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Padasalai.Net’s Special – Centum Coaching Team

Question Paper 2017-2018

STD-XII MARKS :200

MATHEMATICS TIME : 3 Hrs

Section-A

i)All question are compulsory.

ii)Each question carries one mark.

iii)Choose the most suitable answer from the given four alternatives. 40X1=40

1. If A = [2 0 1], then rank of AAT is (1) 1 (2) 2 (3) 3 (4) 0

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

(1) B = O (2) B is singular (3) B is non-singular (4) B = A

3. In a system of 3 linear non-homogeneous equation with three unknowns, if Δ = 0 and Δx = 0, Δy ≠ 0 and

Δz = 0 then the system has (1) unique solution (2) two solutions (3) infinitely many solutions (4) no

solutions

4. The rank of the matrix

is (1) 9 (2) 2 (3) 1 (4) 5

5. The centre and radius of the sphere given by x2 + y

2 + z

2 −6x + 8y −10z + 1 = 0 is

(1) (−3, 4, −5), 49 (2) (−6, 8, −10), 1 (3) (3, −4, 5), 7 (4) (6, −8, 10), 7

6. If a line makes 45°, 60° with positive direction of axes x and y then the angle it makes with the z axis is

(1) 30° (2) 90° (3) 45° (4) 60°

7. If the projection of and projection of are equal then the angle between + and is

(1)

(2)

(3)

(4)

8. If and + are vectors of magnitude λ then the magnitude of is

(1) 2λ (2) 3λ (3) 2λ (4) 1

9. , , are the perpendicular unit vectors then the value of is (1) 3 (2) 9 (3) (4)

10. The work done by the force = a + + in moving the point of application from (1, 1, 1) to (2, 2, 2)

along a straight line is given to be 5 units. The value of a is (1) 3 (2) 3 (3) 8 (4) 8

11. If z represents a complex number then arg (z) + arg ( ) is (1)

(2)

(3) 0 (4)

12. The value of i + i22

+ i23

+ i24

+ i25

is (1) i (2) – i (3) 1 (4) –1

13. If i + 3 is a root of x2 6x + k = 0 then the value of k is (1) 5 (2) (3) (4) 10

14.The value of + is (1) 2 (2) (3) (4)

15. The length of the latus rectum of the parabola y2 − 4x + 4y + 8 = 0 is (1) 8 (2) 6 (3) 4 (4) 2





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

asymptotes is (1) 36 (2) 18 (3) 72 (4) 144

17. The radius of the director circle of the conic 9x2 + 16y

2 = 144 is (1) 7 (2) 4 (3) 3 (4) 5

18. The point of contact of the parabola y2= 4ax and the tangent y = mx+c is

(1)

(2)

(3)

(4)

19. The slope of the tangent to the curve y = 3x2 + 3sinx at x = 0 is (1) 3 (2) 2 (3) 1 (4) – 1

20. The value of ‘c’ of Lagranges Mean Value Theorem for f(x) = x when a = 1 and b = 4 is

(1)

(2)

(3)

(4)

21. The least possible perimeter of a rectangle of area 100m2 is (1) 10 (2) 20 (3) 40 (4) 60

22.

is (1) 1 (2) 1 (3) 0 (4) ∞

23. The curve 9y2 = x

2(4 – x

2) is symmetrical about (1) y-axis (2) x-axis (3) y = x (4) both the axes

24. If x = r cosθ, y = r sinθ, then

is equal to (1) secθ (2) sinθ (3) cosθ (4) cosecθ

25. The area bounded by the line y = x, the x-axis, the ordinates x = 1, x = 2 is (1)

(2)

(3)

(4)

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

(1) 18π (2) 2π (3) 36π (4) 9π

27. The length of the arc of the curve x2/3

+ y2/3

= 4 is (1) 48 (2) 24 (3) 12 (4) 9

28. If f(x) is an odd function then the value of

dx is (1)2

dx (2)

dx (3) 0 (4)

dx

29. 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

30. The integrating factor of dx + xdy = ey

sec2y dy is (1) e

x (2) e

x (3) e

y (4)

31. The differential equation formed by eliminating A and B from the relation y = ex(A cos x + B sin x) is

(1) y2 + y1 = 0 (2) y2 y1 = 0 (3) y2 2y1 + 2 y = 0 (4) y2 2y12 y = 0

32. The order and degree of the different equation

+ y = x

2 is (1) 1,1 (2) 1,2 (3) 2,1 (4) 0,1

33. A monoid becomes a group if it also satisfies the

(1) closure axiom (2) associative axiom (3) identity axiom (4) inverse axiom

34. In the set of integers with operation * defined by a * b = a + b ab, the value of 3 * (4 * 5) is

(1) 25 (2) 15 (3) 10 (4) 5

35. If a compound statement is made up of three simple statements, then the number of rows in the truth

table is (1) 8 (2) 6 (3) 4 (4) 2

36. The value of is (1) (2) (3) (4)





37. Given E(X + c) = 8 and E(X − c) = 12 then the value of c is (1) −2 (2) 4 (3) −4 (4) 2

38. The distribution function F(X) of a random variable X is

(1) a decreasing function (2) a non-decreasing function (3) a constant function

(4) increasing first and then decreasing

39. A random variable X has the following probability distribution

X 0 1 2 3 4 5

P(X= x) 1/4 2a 3a 4a 5a 1/4

Then P(1≤ X ≤4) is (1)

