# Calculus

CBSE TEST PAPER-03 CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) Topic: - application of derivatives Sand is pouring from a pipe at the rate of 12cm3/s. the falling sand forms a cone on the ground in much a way that the height of the cone is always one – sixth of the radius of the here. How fast is the height of the sand cone increasing when the height in 4cm. 2. The total revenue in RS received from the sale of x units of the product is given by R (x) = 13x2 + 26x + 15 find MR when 17 unit are produce. 3. Prove that y =
4 sin θ  π − θ is an increasing function = x of θ in θ ,  2 + cos θ  2

1.







4.

Prove that the function of given by f(x) = log sinx is strictly increasing on
 π π   0, 2  and strictly decreasing on  2 , π    



5.

Find a point on the curve y = (x – 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4) Find the equation of tangent to the curve given by x = a sin 3 t , y = b cos3 t at a point where t = π
2



6.



7. 8. 9.

Find the approximate value of f(3.02) where f(x) = 3x2 + 5x + 3. Find the approximate value of (32.15)
1 5

  

A square piece of tin of side 18cm is to be made into a box without top by cutting a square from each corner and folding of 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 maximum possible?

10.

Show that the right circular cylinder of given surface and maximum volume is much that its height is equal to the diameter of the base.



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