx

1

1 is a)

iyx b) x2 c)

iy2 d)

iyx

11. If z lies in the third quadrant then z lies in the quadrant

a) first quadrant b) second quadrant c) third quadrant d) fourth quadrant

12. The angle between the two tangents drawn from the point (-4, 4) to x16y2 is.

a) 45 b)

30 c) 60 d)

90

13. The asymptotes to the rectangular hyperbola 2cxy are.

a) cy,cx b) cy,0x c) 0y,cx d) 0y,0x

14. .The area of the triangle formed by the tangent at any point on the rectangular hyperbola xy = 72

and its asymptotes is.

a) 36 b) 18 c) 72 d) 144

15. The slope of the tangent to the curve xxy sin33 2 at 0x a) 3 b) 2 c) 1 d) -1

16. If the normal to the curve 323232 ayx makes an angle with the x axis then the slope of the

normal is. a) cot

b) tan c)tan

d) cot

17. If a normal makes at an angle with positive x axis then the slope of the curve at the point where

the normal is drawn is.

www.Padasalai.Net www.TrbTnpsc.com

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

a) cot

b) tan c)tan

d) cot

18. In which region the curve y² (a+x) = x² (3a-x) does not lie ?

a) x > 0 b) 0 < x < 3a. c) x < -a and x > 3a d) –a < x < 3a

19. The area of the region bounded by the graph of y = sin x and y = cos x between x = 0

and x = 4 is. a) 12 b)

12 c)

122 d)

222

20. The length of the arc of the curve x2/3 + y2/3 = 4 is.

a) 48 b) 24 c) 12 d) 96

21. The value of

2/

0 xcosxsin1

xcosxsin

dx is. a) 2

b) 0 c) 4

d)

22. The integrating factor of dx + xdy = e-y sec² y dy is…

a) ex. b) e-x. c) ey. d) e-y.

23. The differential equation of all circles with centre at the origin is.

a) x dy + y d x = 0 b) x dy – y d x = 0 c) x d x + y dy = 0 d) x d x – y d y =0

24. The P.I of (3D²+D-14) y = 13e2x is.. a) 26 x e2x. b) 13 x e2x. c) x e2x. d) x22

e2

x

25. The order of [7] in (Z9, +9) is…

a) 9 b) 6 c) 3 d) 1.

26. In the multiplicative group of nth roots of unity, the inverse of k is (k<n)

a) k1 b)

1 c) kn d)

kn

27. The number of rows in the truth table of ~ [ p ^ (~q) ] is.

a) 2 b) 4 c) 6 d) 8.

28. In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is

a) 5/3 b) 3/5 c) 5/9 d) 9/5

29. If f(x) is a p.d.f. of a normal distribution with mean then

dx)x(f is.

a) 1 b) 0.5 c) 0 d) 0.25

30. In 16 throws of a die getting an even number is considered a success. Then the variance of the

successes is. a) 4 b) 6 c) 2 d) 256

31. 115 12 is a) 55 b) 12 c) 7 d) 11

32. If X is a discrete random variable then which of the following is correct?

a) 10 xF

b) 0F

and 1F

c) 1 nnn xFxFxXP

d) xF

is a constant function

33. The solution of the linear differential equation QPydx

dy where P and Q are functions of x is a)

cdxQFIFIy .. b)

cdyQFIFIx ..

c) cdyQFIFIy ..

d) cdxQFIFIx ..

34.

dxxe mx 7

0

is a)

m

m

7

!

b)7

!7

m c)17

!

m

m

d)8

!7

m

35. The curve 22 21 xxy

has

a) an asymptote x = 1 b) an asymptote x = 2

c) two asymptotes x = 1 and x = 2 d) no asymptote

36. If 1Z and 2Z are complex numbers then which of the following is meaningful ?

a) 21 ZZ b) 21 ZZ

c) 21 ZZ d) 21 ZZ

37. 37. If4,3 vu

and 9 ba then ba is

www.Padasalai.Net www.TrbTnpsc.com

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

a) 73 b) 63 c) 69 d) 69

38. 38. The foot of a perpendicular from a focus of the hyperbola on an asymptote lies on the -----

a) Centre b) corresponding directrix c) vertex d) L.R.

39. 39. The focus of the parabola xy 82 is a) (0,-2) b) (0,2) c) (-2,0) d) (2,0)

40. Cramer’s rule is applicable only ( with three unknowns ) when

a) 0

b) 0

c) 0,0 x d) 0 zyx

Part II Answer Any 10 Of The Following Questions 10 X 6 = 60

Q.no 55 is compulsory

41. Solve. 1664;832 yxyx

42. For

544

434

221

A

show that 1 AA .

43. Prove that the area of a quadrilateral BDAC 2

1where AC and BD are its diagonals.

