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 `1/(sqrt(3))` (b) `-1/(sqrt(3))` `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

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (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

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If the vertices of a triangle are (sqrt(5,)0) , ( sqrt(3),sqrt(2)) , and (2,1) , then the orthocentre of the triangle is (sqrt(5),0) (b) (0,0) (c) (sqrt(5)+sqrt(3)+2,sqrt(2)+1) (d) none of these

Which of the following is the value of sin 27^0-cos 27^0? (a) -(sqrt(3-sqrt(5)))/2 (b) (sqrt(5-sqrt(5)))/2 (c) -(sqrt(5)-1)/(2sqrt(2)) (d) none of these

In A B C , the coordinates of B are (0,0),A B=2,/_A B C=pi/3, and the middle point of B C has coordinates (2,0)dot The centroid o the triangle is (a) (1/2,(sqrt(3))/2) (b) (5/3,1/(sqrt(3))) (c) (4+(sqrt(3))/3,1/3) (d) none of these

The value of cot70^0+4cos70^0 is (a) 1/(sqrt(3)) (b) sqrt(3) (c) 2sqrt(3) (d) 1/2

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

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