`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 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 4:1 (b) 2:1 (c) 8:3 (d) 7:3

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

Let p,q,r be the sides opposite to the angles P,Q, R respectively in a triangle PQR if r^(2)sin P sin Q= pq , then the triangle is

Let p,q,r be the sides opposite to the angles P,Q,R respectively in a triangle PQR. Then 2prsin((P-Q+R)/2) equal

Let p,q,r be the sides opposite to the angles P,Q, R respectively in a triangle PQR if 2prsin((P-Q+R)/(2)) equals

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

If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be m:n, then prove that p^(2)mn=q(m+n)^(2) .

P is a point on the line y+2x=1, and Qa n dR 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

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

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