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

Point P(p ,0),Q(q ,0),R(0, p),S(0,q) from.

If p+q+r=0=a+b+c , then the value of the determinant |[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

If P(2,\ 4),\ \ Q(0,\ 3),\ \ R(3,\ 6) and S(5,\ y) are the vertices of a parallelogram P Q R S , then the value of y is (a) 7 (b) 5 (c) -7 (d) -8

Consider the points P(p,0,0),Q(0,q,0) and R(0,0,r) where pqr!=0 then the equation of the plane PQR is (A) px+qy+r=1 (B) x/p+y/q+z/r=1 (C) x+y+z+1/p+1/q+1/r=0 (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

|(a+1, a+2, a+p), (a+2, a+3, a+q) ,(a+3, a+4, a+r)|=0 , then p, q r are in (A) A P (B) G P (C) H P (D) none of these

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

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

Statement-l: If the diagonals of the quadrilateral formed by the lines px+ gy+ r= 0, p'x +gy +r'= 0, p'x +q'y +r'= 0 , are at right angles, then p^2 +q^2= p^2+q^2 . Statement-2: Diagonals of a rhombus are bisected and perpendicular to each other.

If the numbers p,q,r are in A.P. then m^(7p), m^(7q), m^(7r)(mgt0) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these