The maximum area of the rectangle whose sides pass through the vertices of a given rectangle of sides `a and b` 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 …….

If (a , b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x , then (a) a=2b (b) a^2=2b (c) a^2=2b (d) 2a=b^2

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

Calculate the direction cosines of the sides of the triangle whose vertices are A(4, 5, 0), B(2, 6, 2) and C(2, 3, -1).

If A is the area and 2s is the sum of the sides of a triangle, then Alt=(s^2)/4 (b) Alt=(s^2)/(3sqrt(3)) 2RsinAsinBsinC (d) non eoft h e s e

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) sqrt(2)-1/2 (d) 1/(sqrt(2))

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (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

A rectangle with sides of lengths (2n-1) and (2m-1) units is divided into squares of unit length. The number of rectangles which can be formed with sides of odd length, is (a) m^2n^2 (b) mn(m+1)(n+1) (c) 4^(m+n-1) (d) non of these