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A window of perimeter P (including the b...

A window of perimeter `P` (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with the colored glass while the rectangular part is fitted with the clear glass that transmits three times as much light per square meter as the colored glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?

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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. A window of perimeter P (including the base of the arch) is in the ...

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  2. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

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  3. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

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  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

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  5. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

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  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|} has a local minimum or a loca...

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  7. A rectagular sheet of fixed permeter with sides having thir lengths in...

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  8. A vertical line passing through the point (h, 0) intersects the ellips...

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  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  10. e total number of local maxima and local minima of the function f(x) =...

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  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

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  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

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  13. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

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  14. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

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  15. The length of a longest interval in which the function 3sinx-4sin^(3...

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  16. If f(x)=e^(1-x) then f(x) is

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  17. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

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  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

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  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

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  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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