NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5

NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5 AOD – Application of Derivatives in English Medium Maxima and Minima. NCERT Solutions 2020-2021 are based on latest NCERT Books following the new CBSE Syllabus. Join the Discussion forum to share your knowledge.

1. An inverted cone has a depth of 10 cm and a base of radius 5 cm. Water is poured into it at the rate of 3/2 c.c. per minute. Find the rate at which the level of water in the cone is rising when the depth is 4 cm.
2. A swimming pool is to be drained for cleaning. If L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and L = 200(10 − t)². How fast is the water running out at the end of 5 sec. and what is the average rate at which the water flows out during the first 5 seconds?
3. A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface area. Prove that the radius is decreasing at a constant rate.
4. The length of a rectangle is increasing at the rate of 3.5 cm/sec. and its breadth is decreasing at the rate of 3 cm/sec. Find the rate of change of the area of the rectangle when length is 12 cm and breadth is 8 cm.
5. Find the equation of the tangent to the curve y = x² – 2x + 7 which is (1) Parallel to the line 2x − y + 9 = 0 (2) Perpendicular to the line 5y – 15x = 13.

1. Find the equation of the normal at a point on the curve x² = 4y, which passes through the point (1, 2). Also find the equation of the corresponding tangent.
2. Find the point on the curve 9y² = x³ where the normal to the curve makes equal intercepts with the axes.
3. If the sum of length of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is π/3.
4. Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.
5. A wire of length 36 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces, so that the combined area of the square and the circle is minimum?

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