Find the sum of first 24 terms of on AP `t_(1),t_(2),t_(3),"....",` if it is known that `t_(1) + t_(5) + t_(10) + t_(15) + t_(20) + t_(24)=225.`

Find the sum of first 10 terms an A.P. if T_1 = - 14 and T_5 = 20.

Prove that t_(75) = 2 t_(50) for 1^(st) order reaction.

Determine the sum of first thirty five terms of an arithematic progression if t_(2)=2 and t_(7)=22 .

Find the term indicated in the following case : t_(n)=4^(n)+n^(2)-n+1 ,t_(3) .

Find as indicated in the following case : t_(1)=1,t_(n)=2t_(n-1),(ngt 1) ,t_(6) .

If A, B, C, be the centres of three co-axial circles and t_(1),t_(2),t_(3) be the lengths of the tangents of them any piont, prove that bar(BC).t_(1)^(2)+bar(CA).t_(2)^(2)+bar(AB).t_(3)^(2)=0

The velocity-time graph of particle in one dimensional motion is shown in the fig. Which if the following formulae are correct for describing the motion of the pawrticle over the time interval t_1 to t_2 v(t_2) = v(t_1) + a(t_2 - t_2) , v_(average) = ([x(t_2) - x(t_1)])/((t_2 - t_1)) , x(t_2) - x(t_1) = area under the v - t curve. bounded by the t-axis and the dotted line shown.

Find dy/dx when x = t + 1/t, y = t - 1/t

Find all the points of discontinuity of the function f(t) = (1/(t^2 + t-2)) , where t = 1/(x-1)

If g(t) = 1- 4t^2 , find g’(1).