Ler R1 and R2 be two relations defined as follows :
R1 = {(a, b) R2 : a2 + b2 Q} and R2 = {(a, b) R2: a2 + b2 Q}, where Q is the set of all rational numbers, then
R1 is transitive but R2 is not transitive.
R2 is transitive but R1 is not transitive.
Neither R1 nor R2 is transitive
R1 and R2 are both transitive.
Suppose f(x) is a polynomial of degree four, having critical points at – 1, 0, 1. If T = {x R |f(x) = f(0)}, then the sum of squares of all the elements of T is :
4
6
2
8
If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec.), when the length of a side of the cube is 10 cm, is
20
10
18
9
D.
Let the latus rectum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 25. Then, the distance between the centres of the circles C1 and C2 is :
12
8