The area of the circle `x^2+y^2=16`exterior to the parabola `y^2=6x`is(A) `4/3(4pi-sqrt(3))` (B) `4/3(4pi+sqrt(3))`(C) `4/3(8pi-sqrt(3))` (D) `4/3(8pi+sqrt(3))`

If 0lt=xlt=pi/3 then range of f(x)=sec(pi/6-x)+sec(pi/6+x) is (a)(4/(sqrt(3)),oo) (b) (4/(sqrt(3)),oo) (c)(0,4/(sqrt(3))) (d) (0,4/(sqrt(3)))

If the distance between the centers of two circles of unit radii is 1 the common area of the circles is 1) (2 pi)/(3)-sqrt(3) 2) (2 pi)/(3)+sqrt(3) 3) (2 pi)/(3)-(sqrt(3))/(2) 4) (2 pi)/(3)(sqrt(3))/(3)

the length of intercept made by the line sqrt2x-y-4sqrt2=0 on the parabola y^2=4x is equal to (a) 6sqrt3 (b) 4sqrt3 (c) 8sqrt2 (d) 6sqrt2

If the area of a square is same as the area of the circle, then the ratio of their perimeters, in terms of pi , is (a) pi\ :sqrt(3) (b) 2\ :sqrt(pi) (c) 3\ :pi (d) pi\ :sqrt(2)

The shortest distance between line y-x=1 and curve is : (1)(sqrt(3))/(4) (2) (3sqrt(2))/(8) (3) (8)/(3sqrt(2))(4)(4)/(sqrt(3))

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is (a) pi\ :sqrt(2) (b) pi\ :sqrt(3) (c) sqrt(3)\ :pi (d) sqrt(2)\ :pi

The area ( in sq.units) of the region {(x,y):y^(2)>=2x and x^(2)+y^(2) =0} is :(A)pi-(4)/(3)(B)pi-(8)/(3)(C)pi-(4sqrt(2))/(3) (D) pi-(2sqrt(2))/(3)

The tangent to the graph of the function y=f(x) at the point with abscissae x=1, x=2, x=3 make angles pi/6,pi/3 and pi/4 respectively. The value of int_1^3f\'(x)f\'\'(x)dx+int_2^3f\'\'(x)dx is (A) (4-3sqrt(3))/3 (B) (4sqrt(3)-1)/(3sqrt(3)) (C) (4-3sqrt(3))/2 (D) (3sqrt(3)-1)/2

A pair of tangents is drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60^0 . The area enclosed by these tangents and the arc of the circle is 2/(sqrt(3))-pi/6 (b) sqrt(3)-pi/3 pi/3-(sqrt(3))/6 (d) sqrt(3)(1-pi/6)