31.

Two points A and B move from rest along a straight line with constant acceleration f and f′ respectively. If A takes m sec. more than B and describes ‘n’ units more than B in acquiring the same speed then

• (f - f′)m2 = ff′n

• (f + f′)m² = ff′n

• 1/2(f - f′)m = ff′n²

• 1/2(f - f′)m = ff′n²

The sum of the series 

If the pair of lines ax² + 2(a + b)xy + by² = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

• 3a² – 10ab + 3b² = 0

• 3a² – 2ab + 3b² = 0

• 3a² + 10ab + 3b² = 0

• 3a² + 10ab + 3b² = 0

If both the roots of the quadratic equation x² – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

• (5, 6]

• (6, ∞)

• (-∞, 4)

• (-∞, 4)

If the equation a_nxⁿ +a_n-1x^n-1 +....... +a₁x =0, a₁ ≠ 0, n≥2, has a positive root x =  α, then the equation na_nx^n-1 + (n-1)a_n-1x_n-2 +......+a₁ = 0 has a positive root, which is

• greater than α

• smaller than α

• greater than or equal to α

• greater than or equal to α

If A² – A + I = 0, then the inverse of A is

• A + I

• A

• A – I

• A – I

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is

• reflexive and transitive only

• reflexive only

• an equivalence relation

• an equivalence relation

The differential equation representing the family of curves  , where c > 0, is a parameter, is of order and degree as follows:

• order 1, degree 2

• order 1, degree 1

• order 1, degree 3

• order 1, degree 3

Let f : (-1, 1) → B, be a function defined by  then f is both one-one and onto when B is the interval

• 

• [0, π/2)

• 
• 

If a² + b² + c² = -2 and  then f(x) is a polynomial of degree

• 1

• 0

• 2

• 2