Let the first term a of an infinite G.P. is the value of x, where the function f(x)=7+2xloge25−5x−1−52−x has the greatest value and the common ratio r is equal to limx→0x∫0t2x2tan(π+x) dt. Also, let S be the sum of infinite terms of G.P.List IList II (A)a(P)4(B)1r(Q)3(C)S(R)2(D)a−rS(S)1(T)5Which of the following is the only CORRECT combination?

Let the first term a of an infinite G.P. is the value of x, where the

1.	Let the first term a of an infinite G.P. is the value of x, where the function f(x)=7+2xloge25−5x−1−52−x has the greatest value and the common ratio r is equal to limx→0x∫0t2x2tan(π+x) dt. Also, let S be the sum of infinite terms of G.P.List IList II (A)a(P)4(B)1r(Q)3(C)S(R)2(D)a−rS(S)1(T)5Which of the following is the only CORRECT combination?
Answer» Let the first term $a$ of an infinite G.P. is the value of $x$ , where the function $f (x) = 7 + 2 x {log}_{e} 25 - 5^{x - 1} - 5^{2 - x}$ has the greatest value and the common ratio $r$ is equal to $lim x \to 0 x \int 0 \frac{t^{2}}{x^{2} tan (π + x)} d t$ . Also, let $S$ be the sum of infinite terms of G.P. $\begin{matrix} List I & List II (A) & a & (P) & 4 (B) & \frac{1}{r} & (Q) & 3 (C) & S & (R) & 2 (D) & a - r S & (S) & 1 (T) & 5 \end{matrix}$ Which of the following is the only CORRECT combination?