`O P Q R` is a square and `M ,N` are the midpoints of the sides `P Q` and `Q R` , respectively. If the ratio of the area of the square to that of triangle `O M N` is `lambda:6,` then `lambda/4` is equal to (a)2 (b) 4 (c) 2 (d) 16

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is (a)4:1 (b) 2:1 (c) 8:3 (d) 7:3

Find the area of the square whose side length is m + n -q

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

Each side of triangle ABC is divided into three equal parts. Find the ratio of the are of hexagon P Q R S T U to the area of the triangle ABC.

In a three-dimensional coordinate system, P ,Q , and R are images of a point A(a ,b ,c) in the x-y ,y-z and z-x planes, respectively. If G is the centroid of triangle P Q R , then area of triangle AOG is ( O is the origin) (A) 0 (B) a^2+b^2+c^2 (C) 2/3(a^2+b^2+c^2) (D) none of these

Let O be the origin, and O X x O Y , O Z be three unit vectors in the direction of the sides Q R , R P , P Q , respectively of a triangle PQR. If the triangle PQR varies, then the minimum value of cos(P+Q)+cos(Q+R)+cos(R+P) is: -3/2 (b) 5/3 (c) 3/2 (d) -5/3

If the vertices Pa n dQ of a triangle P Q R are given by (2, 5) and (4,-11) , respectively, and the point R moves along the line N given by 9x+7y+4=0 , then the locus of the centroid of triangle P Q R is a straight line parallel to PQ (b) QR (c) RP (d) N

The equation of a curve passing through (1,0) for which the product of the abscissa of a point P and the intercept made by a normal at P on the x-axis equal twice the square of the radius vector of the point P is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=( l ) x^(( m )4( n ))( o ) (p) (q) (b) ( r ) (s) (t) x^(( u )2( v ))( w )+( x ) y^(( y )2( z ))( a a )=2( b b ) x^(( c c )4( d d ))( e e ) (ff) (gg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )+( j ) y^(( k )2( l ))( m )=4( n ) x^(( o )4( p ))( q ) (r) (s) (d) None of these

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

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