Let the co-efficients of `x'` in `(1+x)^(2n)` & `(1+x)^(2n-1)` be P & Q respectively then `((P+Q)/(Q))^(5) =`

Let the co-efficients of x^n In (1+x)^(2n) and (1+x)^(2n-1) be P & Qrespectively, then ((P+Q)/Q)^5=

In in the expansion of (1+px)^(q) , q belongs to N , the coefficients of x and x^(2) are 12 and 60 respectively then p and q are

If the sum of odd terms and the sum of even terms in (x + a)^n are p and q respectively then p^2 - q^2 =

If the sum of odd terms and the sum of even terms in the expansion of (x+a)^n are p and q respectively then p^2+q^2=

The coefficients of x^(p) and x^(q)(p,q in N) in the expansion of (1+x)^(p+q) are

If the roots of the equation (1-q+p^(2)/2)x^(2) + p(1+q)x+q(q-1) +p^(2)/2=0 are equal, then show that p^(2) = 4q

Let P(x) =x^(2)+ 1/2x + b and Q(x) = x^(2) + cx + d be two polynomials with real coefficients such that P(x) Q(x) = Q(P(x)) for all real x. Find all the real roots of P(Q(x)) =0.

If P be the sum of odd terms and Q be the sum of even terms in the expansion of (x+a)^(n) , then (x+a)^(2n)+(x-a)^(2n) is (i) P^(2)-Q^(2) (ii) P^(2)+Q^(2) (iii) 2(P^(2)+Q^(2)) (iv) 4PQ

If p a n d q are positive, then prove that the coefficients of x^pa n dx^q in the expansion of (1+x)^(p+q) will be equal.

Q. int_0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I