NCERT Class 12 Maths
Chapter 6: Applications Of Derivatives
18 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 6 Applications Of Derivatives — Exercise 6.1
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Find dA/dr for a circle at (a) r=3 cm, (b) r=4 cm.
Question 2
A cube volume increases at 8 cm³/s. Find the surface-area rate when its edge is 12 cm.
Question 3
A circle radius increases at 3 cm/s. Find the area rate at radius 10 cm.
Question 4
A cube edge increases at 3 cm/s. Find its volume rate at edge 10 cm.
Question 5
A circular wave radius increases at 5 cm/s. Find its enclosed-area rate at radius 8 cm.
Question 6
A circle radius increases at 0.7 cm/s. Find its circumference rate.
Question 7
A rectangle length x decreases at 5 cm/min and width y increases at 4 cm/min. At x=8 cm,y=6 cm find (a) perimeter and (b) area rates.
Question 8
A spherical balloon receives 900 cm³/s of gas. Find its radius rate at r=15 cm.
Question 9
For a spherical balloon, find dV/dr at radius 10 cm.
Question 10
A 5 m ladder leans against a wall. Its foot moves away at 2 cm/s. Find the height-decrease rate when the foot is 4 m from the wall.
Question 11
A particle moves on 6y=x³+2. Find points where the y-coordinate changes eight times as fast as x.
Question 12
An air bubble radius increases at 1/2 cm/s. Find its volume rate at radius 1 cm.
Question 13
A spherical balloon diameter is (3/2)(2x+1). Find dV/dx.
Question 14
Sand enters a conical heap at 12 cm³/s. Height is one-sixth of base radius. Find the height rate at h=4 cm.
Question 15
C(x)=0.007x³−0.003x²+15x+4000 rupees. Find marginal cost at x=17.
Question 16
R(x)=13x²+26x+15 rupees. Find marginal revenue at x=7.
Question 17
Find dA/dr for a circle at r=6 cm.
Question 18
If R(x)=3x²+36x+5, find marginal revenue at x=15.