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Mean Value Theorems MATHS - Mean Value Theorems

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 82 questions in this chapter.

Question types

Mean Value Theorems question types

82 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

82
Questions
4
Question groups
5
Question types
Sample Questions

Mean Value Theorems questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The value of $c$ in Lagrange's mean value theorem for the function $f(x) = x(x - 2)$ when $\text{x}\in[1,2]$ is:
  • A
    $1$
  • B
    $\frac{1}{2}$
  • C
    $\frac{2}{3}$
  • ✓
    $\frac{3}{2}$

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark
The value of $c$ in Rolle's theorem for the function $f(x) = x^3 - 3x$ in the interval $\big[0,\sqrt3\big]$ is:
  • ✓
    $1$
  • B
    $-1$
  • C
    $\frac{3}{2}$
  • D
    $\frac{1}{3}$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
If $\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$ in $[0,\pi],$ then c in Rolle's theorem is:
  1. $\frac{\pi}{6}$
  2. $\frac{\pi}{4}$
  3. $\frac{\pi}{2}$
  4. $\frac{3\pi}{4}$
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Q 4M.C.Q (1 Marks)1 Mark
Rolle's theorem is applicable in case of $\phi(\text{x})=\text{a}^{\sin\text{x}},\text{a}>\text{a}$ in:
  1. Any interval.
  2. Any interval $[0,\pi]$
  3. Any interval $\Big[0,\frac{\pi}{2}\Big]$
  4. None of these.
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Q 5M.C.Q (1 Marks)1 Mark
If $4a + 2b + c = 0,$ then the equation $3ax^2+ 2bx + c = 0$ has atleast one real root lying in the interval:
  • A
    $(0, 1)$
  • B
    $(1, 2)$
  • ✓
    $(0, 2)$
  • D
    None of these.

Answer: C.

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Q 62 Marks Questions2 Marks
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\sin\frac{1}{\text{x}}\text{ for}-1\leq\text{x}\leq1$
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Q 72 Marks Questions2 Marks
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3]$
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Q 83 Marks Question3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
$\text{f}(\text{x})=\sqrt{\text{x}^2-4}\text{ on }[2,4]$
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Q 93 Marks Question3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point $'c'$ in the indicated interval as stated by the Lagrange's mean value theorem.
$f(x) = x^2 + x - 1$ on $[0, 4]$
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Q 103 Marks Question3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.$\text{f}(\text{x})=\sin\text{x}-\sin2\text{x}-\text{x}\text{ on }[0,\pi]$
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Q 113 Marks Question3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point $'c\ '$ in the indicated interval as stated by the Lagrange's mean value theorem. $f(x) = 2x^2 - 3x + 1$ on $[1, 3]$
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Q 135 Marks Questions5 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point $'c'$ in the indicated interval as stated by the Lagrange's mean value theorem.
$f(x) = x^{3 }- 5x^2 - 3x$ on $[1, 3]$
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Q 175 Marks Questions5 Marks
Verify Rolle's theorem for the following function on the indicated intervals$\text{f}(\text{x})=\sin2\text{x}\text{ on }\Big[0,\frac{\pi}{2}\Big]$
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