Point `P(p ,0),Q(q ,0),R(0, p),S(0,q)` from (a)parallelogram (b)rhombus (c)cyclic quadrilateral (d) none of these

If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (d) none of these

If the point (0,0),(2,2sqrt(3)), and (P ,q) are the vertices of an equilateral triangle, then (p ,q) is (a) (0,-4) (b) ( 4,4) c)(4,0) (d) (5,0)

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratios of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

If alpha,beta are real and distinct roots of a x^2+b x-c=0a n dp ,q are real and distinct roots of a x^2+b x-|c|=0,w h e r e(a >0), then alpha,beta in (p ,q) b. alpha,beta in [p ,q] c. p ,q in (alpha,beta) d. none of these

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 sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

P is a variable point on the line L=0 . Tangents are drawn to the circles x^(2)+y^(2)=4 from P to touch it at Q and R. The parallelogram PQSR is completed. If P -=(3,4) , then the coordinates of S are

If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q c r a p b r b p c q a|i s a 0 b. p a+q b+r c c. 1 d. none of these

Two points P(a,0) and Q(-a,0) are given. R is a variable point on one side of the line P Q such that /_R P Q-/_R Q P is a positive constant 2alphadot Find the locus of the point Rdot