If p, q, r are any real numbers, then (A) `max (p, q) lt max (p, q, r)` (B) `min(p,q) =1/2 (p+q-|p-q|)`(C) `max (p, q) < min(p, q, r)` (D) None of these

If p,q,r be three distinct real numbers, then the value of (p+q)(q+r)(r+p), is

If A be one A.M. and p ,q be two G.M. ' s between two numbers, then 2A is equal to (a) (p^3+q^3)/(p q) (b) (p^3-q^3)/(p q) (c) (p^2+q^2)/2 (d) (p q)/2

If p ,q be two A.M. ' s and G be one G.M. between two numbers, then G^2= a) (2p-q)(p-2q) (b) (2p-q)(2q-p) c) (2p-q)(p+2q) (d) none of these

The incorrect statement is (A) p →q is logically equivalent to ~p ∨ q. (B) If the truth-values of p, q r are T, F, T respectively, then the truth value of (p ∨ q) ∧ (q ∨ r) is T. (C) ~(p ∨ q ∨ r) = ~p ∧ ~q ∧ ~r (D) The truth-value of p ~ (p ∧ q) is always T

If p,q,r in R and the quadratic equation px^2+qx+r=0 has no real roots, then (A) p(p+q+r)gt0 (B) (p+q+r)gt0 (C) q(p+q+r)gt0 (D) p+q+rgt0

Let A= {p, q, r} . Which of the following is an equivalence relation on A ? (a) R_1 = {(p, q), (q, r), (p, r), (p, q)} (b) R_2 = {(r,q), (r, p), (r.r), (q, r)} (c) R_3 = {(p, p), (q,q), (r, r), (p, q)} (d) one of these

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

If two positive integers a and b are expressible in the form a=p q^2 and b=p^3q ; p ,\ q being prime numbers, then LCM (a ,\ b) is (a) p q (b) p^3q^3 (c) p^3q^2 (d) p^2q^2

If p(q-r)x^(2) + q(r-p)x+ r(p-q) = 0 has equal roots, then show that p, q, r are in H.P.

The sums of first p, q, r terms of an A.P. are a, b, c respectively. Prove that (a)/(p) (q-r) +(b)/(q) (r-p) +(c )/(r) (p-q) =0