If `T_1,T_2,T_8` of a certain GP be `x^-4,x^k and x^52` respectively then prove that k=24

If T_(1),T_(2),T_(8) of a certain GP be x^(-4),x^(k) and x^(5) respectively then prove that k=4

The r^(th),s^(th) and t^(th) terms of a certain G.P. are R,S and T respectively,prove that R^(s-t)*S^(t-r)*T^(r-s)=1

If the 4^(t h) , 10^(t h) and 16^(t h) terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

If k_1 and k_2 are rate constants at temperatures T_1 and T_2 respectively, then according to Arrhenius equation,

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2 then prove that x^3ydy/dx=1 .

Two different first order reaction have rate constants k_1 and k_2 at T_1(k_1 gt k_2) > If temperature is increased from T_1 " to " T_2 . Then new constants become k_3 and k_4 respectively. Which among the following relations is correct /

If k_(1) and k_(2) are rate constants at temperatures T_(1) and T_(2) respectively then according to Arrhenius equation :

if x^2+y^2 = t - 1/t and x^4 + y^4 = t^2 + 1/t^2 then prove that dy/dx = x^3y

If t_0,t_1, t_2,...,t_n are the terms in the expansion of (x+a)^n then prove that (t_0-t_2+t_4-...)^2+(t_1-t_3+t_5-...)^2=(x^2+a^2)^n .

x_1 and x_2 are susceptibility of a Paramagnetic material at temperatures T_1, K and T_2K respectively, then