The roots of the equation `(q-r)x^2+(r-p)x+p-q=0` are (A) `(r-p)/(q-r),1` (B) `(p-q)/(q-r),1` (C) `(q-r)/(p-q),1` (D) `(r-p)/(p-q),1`

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

If t_n denotes the nth term of an A.P. and t_p= 1/q, t_q= 1/p then which one of the following is necessarily a root of the equation (p+2q-3r)x^2+(q+2r-3p)x+(r+2p-3q)=0 (A) t_p (B) t_q (C) t_(pq) (D) t_(p+q)

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

The lines 1) (p-q)x+(q-r)y+(r-p)=0,2)(q-r)x+(r-p)y+(p-q)=0,3)(r-p)x+(p-q)y+(q-r)=0

Which of the following is not equivalent to (p^^~ q)->r (a) ~(q v ~ p)->r (b) ~ r->(~ p v q) (c) ~((p^^(~ q))^^(~ r)) (d) ~ r->(~ p^^q)

If q^2 - 4pr =0 , p gt 0 then the domain of the function f(x) = log(p x^3 +(p+q)x^2 +(q+r) x + r) is (a) R-{-q/2p} (b) R-[(-oo,-1]uu{-q/(2p)}] (c) R-[(-oo,-1)nn{-1/(2p)}] (d) R

If the roots of the equation 1/(x+p)+1/(x+q)=1/r are equal in magnitude and opposite in sign, then (A) p+q=r (B)p+q=2r (C) product of roots=- 1/2(p^2+q^2) (D) sum of roots=1

The points (p,q +r) , (q, r+p) and (r, q+p) are "_______" .

. 1/(p+q),1/(q+r),1/(r+p) are in AP, then

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