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

Given b=2,c=sqrt(3),/_A=30^0 , then inradius of A B C is (sqrt(3)-1)/2 (b) (sqrt(3)+1)/2 (c) (sqrt(3)-1)/4 (d) non eoft h e s e

If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |costheta| is equal to (a) 1/(2|b|)sqrt(d^2-a^2) (b) 1/(2|a|)sqrt(d^2-a^2) (c) 1/(2|d|)sqrt(d^2-a^2) (d) none of these

If the sides of a right-angled triangle are in A.P., then the sines of the acute angles are 3/5,4/5 b. 1/(sqrt(3)),sqrt(2/3) c. 1/2,(sqrt(3))/2 d. none of these

A(1/(sqrt(2)),1/(sqrt(2))) is a point on the circle x^2+y^2=1 and B is another point on the circle such that arc length A B=pi/2 units. Then, the coordinates of B can be (a) (1/(sqrt(2)),-1/sqrt(2)) (b) (-1/(sqrt(2)),1/sqrt(2)) (c) (-1/(sqrt(2)),-1/(sqrt(2))) (d) none of these

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

Complete solution set of tan^2(sin^(-1)x)>1 is (a) (-1,-1/(sqrt(2)))uu(1/(sqrt(2)),1) (b) (-1/(sqrt(2)),1/(sqrt(2)))~{0} (c) (-1,1)~{0} (d) none of these

The angles A, B, C of triangle ABC are in A.P. and b:c = sqrt(3): sqrt(2) . Find A.

The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), which makes equal angles with the axes is a. 2//sqrt(3) b. sqrt(14//3) c. 16//sqrt(3) d. 5//sqrt(3)

A(p,1,-1), B (2p,0,2) and C(2+2p,p,p) are three points . Find the value of p so that the vectors vec(AB) and vec(BC) are perpendicular to each other .