Statement-1- For `n in N` `2^n > 1+ n(sqrt(2^(n-1 )))` Because Statement-11-GM. > HM. and `(AM) (HM) = (GM)^2`

Statement-1 :The A.M. of series 1,2,4,8,16,…… 2^n is (2^(n+1)-1)/(n+1) Statement-2 : Arithmetic mean (A.M.) of ungrouped data is (Sigmax_i)/n where x_1,x_2 …. x_n are n numbers .

Statement-1 :The A.M. of series 1,2,4,8,16,…… 2^n is (2^(n+1)-1)/(n+1) Statement-2 : Arithmetic mean (A.M.) of ungrouped data is (Sigmax_i)/n where x_1,x_2 …. x_n are n numbers .

Statement-I: X={8n+1:n in N}, then X nn Y=Y,Y={(2n+1)^(2):n in N} because statement -II:x is a subset of y

Statement -I: X={8n+1:n inN},then XnnY=Y, Y={(2n+1)^2:n in N} because statement -II:x is a subset of y

Statement-1: For every natural number n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn Statement-2: For every natural number n ge 2, sqrt(n(n+1) lt n+1

The statement n! gt 2^(n-1), n in N is true for

The statement n! gt 2^(n-1), n in N is true for

Statement -1 : For every natural number n ge 2, (1)/( sqrt1) + (1)/( sqrt2) + (1)/( sqrt3) + … + (1)/( sqrtn) gt sqrtn . Statement - 2 : For every natural number n ge 2, sqrt(n(n+1) ) lt n+1

Statement 1: sum_(r=0)^n(r+1)^n c_r=(n+2)2^(n-1)dot Statement 2: sum_(r=0)^n(r+1)^n c_r=(1+x)^n+n x(1+x)^(n-1)dot (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1 (3) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1. (4) Statement 1 is true, Statement 2 is false.

Statement 1 If a,b,c are three positive numbers in GP, then ((a+b+c)/(3))((3abc)/(ab+bc+ca))=(abc)^((2)/(3)) . Statement 2 (AM)(HM)=(GM)^(2) is true for positive numbers.