If `n/2+n/3=7`then the value of n is equal to?

In the expansion of (3+x/2)^(n) the coefficients of x^(7) and x^(8) are equal, then the value of n is equal to

If S_n , denotes the sum of n terms of an AP, then the value of (S_(2n)-S_n) is equal to

Consider the set A= {3, 4, 5} and the number of null relations, identity relation, universal relations,reflexive relation on A are respectively n_1,n_2,n_3,n_4 ,Then the value of n_1+n_2+n_3+n_4 is equal to

If I_(n)=int_(0)^(2)(2dx)/((1-x^(n))) , then the value of lim_(nrarroo)I_(n) is equal to

If the coefficients of x^7 and x^8 in the expansion of [2 +x/3]^n are equal, then the value of n is : (A) 15 (B) 45 (C) 55 (D) 56

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

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 the sum of the series 1+(3)/(2)+(5)/(4)+(7)/(8)+……+((2n-1))/((2)^(n-1)) is f(n) , then the value of f(8) is

If S_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!) then lim_(n rarr infty) S_(n) is equal to

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n