The area inside the parabola `5x^2-y=0` but outside the parabola `2x^2-y+9=0` is `12sqrt(3)s qdotu n i t s` `6sqrt(3)s qdotu n i t s` `8sqrt(3)s qdotu n i t s` (d) `4sqrt(3)s qdotu n i t s`

The area bounded by the curve y^2=8x\ a n d\ x^2=8y is (16)/3s qdotu n i t s b. 3/(16)s qdotu n i t s c. (14)/3s qdotu n i t s d. 3/(14)s qdotu n i t s

Let f(x)=x^3+3x+2a n dg(x) be the inverse of it. Then the area bounded by g(x) , the x-axis, and the ordinate at x=-2a n dx=6 is (a) 9/4s qdotu n i t s (b) 4/3s qdotu n i t s (c) 5/4s qdotu n i t s (d) 7/3s qdotu n i t s

The area of the triangle formed by the positive x- axis and the normal and tangent to the circle x^2+y^2=4 at (1,sqrt(3)) is (a) 2sqrt(3)s qdotu n i t s (b) 3sqrt(2)s qdotu n i t s (c) sqrt(6)s qdotu n i t s (d) none of these

The area bounded by the curve a^2y=x^2(x+a) and the x-axis is (a^2)/3s qdotu n i t s (b) (a^2)/4s qdotu n i t s (3a^2)/4s qdotu n i t s (d) (a^2)/(12)s qdotu n i t s

The area enclosed between the curve y^2(2a-x)=x^3 and the line x=2a above the x-axis is (a) pia^2s qdotu n i t s (b) (3pia^2)/2s qdotu n i t s (c) 2pia^2s qdotu n i t s (d) 3pia^2s qdotu n i t s

The minimum area of circle which touches the parabolas y=x^2+1 and y^2=x-1 is (9pi)/(16)s qdotu n i t (b) (9pi)/(32)s qdotu n i t (9pi)/8s qdotu n i t (d) (9pi)/4s qdotu n i t

The graph of y^2+2x y+40|x|=400 divides the plane into regions. Then the area of the bounded region is (a) 200s qdotu n i t s (b) 400s qdotu n i t s (c) 800s qdotu n i t s (d) 500s qdotu n i t s

The area bounded by the loop of the curve 4y^2=x^2(4-x^2) is (a)7/3 sq. units (b) 8/3s qdotu n i t e s (11)/3s qdotu n i t s (d) (16)/3s qdotu n i t s

A rhombus is inscribed in the region common to the two circles x^2+y^2-4x-12=0 and x^2+y^2+4x-12=0 with two of its vertices on the line joining the centers of the circles. The area of the rhombus is (a) 8sqrt(3)s qdotu n i t s (b) 4sqrt(3)s qdotu n i t s 6sqrt(3)s qdotu n i t s (d) none of these

Area of the triangle formed by the line x+y=3 and the angle bisectors of the pairs of straight lines x^2-y^2+2y=1 is 2s qdotu n i t s (b) 4s qdotu n i t s 6s qdotu n i t s (d) 8s qdotu n i t s