Let A = {1, 2, 3, ...., 100} and R be a relation on A such that R = {(a, b): a = 2b+1}. Let (a1, аг), (аг, аз), (аз, а4),...., (ak, ak+1) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is equal to :

If the complex number z satisfies |z| = 1 and z ≠ -1, then z/(1+z^2) is purely:

A particle moves along a straight line such that its displacement x changes with time t as x = t^3 - 6t^2 + 3t + 4. What is the velocity when acceleration is zero?

Let A = {-2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by Ry if and only if y = max{x, 1}. Let I be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then l + m + n is equal to

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip. The acceleration is: