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Padasalai.Net’s Special – Centum Coaching Team

Question Paper 2016-17

REGISTER

NUMBER:

STD : XII TIME : 3 Hrs.

DATE :22.12.2016 MATHEMATICS MARKS: 200

I . Choose the correct answer 1 x 40 = 40

1. The rank of the matrix

12

17 is

1. 9 2. 2 3. 1 4. 5

2. If I is unit matrix of order n, where k≠0 is a constant, then adj(kI)=

1) kn(adj I) 2) k(adj I) 3) k

2(adj I)) 4) k

n-1(adj I)

3. If A =

50

00 , then A

12 is 1)

600

00 2)

1250

00 3)

00

00 4)

10

01

4. If the equation -2x + y + z = l ; x - 2y +z = m ; x + y -2z = n such that l+m+n = 0, then the system has

1) a non-zero unique solution 2) trivial solution 3) infinitely many solution 4) No solution

5. If a

and b

include an angle 1200

and their magnitude are 2 and 3 then ba

. is equal to

1) 3 2) - 3 3)2 4) - 2

3

6. The vectors kcjbiaandkji

432 are perpendicular when

1) a = 2 , b = 3 , c = -4 2) a = 4 , b = 4 , c = 5 3) a = 4 , b = 4 , c = -5 4) a = -2 , b = 3 , c = 4

7. The projection of OP on a unit vector OQ equals thrice the area of parallelogram OPRQ.

Then POQ is 1) tan-1

3

1 2) cos-1

10

3 3) sin-1

10

3

4) sin-1

3

1

8. If cba

,, are a right handed triad of mutually perpendicular vectors of magnitude a , b , c then the value

of ],,[ cba

is 1) a2b

2c

2 2) 0 3) abc

2

1 4) abc

9. The vector equation of a plane passing through a point whose position vector is a

and perpendicular to a

vector n

is 1. nanr

2. nanr

3. nanr

4. nanr

10. The angle between the line btar

and the plane qnr

is connected by the relation

1. q

na

cos 2.

nb

nb

cos 3. n

ba

sin 4. nb

nb

sin

11. If )4()5( nim is the complex conjugate of (2m +3) + i (3n - 2), then ( n, m ) are

1)

8,

2

1 2)

8,

2

1 3)

8,

2

1 4)

8,

2

1



12. Which of the following are correct?

a. zz )(Re b. zzmI )( c. zz d. nn zz

1. (a), (b) 2. (b), (c) 3. (b), (c) and (d) 4. (a), (c) and (d)

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

1) first quadrant 2) second quadrant 3) third quadrant 3) fourth quadrant

14. If is the cube root of unity then the value of (1- ) ( 1- 2 ) ( 1- 4 ) ( 1 - 8 ) is

1) 9 2) -9 3) 16 4) 32

15. The equation of chord of contact of tangents from the point (-3, 1) to the parabola xy 82 is

1. 0124 yx 2. 0124 yx 3. 0124 xy 4. 0124 xy

16. If the length of major and semi-minor axes of an ellipse are 8,2 and their corresponding

equations are y - 6 = 0 and x + 4 = 0 then the equations of the ellipse is

1) 116

)6(

4

)4(22

yx

2) 14

)6(

16

)4(22

yx

3) 14

)6(

16

)4(22

yx

4) 1

16

)6(

4

)4(22

yx

17. The line 5x - 2y + 4k = 0 is a tangent to 4x2 - y2 = 36 then k is

1) 9

4 2)

3

2 3)

4

9 4)

16

81

18. The asymptotes of the rectangular hyperbola xy = c2 are

1) x = c , y = c 2) x = 0 , y = c 3) x = c , y = 0 4) x = 0 , y = 0

19. f is a real valued function defined on an interval RI (R being the set of real numbers) increases on I.