(2)

(3)

(4)

40. The mean and variance of the standard normal distribution is (1) μ,σ2 (2) μ,σ (3) 0,1 (4) 1,1

Section-B

i)Answer any ten questions.

ii)Question no.55 is compulsory and choose any nine questions from the remaining. 10X6=60

iii)Each question carries six marks.

41. If A =

and B =

verify that

42. Solve the following non-homogeneous system of linear equations by determinant method

4x + 5y = 9 , 8x + 10y = 18

43. i) A force of magnitude 5 units acting parallel to 2 2 + displaces the point of application from (1,

2, 3) to (5, 3, 7). Find the work done.

ii) Find the area of the triangle whose vertices are (3, 1, 2), (1, 1, 3) and (4, 3, 1)

44. Solve : 6x4 25x

3 + 32x

2 + 3x 10 = 0 given that one of the roots is 2 i

45. If x = cosα + i sinα ; y = cosβ + i sinβ prove that xm

yn +

= 2 α β

46. Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a triangle of

constant area.

47. i) Obtain the Maclaurin’s Series expansion for

ii) Evaluate :

48. Test for points of inflection of the curve y = sinx, x ∈ (0, 2π)

49. Using chain rule find

w = log (x

2 + y

2) where x = , y =

50. Evaluate :

dx

51. Solve : x dy = (y + 4x5

) dx

52. Find the order of each element of the group ( , )





53. A continuous random variable X has p.d.f. f(x) = 3x2, 0 ≤ x ≤ 1, Find a and b such that.

(i) P(X ≤ a) = P(X > a) and (ii) P(X > b) = 0.05

54. If the probability of a defective fuse from a manufacturing unit is 2% in a box of 200 fuses find the

probability that (i) exactly 4 fuses are defective (ii) more than 3 fuses are defective [ = 0.0183].

55. i) Find the angle between the planes 2x + y z = 9 and x + 2y + z = 7

ii) Find the centre and radius of the sphere x2 + y

2 + z

2 + 4x 8y + 2z = 5

(OR)

Prove that the set of all roots of unity forms an abelian group under multiplication.

Section-C

i)Answer any ten questions.

ii)Question no.70 is compulsory and choose any nine questions from the remaining. 10X10=100

iii)Each question carries ten marks.

56. Verify whether the given system of equations is consistent. If it is consistent, solve them 2x + 5y + 7z =

52, x + y + z = 9, 2x + y z = 0 (by using rank method)

57. 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 2xy+3z+3 = 0.

58. P represents the variable complex number z. Find the locus of P, if Im

= 2

59. Find the axis, vertex, focus, directrix, equation of the latus rectum, length of the latus rectum of the

parabola and hence draw their graph. x2 2x + 8y + 17 = 0

60. A ladder of length 15m moves with its ends always touching the vertical wall and the horizontal floor.

Determine the equation of the locus of a point P on the ladder, which is 6m from the end of the ladder in

contact with the floor.

61. Find the equation of the hyperbola if its asymptotes are parallel to x + 2y 12 = 0 and x 2y + 8 = 0, (2,

4) is the centre of the hyperbola and it passes through (2, 0).

62. At noon, ship A is 100 km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at

25 km/hr. How fast is the distance between the ships changing at 4.00 p.m.

63.Verify

=

for the function u =

64. Find the area of the region bounded by the ellipse

between the two latus rectums.

65. Find the length of the curve

+

= 1

66. Solve :

3

+2y = 2 when x = log2, y = 0 and when x = 0, y = 0

67.The sum of Rs. 1000 is compounded continuously, the nominal rate of interest being four percent per

annum. In how many years will the amount be twice the original principal? ( = 0.6931).





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

for all a, b ϵ G.

69. Find c , μ and σ2 of the normal distribution whose probability function is given by

f(x) = c , < x <

70. Prove that sin (A +B) = sin A cos B + cos A sin B.

(OR)

Find the dimensions of the rectangle of largest area that can be

inscribed in a circle of radius r.

Prepared by,

T.KUMARAN, MSc.,BEd.,

PG Assistant in Mathematics,

Govt.Hr.Sec.School,

Muttam-608306,

Cuddalore-Dt. Cell-9042261379.

Answer Scripts Send To This Address:

Mr. T KUMARAN, 8C,IYYANAR KOVIL STREET, UDAIYAR GUDI-PO, KATTUMANNAR KOIL-TK CUDDALORE-Dt. PIN-608301.

Cell: 9042261379




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