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 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 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=1-x and the lines y=(|x|)/x ,x=-1,a n dx=1/2i s 3/(sqrt(2))-(11)/6s qdotu n i t s (b) 3sqrt(2)-(11)/4s qdotu n i t s 6/(sqrt(2))-(11)/5s qdotu n i t s (d) none of these

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s (c) 3pia^2s qdotu n i t s (d) None of these

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

Area bounded by y=sqrt(5-x^2)a n dy=|x-1| is: (A) (5pi-2)/3 s qdotu n i t s (B) (5pi-2)/4 s qdotu n i t s (C) (5pi)/4 s qdotu n i t s (D) none of these

If the extremities of the base of an isosceles triangle are the points (2a ,0) and (0, a), and the equation of one of the side is x=2a , then the area of the triangle is (a) 5a^2s qdotu n i t s (b) (5a^2)/2s qdotu n i t s (c) (25 a^2)/2s qdotu n i t s (d) none of these

If the extremities of the base of an isosceles triangle are the points (2a ,0) and (0, a), and the equation of one of the side is x=2a , then the area of the triangle is (a) 5a^2s qdotu n i t s (b) (5a^2)/2s qdotu n i t s (25 a^2)/2s qdotu n i t s (d) none of these

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s 3pia^2s qdotu n i t s (d) None of these