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Maxima and Minima Maths - Maxima and Minima

Maharashtra Board - STD 12 Science - Maths (MSBSHSE - English Medium). 140 questions in this chapter.

Question types

Maxima and Minima question types

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

140
Questions
4
Question groups
5
Question types
Sample Questions

Maxima and Minima questions

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

Q 1MCQ1 Mark
If $\text{f}(\text{x})=\frac{1}{4\text{x}^{2}+2\text{x}+1}$, then its maximum value is :
  • ✓
    $\frac{4}{3}$
  • B
    $\frac{2}{3}$
  • C
    $1$
  • D
    $\frac{3}{4}$

Answer: A.

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Q 2MCQ1 Mark
If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is:
  • A
    $\frac{3}{4}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{4}$
  • ✓
    $\frac{2}{3}$

Answer: D.

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Q 3MCQ1 Mark
The sum of two non$-$zero number is $8$, the minimum value of the sum of the reciprohcle is :
  • A
    $\frac{1}{4}$
  • ✓
    $\frac{1}{2}$
  • C
    $\frac{1}{8}$
  • D
    None of these.

Answer: B.

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Q 4MCQ1 Mark
if $x$ lies in the interval $[0, 1]$, then the least value of $x^2 + x + 1$ is :
  • A
    $3$
  • B
    $\frac{3}{4}$
  • ✓
    $1$
  • D
    none of these.

Answer: C.

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Q 5MCQ1 Mark
The minimum value of $\frac{\text{x}}{\log_{\text{e}}\text{x}}$ is .
  • ✓
    $\text{e}$
  • B
    $\frac{1}{\text{e}}$
  • C
    $1$
  • D
    None of these

Answer: A.

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Q 12Solve the Following Question.(3 Marks)3 Marks
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\text{x}\sqrt{1-\text{x}}, \text{x}\geq0$
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Q 13Solve the Following Question.(3 Marks)3 Marks
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\text{x}^{3}-6\text{x}^{2}+9\text{x}+15$
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Q 16Solve the Following Question.(5 Marks)5 Marks
A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?
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Q 17Solve the Following Question.(5 Marks)5 Marks
Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following functions. Also, find the points of inflection,
$\text{f}(\text{x})=\text{x}+\sqrt{1-\text{x}},\text{x}\leq 1$
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Q 18Solve the Following Question.(5 Marks)5 Marks
A beam is supported at the two ends and is uniformly loaded. The bending moment M at a distance x from one end is given by
$\text{M}=\frac{\text{WL}}{2}\text{x}-\frac{\text{W}}{2}\text{x}^{2}$
Find the point at which M is maximum in each case.
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Q 20Solve the Following Question.(5 Marks)5 Marks
A tank with rectangular base and rectangular sides, open at the top is to the constructed so that its depth is $2\ m$ and volume is $8m^3.$ If building of tank cost $70$ per square metre for the base and Rs $45$ per square matre for sides, what is the cost of least expensive tank?
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