(C) 2? + 3 1+i 39. If = 1, then 1-i (A) x = 2n+1 (C) x = 2n

If ((1 +i)/(1 -i))^(x) =1 , then (A) x=2n+1 (B) x=4n (C) x=2n (D) x=4n+1, n in N.

If ((1 +i)/(1 -i))^(x) =1 , then (A) x=2n+1 (B) x=4n (C) x=2n (D) x=4n+1, n in N.

If ((1+i)/(1-i))^(x)=1 AA n in N is (i) x = 2n+1 (ii) x =4n (iii) x=2n (iv) x=4n+1

If cos^2x+cos^2 2x+cos^2 3x=1 then (a) x=(2n+1)pi/4,\ n in I (b) x=(2n+1)pi/2,\ n in I (c) x=npi+-\ pi/6,\ n in I (d) none of these

(lim)_(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} a. I n\ (1/3) b. I n\ (2/3) c. I n\ (3/2) d. I n\ (4/3)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " 1^(2)*C_(1) + 2^(2) *C_(2) + 3^(2) *C_(3) + …+ n^(2) *C_(n) = n(n+1)* 2^(n-2) .

If (x + a_(1)) (x + a_(2)) (x + a_(3)) …(x + a_(n)) = x^(n) + S_(1) x^(n-1) + S_(2) x^(n-2) + …+ S_(n) where , S_(1) = sum_(i=0)^(n) a_(i), S_(2) = (sumsum)_(1lei lt j le n) a_(i) a_(j) , S_(3) (sumsumsum)_(1le i ltk le n) a_(i) a_(j) a_(k) and so on . If (1 + x)^(n) = C_(0) + C_(1) x + C_(2)x^(2) + ...+ C_(n) x^(n) the cefficient of x^(n) in the expansion of (x + C_(0))(x + C_(1)) (x + C_(2))...(x + C_(n)) is

(lim)_(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} I n\ (1/3) b. I n\ (2/3) c. I n\ (3/2) d. I n\ (4/3)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .