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A square piece of tin of side 18 cm i...

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maxi

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3 cm
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A cubical box of side 1 m contains helium gas (atomic weight 4) at a pressure of 100 N//m^2 . During an observation time of 1 second , an atom travelling with the root - mean - square speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms . Take R = (25)/3 j //mol - K and k = 1.38 xx 10^-23 J//K . (a) Evaluate the temperature of the gas. (b) Evaluate the average kinetic energy per atom. ( c) Evaluate the total mass of helium gas in the box.

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NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum value of 2x^3-24 x+107in the interval [1, 3]. Find t...

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  2. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

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  3. Find the maximum and minimum values of the function f(x) = x+ sin 2x, ...

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  4. Find two numbers whose sum is 24 and whose product is as large as p...

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

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  6. Find two positive numbers x and y such that their sum is 35 and the ...

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

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  8. A square piece of tin of side 18 cm is to be made into a box withou...

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  9. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box ...

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

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  11. Show that the right circular cylinder of given surface and maximum ...

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  12. Of all the closed cylindrical cans (right circular), of a given vol...

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  13. A wire of length 28 m is to be cut into two pieces. One of the piec...

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  14. Prove that the volume of the largest cone that can be inscribed in a ...

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  15. Show that the right-circular cone of least curved surface and given...

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  16. Show that the semi-vertical angle of the cone of the maximum volume a...

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  17. Show that semi-vertical angle of right circular cone of given surface...

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  18. The point on the curve x^2=2ywhich is nearest to the point (0, 5) is(A...

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  19. For all real values of x, the minimum value of (1-x+x^2)/(1+x+x^2)is(...

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  20. The maximum value of [x(x-1)+1]^(1/3),0lt=xlt=1is(A) (1/3)^(1/3) (B) ...

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