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JEE • MATHEMATICS • MEAN VALUES THEOREM

Mean values theorem practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 4

Analyzing +4 | -1

f\left( x \right) = {x^\alpha }\log x

and

f\left( 0 \right) = 0

, then the value of α for which Rolle’s theorem can be applied in [0, 1], is

View answer and explanation

Correct option: D

\frac{1}{2}

Option D (

\frac{1}{2}

) is correct because it satisfies the conditions for Rolle's theorem to be applicable in the given interval.

2 Hard

2 of 4

Application +4 | -1

If the function

f\left( x \right) = {x^3} - 6{x^2} + ax + b

satisfies Rolle’s theorem in the interval [1, 3] and

f'\left( {\frac{{2\sqrt 3 + 1}}{{\sqrt 3 }}} \right) = 0

, then

View answer and explanation

Correct option: D

a = 11

Option D (

a = 11

) is correct because it satisfies Rolle's theorem conditions, where the derivative at a point within the interval [1, 3] is zero, allowing us to solve for 'a'.

3 Hard

3 of 4

Analyzing +4 | -1

In [0, 1] Lagranges Mean value theorem is NOT applicable to

View answer and explanation

Correct option: A

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {\frac{1}{2} - x,\;\;\;\;\;x < \frac{1}{2}}\\ {{{\left( {\frac{1}{2} - x} \right)}^2},\;\;\;x \ge \frac{1}{2}} \end{array}} \right.

The correct answer is A because Lagrange's Mean Value Theorem requires the function to be differentiable, and option A is not differentiable at x = 1/2.

4 Hard

4 of 4

Analyzing +4 | -1

If [0, 1], Lagrange’s mean value theorem is NOT applicable to

View answer and explanation

Correct option: D

f\left( x \right) = \left| x \right|

Option D (

f(x) = |x|

) is correct because it is not differentiable at x = 0, which lies within the interval [0, 1], thus violating the conditions for Lagrange's Mean Value Theorem.

Revision notes and key takeaways

Review MEAN VALUES THEOREM in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 4 single-correct-answer MCQs on MEAN VALUES THEOREM.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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