44. The mid point of the hypotenuse of a right angled triangle is equidistant from its vertices

45. If

61arg

z

and

321arg

zthen prove that 1z

46. Show that for any polynomial equation 0xP with real coefficients imaginary roots occur

in conjugate pairs.

47. It took 14 sec for a thermometer to rise from -19° C to 100°C when it was taken from a

freezer and placed in boiling water. Show that somewhere along the way the mercury was

rising at exactly 8.5 ° C / sec.

48. Prove that the function 12 xxxf is neither increasing nor decreasing in 1,0

49. The time of swing T of a pendulum is given by kT where k is a constant. Determine the

percentage error in the time of swing if the length of the pendulum / changes from 32.1 cm to 32.0 cm.

50. Find the volume of the solid that results when the ellipse

012

2

2

2

bab

y

a

x is revolved about the minor axis.

51. Solve : x

y

x

y

dx

dytan

52. Show that qpq ~ is a contradiction

53. Show that .,0R is an infinite abelian group. Here denotes usual multiplication.

54. A continuous random variable X has p.d.f. 23xxf , 10 x ,Find a and b such that.

(i) aXPaXP

and (ii) 05.0 bXP

55. The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months. (Or) Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a triangle of constant area.

Part III Answer Any 10 Of The Following Questions 10 X 10 = 100 Q.no 70 is compulsory

56. A bag contains 3 types of coins namely Re.1, Rs. 2 and Rs. 5. There are 30 coins

amounting to Rs. 100 in total. Find the number of coins in each category. 57. Derive the equation of the plane in the intercept form.( both in vector and cartesion form )

www.Padasalai.Net www.TrbTnpsc.com

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

58. Show that the lines0

1

1

1

3

1

zyx and

3

1

02

4

zyx intersect and hence find the

point of intersection

59. If 2sin2cos,2sin2cos ibia and 2sin2cos ic Prove that

(i) cos2

1

abcabc

(ii)

2cos2222

abc

cba

60. A cable of a suspension bridge is in the form of a parabola whose span is 40 mts. The road

way is 5 mts below the lowest point of the cable. If an extra support is provided across

the cable 30 mts above the ground level find the length of the support if the height of

the pillars are 55 mts.

61. Prove that the line 9125 yx touches the hyperbola 99 22 yx and find its point of

contact.

62. Assume that water issuing from the end of a horizontal pipe, 7.5m above the ground,

describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position 2.5m below the line of the pipe, the flow of water has curved outward 3m beyond the vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground?

63. Two sides of a triangle have length 12 m and 15 m. The angle between them is increasing at a rate of 2° / min. How fast is the length of third side increasing when the angle between the sides of fixed length is 60° ?

64. If veuw 2 where

y

xu and ,log xyv find

x

w

and

y

w

65. Find the area bounded by x-axis and an arch of the cycloid tayttax 2cos1,2sin2 .

66. Find the length of the curve 1

3232

a

y

a

x

67. For a postmortem report, a doctor requires to know approximately the time of death of the

deceased. He records the first temperature at 10.00 a.m. to be 93.4 ° F. After 2 hours he

finds the temperature to be 91.4° F. If the room temperature ( which is constant) is 72° F,

estimate the time of death. (Assume normal temperature of a human body to be 98.6° F).

19.4 26.6log 0.0426 2.303 log 0.00945 2.303

21.4 21.4e eand

68. Show that the set of all matrices of the form 0,00

0

Ra

aforms an abelian group

under matrix multiplication

69. The air pressure in a randomly selected tyre put on a certain model new car is normally

distributed with mean value 31 psi and standard deviation 0.2 psi.

(i) What is the probability that the pressure for a randomly selected tyre (a)

between 30.5 and 31.5 psi

(b) between 30 and 32 psi

(ii) What is the probability that the pressure for a randomly selected tyre exceeds 30.5

psi?

70. Find the cubic polynomial in x which attains its maximum value 4 and minimum value 0

at x = -1 and 1 respectively. (Or)

A closed (cuboid) box with a square base is to have a volume of 2000 c.c. The material for

the top and bottom of the box is to cost Rs. 3 per square cm. and the material for the sides

www.Padasalai.Net www.TrbTnpsc.com

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

is to cost Rs. 1.50 per square cm. If the cost of the materials is to be the least, find the

dimensions of the box

ALL THE BEST

CREATED BY,

S.SARAVANA KUMAR , TEACHER

MARY ANN MATRIC HIGHER SECONDARY SCHOOL

K.PUDUR, MADURAI -625007

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, 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) No: 2/291, KULANTHAI YESU

STREET BACK STREET, ANKAYAR KANNI COLONY, AATHIKULAM,

K.PUDUR, MADURAI –PINCODE - 625007, PHONE: 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