57. The sides of a triangle are in the ratio , then the angles of the triangle are in the ratio

a) 1 : 3 : 5 b) 2 : 3 : 4

c) 3 : 2 : 1 d) 1 : 2 : 3

Ans: d

Let a = x,

.

58. Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines is

a) 2 sq. units b) 4 sq. unit

c) 6 sq. unit d) 8 sq. unit

Ans: a

Equations of lines are y = x + 1, y = -x + 1

angle bisectors are y = 1 and x = 0

area of triangle

59. If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

a) 4/ 25 b) 4/35

c) 4/33 d) 4/1155

Ans: d

Numbers between 1 and 100 which are divisible by both 2 and 3 are 16.

Hence the probablity is .

60. The area enclosed between the curves ( a> 0) is 1 sq. unit, then the value of a is

a) b) 1/2

c) 1 d) 1/3

Ans: a

Points of intersection of and are ( 0, 0) and
Hence

61. Given both are acute angles and , , then the value of belongs to

a) b)

c) d)

Ans: b

62. If tangents are drawn to the ellipse , then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

a) b)

c) d)

Ans: a

Equation of tangent at any point is and the midpoint of its intercept between the axes is .

63. If is differentiable and , then equals

a) 2/5 b) -5/2

c) 1 d) 5/2

Ans. a

Differentiating both sides, we get