If` 2^-2. 2^n=2^2` then the value of n is?

If 1^2+2^2+3^2+n^2=1015 then the value of n is equal to (A) 13 (B) 14 (C) 15 (D) none of these

If (nC_0)/(2^n)+2.(nC_1)/2^n+3.(nC_2)/2^n+....(n+1)(nC_n)/2^n=16 then the value of 'n' is

If n is a positive integer satisfying the equation 2+(6*2^(2)-4*2)+(6*3^(2)-4*3)+"......."+(6*n^(2)-4*n)=140 then the value of n is

If |(alpha^(2n),alpha^(2n+2),alpha^(2n+4)),(beta^(2n),beta^(2n+2),beta^(2n+4)),(gamma^(2n),gamma^(2n+2),gamma^(2n+4))|=((1)/(beta^(2))-(1)/(alpha^(2)))((1)/(gamma^(2))-(1)/(beta^(2)))((1)/(alpha^(2))-(1)/(gamma^(2))) {where alpha^(2), beta^(2) and gamma^(2) are al distinct}, then the value of n is equal to

If x^2-2xcos theta+1=0 , then the value of x^(2n)-2x^n cosntheta+1, n in N is equal to

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

If A_r=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value of sum_(r=1)^n A_r is n (b) 2n (c) -2n (d) n^2

If .^(n+2)C_(8) : ^(n-2)P_(4)=57:16 , then the value of (n)/(2) is

If (1^(2)-a_(1))+(2^(2)-a_(2))+(3^(2)-a_(3))+…..+(n^(2)-a_(n))=(1)/(3)n(n^(2)-1) , then the value of a_(7) is

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is