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A man 2 metres high walks at a uniform s...

A man 2 metres high walks at a uniform speed of 5 km/hr away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases.

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A man of height 2 metres walks at a uniform speed of 5 km/h away from a lamp post which is 6 metres high. Find the rate at which the length of his shadow increases.

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A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2m"/"s . If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

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Two roads OA and OB intersect at an angle 60^(@) . A car driver approaches O from A, where OA = 800 metres, at a uniform speed of 20 m/sec. Simultaneasly, O runner starts running from O towards B at uniform speed of 5 m/sec. Find the time when the car and the runner are closest.

The water level on a tank is 5m high. There is a hole of 1 cm^(2) cross-section at the bottom of the tank. Find the initial rate with which water will leak through the hole. ( g= 10ms^(-2) )

A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is ............

NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. A man 2 metres high walks at a uniform speed of 5 km/hr away from a ...

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  2. Using differentials, find the approximate value of each of the followi...

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

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

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

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  6. Show that the normal at any point theta to the curve x=acostheta+at...

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  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

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

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

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

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  11. The sum of the perimeter of a circle and square is k, where k is so...

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  12. A window is in the form of a rectangle surmounted by a semicircular...

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

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

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  15. Find the absolute maximum and minimum values of the function f give...

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  16. Show that the altitude of the right circular cone of maximum volume...

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  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

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  18. Show that the height of the cylinder of maximum volume that can be ...

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

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

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

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