Differentitate `(1/t^3+2sqrtt)`with respect to t.

Find the rate of change of s = (t)/(sqrt(t + 1)) with respect to t at t = 3 .

Differentiate the following functions w.r.t. t : (t^(-2)+t^(2))(2^(t)-3^(t))

If the time taken by a particle moving at constant acceleration to travel equal distances along a straight line are t_(1), t_(2), t_(3) respectively prove that (1)/(t_(1))-(1)/(t_(2))+(1)/(t_(3))=(3)/(t_(1)+t_(2)+t_(3)) .

The curve x=1-3t^(2), y=t-3t^(3) is symmetrical with respect to -

Thicknesses of two iron discs of radii r and 4r are t and (t)/(4) respectively. If their moments of inertia are I_(1) and I_(2) respectively then

A partical traveIIing with uniform acceleration along a straight line has average velocities v_(1),v_(2) and v_(3) in successive time intervals t_(1),t_(2) and t_(3) respectively . Prove that, (v_(2)-v_(1))/(v_(3)-v_(2))=(t_(1)+t_(2))/(t_(2)+t_(3))

Football teams T_(1)and T_(2) have to play two games are independent. The probabilities of T_(1) winning, drawing and lossing a game against T_(2) are 1/6,1/6and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_(1) and T_(2) respectively, after two games. P(X=Y) is

The coordinates of moving point P are ((2t+1)/(3t-2),(t-1)/(t+1)) , where t is a variable parameter . Find the equation to the locus of P.

Multiple Choice questions (MCQ) If ₹ x, ₹y and ₹ z are invested for the time t_1 years, t_2 years t_3 years respectively, then the total profit will be distributed in the ratio