Then

1. )()(21

xfxf whenever Ixxifxx 2121

,, 2. )()(21


,,

3. )()(21


,, 4. )()(21


,,

20. The angle between the curve y = emx and y = e-mx for m> 1 is

1)

1

2tan

2

1

m

m 2)

2

1

1

2tan

m

m 3)

2

1

1

2tan

m

m 4)

1

2tan

2

1

m

m

21. x

limx

e

x2

is = 1) 2 2) 0 3) 4) 1

22. Which of the following curves is concave down?

1) y = - x 2 2) y = x

2 3) y = e

x 4) y = x

2 + 2x - 3

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

1) x > 0 2) 0 < x < 3a 3) x -a and x > 3a 4) -a < x < 3a

24. If u = f

x

y then y

uy

x

ux

is equal to

1) 0 2) 1 3) 2u 4) u



25. dxxfa

)(

0

+ dxxafa

)2(

0

=

1. dxxfa

)(

0

2. 2 dxxfa

)(

0

3. dxxf

a

)(

2

0

4. dxxaf

a

)(

2

0

26. The area of the region bounded by the graph of y = sinx and y = cosx between x = 0 and x = 4

is

1) 12 2) 12 3) 2 22 4) 2 22

27. The volume generated by rotating the triangle with vertices at (0 , 0) , (3 , 0) and (3 , 3) about x-axis is

1)18 2) 2 3) 36 4) 9

28. The surface area of the solid of revolution of the region bounded by y = 2x , x = 0 and x = 2 about x-axis is

1) 8 5 2) 2 5 3) 5 4) 4 5

29. The order and degree of the differential equation 0

2

3

3

3

2

2

dx

yd

dx

dyy

dx

yd are

1. 2, 3 2. 3, 3 3. 3, 2 4. 2,2

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

1) x dy + y dx = 0 2) x dy - y dx = 0 3) x dx + y dy = 0 4) x dx - y dy = 0

31. If f (x) = x and f (1) = 2, then f (x) is

1) )2(3

2 xx 2) )2(

2

3xx 3) )2(

3

2xx

4) )2(

3

2xx

32. The particular integral of (3D2 + D-14)y = 13e2x is

1) 26xe2x

2)13xe2x

3) xe2x

4) x

ex 2

2

2

33. 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

1) (i) , (ii) , (iii) 2) (i) , (ii) , (iv) 3) (i) , (iii) , (iv) 4) (ii) , (iii) , (iv)

34. The conditional statement p q is equivalent to

1) p q 2) p ~q 3) ~ p q 4) p q

35. ‘-’ is a binary operation on

1. N 2. Q-{0} 3. R-{0} 4. Z

36. Which of the following is correct ?

1. an element of a group can have more than one inverse.

2. If every element of a group is its own inverse, then the group is abelian.

3. The set of all 2x2 real matrices forms a group under matrix multiplication.

4. (a * b)-1 = a-1 * b-1 for all a , b G

37. A continuous random variable X has probability density function ‘f(x)’ then

1. 1)(0 xf 2. 0)( xf 3. 1)( xf 4. 1)(0 xf

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

1) -2 2) 4 3) -4 4) 2



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

1) log k

1 2) log k 3) e 4)

k

1

40. The random variable X follows normal distribution f(x) = c25

)100(212

x

e . Then the value of ‘c’ is

1) 2 2) 2

1 3) 5 2 4)25

1

II. Answer any 10 question (Q.NO 55 COMPULSORY) 10 X 6 = 60

41.i) Find the adjoint of the matrix

342

050

321

ii) Solve the following non-homogeneous system of linear equations by determinant method:

2x+3y = 5; 4x+6y = 12.

42. Find the rank of the matrix

2751

5121

1513

43. Let

a ,

b ,

c be unit vectors such that

a .

b =

a .

c = 0 and the angle between

b and

c and is 6

. Prove

that

a 2(

b x

c ).

44. Find the coordinates of the centre and the radius of the sphere whose vector equation is

050)1068(.2

kjirr

.

45. Find the square root of (5-12i).

46. If n is a positive integer, prove that

2sin

2cos

cossin1

cossin1nin

i

in

47. The tangent at any point of the rectangular hyperbola xy = c2 makes intercepts a, b and the normal at the

point makes intercepts p, q on the axes. Prove that ap+bq = 0.

