`int(ax+b)^(n)dx` is equal to :
(A) `(1)/(a)((ax+b)^(n+1))/(n+1)`
(B) `((ax+b)^(n+1))/(n+1)`
(C) `(1)/(b)((ax+b)^(n+1))/(n+1)`
(D) None of these

The value of sum_(r=1)^n{(2r-1)a+1/(b^r)} is equal to (a) a n^2+(b^(n-1)-1)/(b^n(b-1)) . (b) a n^2+(b^(n)-1)/(b^n(b-1)) (c) a n^3+(b^(n-1)-1)/(b^n(b-1)) (d) none of these

d/(dx) (Ax + B)^(n)

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

(d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

If A=[(1,1),(1,0)] and n epsilon N then A^n is equal to (A) 2^(n-1)A (B) 2^nA (C) nA (D) none of these

The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ . . .. . . . , is (A) n^(2) (B) n(n+1) (C) n(1+(1)/(n))^(2) (D)None of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

If I_n=int_(pi/4)^(pi/2) (tanx)^-n dx(ngt1) , then I_n+I_(n+2)= (A) 1/(n-1) (B) 1/(n+1) (C) -1/(n+1) (D) 1/n-1