If `\ ^ C_1=\ \ ^n 2` then `2m=n` m=(n-1)` d. `2n=m(m-1)`

If .^(m)C_(1)=.^(n)C_(2) prove that m=(1)/(2)n(n-1) .

Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p be the left hand derivative of |x - 1| at x = 1. If lim_(x->1) g(x) =p, then (A) n=1,m=1 (B) n=1,m=-1 (C) n=2,m=2 (D) n>2,m=n

If f(x)={m x+1\ \ \ ,\ \ \ xlt=pi/2,\ \ \ \ \ \sinx+n\ \ \ ,\ \ \ x >pi/2 is continuous at x=pi/2 , then m=1,\ \ n=0 (b) m=(npi)/2+1 (c) n=(mpi)/2 (d) m=n=pi/2

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a)^m+n C_(n-1) (b)^m+n C_(n-1) (c)^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d)^m+1C_(m-1)

Prove that : sum_(m=1)^n\ \ \ tan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2), t h e n(a_m)/(a_n)= a.(2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1) = 2, " then" f'(1) is equal to