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

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))

Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta in (0,pi/4)uu(pi/4,pi/2) . Then the value(s) of f(1/3) is (are) (a) 1-sqrt(3/2) (b) 1+sqrt(3/2) (c) 1-sqrt(2/3) (d) 1+sqrt(2/3)

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

Find the value of 2 cos^(-1). (sqrt(3))/2 + sin^(-1). (sqrt(3))/2

If we consider only the principal values then the value inverse trigonometric functions then the value of (cos^-1(1/(5sqrt2) (-sin^-1)4/sqrt(17)) is (a) sqrt(29)/3 (b) 29/3 (c) sqrt3/29 (d) 3/29

If the area enclosed between the curves y=kx^2 and x=ky^2 , where kgt0 , is 1 square unit. Then k is: (a) 1/sqrt(3) (b) sqrt(3)/2 (c) 2/sqrt(3) (d) sqrt(3)

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)))

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

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 ("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