There are three coplanar parallel lines. If any `p` points are taken on each of the lines, the maximum number of triangles with vertices on these points is a. `3p^2(p-1)+1` b. `3p^2(p-1)` c. `p^2(4p-3)` d. none of these

If P be any point on the plane lx+my+nz=p and Q be a point on the line OP such that OP.OQ=p^(2) , then find the locus of the point Q.

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) 1/(sqrt(2)) (d) none of these

Compute the resultant of three coplanar vectors P, 2P and 3P inclined at 120^@ with one another.

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 point (0,0),(2,2sqrt(3)), and (p,q) are the vertices of an equilateral triangle, then (p ,q) is

If the roots of the quadratic equation (4p-p^2-5)x^2-(2p-1)x+3p=0 lie on either side of unit, then the number of integer values of p is a. 1 b. 2 c. 3 d. 4

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 (c) 2sqrt(2)-1 (d) 1

A sample space consists of 3 sample points with associated probabilities given as 2p ,p^2,4p-1. Then the value of p is p= a. sqrt(11)-3 b. sqrt(10)-3 c. 1/4 < p <1/2 d.none

A line through point A(1,3) and parallel to the line x-y+1 = 0 meets the line 2x-3y + 9 = 0 at point P. Find distance AP without finding point P.

If P is non-singular matrix, then value of adj(P^(-1)) in terms of P is (A) P/|P| (B) P|P| (C) P (D) none of these