The `nth` derivative of the function `f(x)=1/(1-x^2)` [where `in(-1,1)` at the point `x=0` where `n` is even is (a) `0` (b) `n!` (c) `n^nC_2` (d) `2^nC_2`

m points on one straight line are joined to n points on another straight line. The number of points of intersection of the line segments thus formed is (A) ^mC-2.^nC_2 (B) (mn(m-1)(n-1))/4 (C) (^mC_2.^nC_2)/2 (D) ^mC_2+^nC_2

If f(x)={0, where x=(n)/(n+1),n=1,2,3... and 1 else where then the value of int_(0)^(2)f(x)dx is

If f(x)={0, where x=(n)/(n+1),n=1,2,3... and 1, else where ,then the value of int_(0)^(2)f(x)dx

The period of f(x)=[x]+[2x]+[3x]+[4x]+...[nx]-(n(n+1))/(2)x where n in N, is (where [.] represents greatest integer function).n (b) 1 (c) (1)/(n) (d) none of these

If ^(n+1)C_3=2.^nC_2, then n= (A) 3 (B) 4 (C) 5 (D) 6

If (1+x)^(n)=nC_(0)+nC_(1)x+....+nC_(n)x^(n) where n is a positive integer,then find the value of nC_(0)+nC_(4)+nC_(8)+....

The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^n is (A) ^nC_4 (B) ^nC_4+^nC_2 (C) ^nC_4+^nC_2+^nC_4.^nC_2 (D) ^nC_4+^nC_2+^nC_1.^nC_2

Let A={1,2,..., n} and B={a , b }. Then number of surjections from A into B is nP2 (b) 2^n-2 (c) 2^n-1 (d) nC2

With the notation C_r= ^nC_2 = (n!)/(r!(n-r)! ) when n is positive inteer let S_n=C_n-(2/3)C_(n-1)+(2/3)^2C_(n-2)+- ……..+ (-1)^n(2/3)^n.C_0

If (x-a)^(2m)(x-b)^(2n+1), where m and n are positive integers and a>b, is the derivative of a function f then-