Home › NEET Maths MCQs › Application of Derivatives
JEE · Maths · Class 12

Application of Derivatives — NEET Maths MCQs

30 questions written by hand against the NCERT chapter. Every wrong option is explained, not just the right one.

30questions
10/14/6easy / medium / hard
₹0no login
Take the Application of Derivatives test →
Free · your all-India rank after you finish

Sample questions from this chapter

If A=πr², then dA/dr at r=5 is
  1. 10π ✓
  2. 5π
  3. 25π
  4. 2π
Answer: A. Differentiate the area before substituting the radius: dA/dr=2πr, not πr². At r=5 this rate is 10π.
Why not B: This omits the factor 2 in d(πr²)/dr and uses πr instead of 2πr.
Why not C: This substitutes r=5 into the area πr², confusing the area with its rate of change.
Why not D: This differentiates to 2πr but fails to substitute r=5, reporting only the coefficient 2π.
For f=x³−3x, critical points are
  1. x=0 only
  2. x=±√3
  3. x=±1 ✓
  4. x=3
Answer: C. f′=3x²−3=0 gives x=±1.
Why not A: Solves f=0 rather than f′=0.
Why not B: Sets x²−3=0 after forgetting derivative multiplier.
Why not D: Uses a coefficient as the root.
For a sphere V=4πr³/3, dV/dt when r=2 and dr/dt=3 is
  1. 48π ✓
  2. 16π
  3. 12π
  4. 36π
Answer: A. dV/dt=4πr² dr/dt=4π·4·3=48π.
Why not B: This computes dV/dr=4πr² but omits the chain-rule factor dr/dt, so it is not the time rate.
Why not C: This drops the r² factor after differentiating r³, using only 4π·dr/dt=12π.
Why not D: Uses 2πr·dr/dt.

These are 3 of the 30 questions in the test. Take the full chapter test →

Read the chapter first

Every NCERT question in this chapter is solved, free: NCERT solutions — Application of Derivatives →

Other NEET Maths chapters

SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsLinear InequalitiesPermutations and Combinations

All 27 chapters →

Questions

How many NEET questions are there on Application of Derivatives?

This chapter test has 30 questions — 10 easy, 14 medium and 6 hard — all written against the NCERT Class 12 chapter.

Is this NEET Maths chapter test free?

Yes. Every chapter test is free with no login, and you get your all-India rank on every one. Nothing on the site is on sale right now.

Do the questions explain the wrong options?

Yes — every distractor carries its own explanation naming the specific misconception that makes a student pick it. That is the part most question banks skip, and it is the part that changes your next attempt.