(i) The two sides of a rectangle are x units and (10 - x) units. For what value of x, the area of rectangle will be maximum?
(ii) Prove that a rectangle, whose area is constant has minimum perimeter if it is a square.
Correct Answer - A::C
Given equation is `x^(2) + 2x sin(cos^(-1) y) + 1 =0`
Since x is real, `D ge 0`. Therefore,
`4(sin(cos^(-1)y))^(2) -4 ge 0`
or `(sin(cos^(-1)y))^(2) ge 1`...
Correct Answer - A
Let the vertices be `O(0,0),A(alpha,0)`, and `B(alpha_1,beta_1)`, where `0le alphale1 ` and `1lealpha_(1)^(2)+beta_(1)^(2) le4`
So, the area of `DeltaOAB` is maximum where `alpha=1` and `(alpha_1,beta_1)` is (2,0)...
Let a be the radius of the circle. Then,
`S_(1)` = Area of regular polygon of `n` sides inscribed in the circle
`= (1)/(2) na^(2) sin ((2pi)/(n)) = na^(2) sin.(pi)/(n)...
let length of the rectangle be L and breadth be B
so by the problem perimeter 2(IL+B)=34
=> L+B =17 .......(1)
=> L2+B2+2LB=289 ..........(2)
and the square of the diagonal = L2+B2=132 =169 .....(.3)
By...