48. Two sides of a triangle are 4m and 5m in length and the angle between them is increasing at a rate of

0.06rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides

of fixed length is .3

49.i) Evaluate x

x e

x2

lim

ii) Find the critical numbers of )4(53

xx .

50. Verify Euler’s theorem for 22

1),(

yx

yxf

.

51. Solve (D2

-13D+12)y = ex2

+ e x5

52. Show that (pq ) (p q ) is a tautology

53. Prove that the set of all 2x2 non-singular matrices forms a non-abelian infinite group under matrix



multiplication, (where the entries belong to R).

54. Find the mean and variance for the following probability density function

elsewhere

xifxexf

x

,0

0,)(

55.i) Find the area bounded by the curve y = sin2x between the ordinates x = 0 and x = and x-axis

ii) For the p.d.f f(x) =

elsewhere

xxcx

,0

10,)1(3

Find (i) the constant c (ii)

2

1xP

III. . Answer any 10 question (Q.NO 70 COMPULSORY) 10 X 10 = 100

56. bag contains 3 types of coins namely Re.1, Rs.2 and Rs.5. There are30 coins amounting to Rs.100 in total.

Find the number of coins in each category.

57. If

kjia 32 ,

,52 kib

kjc 3 , Verify that

cbabcacba )()()( .

58. Find the vector and Cartesian equation to the plane through the point (-1, -2,1) and perpendicular to the

planes x+2y+4z+7=0 and 2x-y+3z+3=0.

59. 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?

60.Find the eccentricity , centre, foci, vertices of the ellipse x2+4y2-8x-16y-68 = 0 and draw the diagram

61. Find the equation of the rectangular hyperbola which has for one of its asymptotes the line x+2y-5=0 and

passes through the points (6,0) and (-3,0).

62. Find the angle between the curves y = x2 and y = (x-2)2 at the point of intersection.

63. Find the intervals of concavity and the points of inflection of the function 432 212 xxxy 64. the area of the curve y2 = (x-5)2(x-6) (i) the area between x = 5 and x = 6 (ii) between x = 6 and x = 7

65. Find the perimeter of the circle with radius “a”.

66. Solve: 0322 xydydxyx

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 93.4F. After 2 hours he finds the temperature to be

91.4F. If the room temperature(which is constant) is 72F, estimate the time of death.(Assume normal

temperature of a human body to be 98.6F) [log 0426.04.21

4.19

e

x 2.303 and

]303.20945.04.21

6.26log

e

68. Show that the set G of all positive rationals forms a group under the composition * defined by 3

*ab

ba for

all a, G.

69. number of accident in a year involving taxi drivers in a city follows a Poisson distribution with

mean equal to 3. Out of 1000 taxi drivers find approximately the number of drivers with (i) no accident

in a year (ii) more than 3 accidents in a year ]0498.0[ 3 e .

70.i) If ,2sin2cos ia 2sin2cos ib and 2sin2cos ic , then prove that



(i) )cos(21

abc

abc (ii) )(2cos2222

abc

cba

(OR)

ii) Find the absolute maximum and absolute minimum values of .20,sin2)( xxxxf

Please Send Your Answer Scripts To This Address:

P.THANGARAJU M.SC.,B.ED., (Teacher)

S/o Pachamuthu,

Reddipatty, U Maramangalam Post,

Omalur TK, Salem Dt. – Pincode 636503.

Designation Address:

P.THANGARAJU M.SC.,B.ED.,

BT Asst,

WISDOM GATES MAT. HR.SEC.SCHOOL

VELAGOUNDANUR

PACHANAMPATTY POST

OMALUR (TK)

SALEM (DT)

PH : 9677423292


Padasalai.Net’s Centum Coaching Team


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P.THANGARAJU M.SC.,B.ED., (Teacher) S/o Pachamuthu, Reddipatty, U Maramangalam

Post, Omalur TK, Salem Dt. – Pincode 636503.

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