Sheela says the sum of 2pq and 4pq is 8`p^2``q^2` is she right ? Give your explanation.

Rehan says there are 37 non square numbers between 9^(2) and 11^(2) . Is he right ? Give your reason.

The value of p-q + pq for p = -1, q = -2 is

Find the degree of: pq+p^2q-p^2q^2

If P and Q are the sum of odd terms and the sum of even terms respectively in the expansion of (x+a)^(n) then prove that 4PQ=(x+a)^(2n)-(x-a)^(2n)

If P and Q are the sum of odd sum terms and the sum of even terms respectively in the expansion of (x +a)^n then prove that 4PQ = (x+a)^(2n) - (x - a)^(2n)

(p + q) ( p^2 - pq + q^2 ) = ____

Factorise the expressions : p^2q - pr^2-pq + r^2 .

The abscissae of two points P,Q are the roots of the equation 2x^2+4x-7=0 and their ordinates are the roots of the equation 3x^2-12x-1=0 . Then the centre of the circle with PQ as a diameter is

In an A.P. if p^(th) term is 1/q and q^(th) term is 1/p , prove that the sum of first pq terms is 1/2(pq+1) , where p ne q .

Prove that the sum of any two of the roots of the equation x^4 +px^3 +qx^2 +rx +s =0 is equal to the sum of the remaining two roots of the equation iff p^3 -4pq +8r =0