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Prove that the area of right-angled tria...

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 1 (f) (Long Answer Type Questions (I))
  1. Find two positive numbers x and y such that their sum is 35 and the ...

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  2. Find two positive numbers whose sum is 16 and the sum of whose cube...

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  3. Find two positive numbers x and y such that x + y = 60and x y^3is max...

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  4. How should we choose two numbers, each greater than or equal to -2 ...

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  5. Find the maximum slope of the curve y=-x^3+3x^2+2x-27 .

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  6. Two sides of a triangle are given. The angle between them such that th...

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  7. A wire of length 36m is to be cut into two pieces. One of the piece...

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  8. A wire of length 36cm is cut into the two pieces, one of the pieces is...

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  9. Prove that the perimeter of a right - angled triangle of given hypoten...

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  10. Prove that the area of right-angled triangle of given hypotenuse is...

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  11. Prove that the least perimeter of an isosceles triangle in which a cir...

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  12. Show that of all the rectangles of given area, the square has the s...

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  13. Show that the rectangle of maximum perimeter which can be inscribed...

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  14. Show that the rectangle of maximum area that can be inscribed in a ...

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  15. Show that of all the rectangles inscribed in a given fixed circle, ...

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  16. A rectangle is inscribed in a semi-circle of radius r with one of its ...

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  17. Of all rectangles, each of which has perimeter : (i) 40 cm (ii) 60...

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  18. An open box with a square base is to be made out of a given quantit...

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  19. Show that the semi - vertical angle of the right - circular cone of ma...

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  20. Prove that the semi-vertical angle of the right circular cone of given...

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