If `m,n,k` are rational and `m=k+(n)/(k)` ,then the roots of `x^(2)+mx+n=0` are

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

If f(x) = sum_(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)) , then the product of root of f(x) = 0 as n rarr oo , is

Number of non-negative integral values of 'k' for which roots of the equation x^(2)+6x+k=0 are rational is-

The integral value of m for which the root of the equation m x^2+(2m-1)x+(m-2)=0 are rational are given by the expression [where n is integer] (A) n^2 (B) n(n+2) (C) n(n+1) (D) none of these

If m is selected at random from set {1,2,…..,10} and the probability that the quadratic equation 2x^(2)+2mx+m+1=0 has real roots is k then value of 10k is ______________

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }

If the value of the sum n^(2) + n - sum_(k = 1)^(n) (2k^(3)+ 8k^(2) + 6k - 1)/(k^(2) + 4k + 3) as n tends to infinity can be expressed in the form (p)/(q) find the least value of (p + q) where p, q in N

The quadratic equation x^2+m x+n=0 has roots which are twice those of x^2+p x+m=0a dm ,na n dp!=0. The n the value of n//p is _____.

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m