The three sides of a trapezium are equal, each being 8cm. The area of the trapezium, where it is maximum, is (a)`24sqrt(3)` `c m^2` (b) `48sqrt(3)c m^2` (c)72`sqrt(3)c m^2` (d) none of these

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

C_1 is a circle of radius 1 touching the x- and the y-axis. C_2 is another circle of radius greater than 1 and touching the axes as well as the circle C_1 . Then the radius of C_2 is (a) 3-2sqrt(2) (b) 3+2sqrt(2) (c) 3+2sqrt(3) (d) none of these

A rectangle of the greatest area is inscribed in a trapezium A B C D , one of whose non-parallel sides A B is perpendicular to the base, so that one of the rectangles die lies on the larger base of the trapezium. The base of trapezium are 6cm and 10 cm and A B is 8 cm long. Then the maximum area of the rectangle is 24c m^2 (b) 48c m^2 36c m^2 (d) none of these

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (c) (3sqrt(3))/8R^2 (d) R^2

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)

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

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

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these

If A is the area and 2s is the sum of the sides of a triangle, then (a) Alt=(s^2)/4 (b) Alt=(s^2)/(3sqrt(3)) (c) 2RsinA (d) none of these

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)