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Mean Value Theorems — Practice Quiz

ICSE · Class 12 · Mathematics

Try a 4-question quiz on Mean Value Theorems for ICSE Class 12 Mathematics: tap an answer to check it and see why. 105 questions in the full chapter test.

105 questions24 flashcards12 formulas & key relations5 concepts

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Quick Quiz: Mean Value Theorems

0/4

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1

For the function f(x) = x³ + ax² + bx defined on [1, 2], Rolle's theorem holds at c = 4/3. What are the values of a and b?

2

For f(x) = x³ - 6x² + ax + b on [1, 3], Rolle's theorem holds with c = 2 + 1/√3. What is the value of a?

3

Rolle's theorem is applied to f(x) = (x - a)^n (x - b)^m on [a, b] where m, n ∈ ℕ. The value of c guaranteed by Rolle's theorem is:

4

For f(x) = log[(x² + ab)/(x(a+b))] on [a, b] where 0 < a < b, the value of c guaranteed by Rolle's theorem is:

105 Questions·
mcqmultiple choice

Sample Questions

1mcq

Rolle's Theorem guarantees the existence of c ∈ (a,b) such that:

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f'(c) = 0

The conclusion of Rolle's Theorem is that f'(c) = 0 for some c in the open interval (a,b).

2mcq

How many conditions does Rolle's Theorem require?

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3

Three conditions: (i) f continuous on [a,b], (ii) f differentiable on (a,b), (iii) f(a) = f(b).

3mcq

Lagrange's MVT does NOT require which of the following?

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f(a) = f(b)

LMVT only requires continuity on [a,b] and differentiability on (a,b). The condition f(a)=f(b) is needed only for Rolle's Theorem.

4mcq

The conclusion of LMVT is:

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f'(c) = [f(b)-f(a)]/(b-a)

LMVT states f'(c) = [f(b)-f(a)]/(b-a) for some c ∈ (a,b). This equals the slope of chord AB.

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Frequently Asked Questions

What are the important topics in Mean Value Theorems for ICSE Class 12 Mathematics?
Key topics in Mean Value Theorems include Core Ideas and Geometrical Meaning, Rolle's Theorem: Conditions, Checks, and Standard Examples, Worked Examples for Rolle's Theorem, Role of Rolle's Theorem in Algebraic Problems. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many practice questions are there for Mean Value Theorems?
There are 105 questions on Mean Value Theorems. Try the 4-question sample quiz on this page first; each answer shows an explanation when you tap it.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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