(1) If `5^(n+2)=625 ,f i n d[(n+3)]^(1/3)`: (2) If `(32/243)^n=8/27 ,f i n d((n+0. 4)/1024)^(-n)`

(1) If 5^(n+2)=625, find [(n+3)]^((1)/(3)):(2) If ((32)/(243))^(n)=(8)/(27), find ((n+0.4)/(1024))^(-n)

The following are the steps involved in solving the problem, if (32/243)^(n)=8/27 , find ((n+0.4)/1024)^(-n) . Arrange them in sequential order from the first to the last. (A) (32/243)^(n)=8/27 implies ((2/5)^(5))^(n)=(2/3)^(3) (B) (2^(-10))^((-3)/5)=2^(6)=64 (C) 5n=3implies n=3/5 (D) ((n+0.4)/1024)^(-n)=((3/5+0.4)/1024)^((-3)/5)=(1/1024)^((-3)/5)

If f(n)=1^2+2.2^2+3^2+2.4^2+5 .6^2+2.6^2+...+ n terms ,then (A) f(n)= (n(n+1)^2)/2 , if n is even (B) f(n)= (n^2(n+2)^2)/2, if n is even (C) f(n)= (n^2(n+1))/2 , if n is odd (D) f(n)= (n(n+3)^2)/2 if n is odd

Assign the position of the element having outer electronic configuration (i) ns^(2) np^(2) for n = 2 (ii) (n-1) d^(5) ns^(1) for n = 4 , and (iii) (n-2) f^(14) (n-1) d^(0) ns^(2) for n = 6 in the Modern periodic table.

Assign the position of the element having outer electronic configuration (i) ns^(2) np^(2) for n = 2 (ii) (n-1) d^(5) ns^(1) for n = 4 , and (iii) (n-2) f^(14) (n-1) d^(0) ns^(2) for n = 6 in the Modern periodic table.

If\ \ sqrt(2^n)=1024 ,\ \ then 3^(2(n/4-4))= (a)3 (b) 9 (c) 27 (d) 81