If `(1+ax)^(n)=1+8x+24x^(2)+…`, then a =… and n= ….

If (1 + ax)^n= 1 +8x+ 24x^2 +..... then the value of a and n is

If alpha an integer and P (alpha, alpha^2) is a point in the interior of the quadrilateral x=0, y=0, 4x+y-21=0 and 3x+y-4=0, and (1+ax)^n = 1 + 8x+24x^2 + …, then alpha= (A) a (B) -a (C) a^2 (D) none of these

If (1+ax)^n = 1 + 8x + 24x^2 + … and a line through P(a, n) cuts the circle x^2 + y^2 = 4 in A and B , then PA.PB =

If the first three terms in the expansion of (1 + ax)^(n) in ascending powers of x are 1+ 12x + 64x^(2) , find n and a .

If in the expansion of (1 + ax)^(n),n in N, the coefficient of x and x^(2) are 8 and 24 respectively, then

If barx is the mean of x_(1), x_(2), …………., x_(n) , then for a ne 0 , the mean of ax_(1), ax_(2),…….., ax_(n), x_(1)/a, x_(2)/a, ……….., x_(n)/a is

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 + 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) .

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_(1)=2 and x_(n+1)=sqrt(x_(n)^(2)+8) , then x_(4)=