If `x` is real, then `x//(x^2-5x+9)`=y lies between `-1a n d-1//11` b. `1a n d-1//11` c. `1a n d1//11` d. none of these

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4n b. 4n-3 c. 4n+1 d. none of these

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

The value of the determinant of n^(t h) order, being given by |x1 11x11 1x | is (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

Let A ,B ,C ,D be independent events such that P(A)=1//2,P(B)=1//3, P(C)=1//5, a n dP(D)=1//6. Then theprobability that none of A ,B ,C ,a n dD occurs a. 1//180 b. 1//45 c. 1//18 d. none of these

If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt(1-a^2)=0 are a. real b. imaginary c. both equal d. none of these

Let f(x)=a_0+a_1x+a_2x^2++a_n x^n+ and (f(x))/(1-x)=b_0+b_1x+b_2x^2++b_n x^n+ , then b_n+b_(n-1)=a_n b. b_n-b_(n-1)=a_n c. b_n//b_(n-1)=a_n 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 f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If |[x^n, x^(n+2),x^(2n)],[1,x^a, a],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R ,where n in N , then value of a is (a) n (b) n-1 (c) n+1 (d) none of these