If P and q are in inverse variation then (p+2) , (q-2) are also inverse variation

What is variation ? Name two types of variations . What is the condition for two quantities to be in inverse variation .

If p and q are positive real numbers such that p^2+ q^2=1 , then the maximum value of (p +q) is :

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

Factorise : 4p^2 – 9q^2

p and q are two inegers such that p is the successor of q.Find the value of p-q.

Let C_1 and C_2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let P be any point on C_1 and Q be any point C_2 . Let P_1 and Q_1 be the reflection of P and Q, respectively w.r.t the line y = x then prove that P_1 lies on C_2 and Q_1 lies on C_1 and PQ >= [P P_1, Q Q_1] . Hence or otherwise , determine points P_0 and Q_0 on the parabolas C_1 and C_2 respectively such that P_0 Q_0 <= PQ for all pairs of points (P,Q) with P on C_1 and Q on C_2

Find the product : (p^2 – q^2) (2p + q)

Suppose X is a binomial variate B(5,p) and P(X=2)=P(X=3), then p is equal to