Let P_1, P_2…, P_15 be 15 points on a circle. The number of distinct triangles formed by points P_i, P_j, P_k such that i + j + k ne 15 , is :

Let P_1, P_2…, P_15 be 15 points on a circle. The number of distinct triangles formed by points P_i, P_j, P_k such that i + j + k ne 15 , is :

If P_(1),P_(2),P_(3)=(k Delta^(2))/(R) then k^(3) is divisible by (where P_(1),P_(2),P_(3) are the altitudes of the triangle,R is the circumradius and is Delta is the area of the triangle)

Players P_(1),P_(2),P_(3),P_(4) play knock out tournament.It is known that if P_(i), and P_(j) play,then P_(i), will win if i

The P.V.'s of the vertices of a triangle are 2i+3j+4k,4i+6k+3k,3i+2j+3k P.V.of orthocentre is :

The line join of the points (2,3) and (-1,5) subtends a right angle at P. If the locus of P is a circle then its radius is

For what value of p, is (hat i+hat j+hat k)p a unit vector?

Let overline a be vectors parallel to line of intersection of planes p_1 and p_2 through origin. If p_1 is parallel to the vectors 2overline j + 3 overline k and 4overline j - 3 overline k and p_2 is parallel to overline j - overline k and 3overline i - 3overline j, then the angle between overline a and 2overline i + overline j - 2overlinek is (A) pi/2 (B) pi/4 (C) pi/3 (D) pi/6