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A cylindrical tank of radius 10 m is bei...

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of(A) 1 `m^3//h` (B) 0.1 `m^3//h` (C) 1.1 `m^3//h` (D) 0.5 `m^3//h`

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To find the rate at which the depth of the wheat in the cylindrical tank is increasing, we can follow these steps: ### Step 1: Understand the Volume of the Cylinder The volume \( V \) of a cylindrical tank is given by the formula: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height (or depth in this case). ...
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NCERT-APPLICATION OF DERIVATIVES-MISCELLANEOUS EXERCISE
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  2. A window is in the form of a rectangle surmounted by a semicircular o...

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  3. The sum of the perimeter of a circle and square is k, where k is some...

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  4. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3ha...

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  5. A point on the hypotenuse of a triangle is at distance a and b from t...

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  6. A cylindrical tank of radius 10 m is being filled with wheat at the r...

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  7. Show that height of the cylinder of greatest volume which can be insc...

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  8. Find the intervals in which the function f given byf(x)=(4sinx-2x-x co...

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  9. Find the intervals in which the function f given by f(x)=x^3+1/(x^3), ...

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  10. Find the equation of the normal to curve x^2=4ywhich passes through t...

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  11. Show that the normal at any point thetato the curvex=acostheta+athetas...

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  12. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

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  13. The two equal sides of an isosceles triangle with fixed base b are de...

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  14. Find the maximum area of an isosceles triangle inscribed in the ellip...

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  15. A tank with rectangular base and rectangular sides, open at the top ...

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  16. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

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  17. The line y = m x + 1is a tangent to the curve y^2=4xif the value of m...

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  18. The normal at the point (1,1) on the curve 2y+x^2=3is(A) x + y = 0 (B)...

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  19. The normal to the curve x^2=4ypassing (1,2) is(A) x + y = 3 (B) x - y...

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  20. The points on the curve 9y^2=x^3, where the normal to the curve makes ...

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