The maximum area of the rectangle whose sides pass through the vertices of a given rectangle of sides `aa n db` is (a)`2(a b)` (b) `1/2(a+b)^2` (c)`1/2(a^2+b^2)` (d) `non eoft h e s e`

The maximum area of the triangle whose sides a,b and c satisfy 0leqaleq1,1leqbleq2 and 2leqcleq3 is

The area of the triangle whose vertices are A(1,-1,2),B(2,1-1)C(3,-1,2) is …….

In A B C with fixed length of B C , the internal bisector of angle C meets the side A Ba tD and the circumcircle at E . The maximum value of C D.D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

If the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is inscribed in a rectangle whose length to breadth ratio is 2:1 , then the area of the rectangle is (a) 4.(a^2+b^2)/7 (b) 4.(a^2+b^2)/3 (c) 12.(a^2+b^2)/5 (d) 8.(a^2+b^2)/5

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is a) 2-sqrt(2) b) sqrt(2)-1 c) 1//2 d) 1/(sqrt(2))

Let aa n db represent the lengths of a right triangles legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, the d+D equals. (a) a+b (b) 2(a+b) (c) 1/2(a+b) (d) sqrt(a^2+b^2)

Find the area of the greatest rectangle that can be inscribed in the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.

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

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a+b)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (d) none of these