Areas of Bounded Regions - Maharashtra Board STD 12 Maths Questions - Vidyadip

Question types

Areas of Bounded Regions question types

122 questions across 2 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

122

Questions

2

Question groups

5

Question types

MCQ

Solve the Following Question.(5 Marks)

Sample Questions

Areas of Bounded Regions 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

The area of the region $\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\leq1\leq\text{x}+\text{y}\}$ is:

A
$\frac{\pi}{5}$
B
$\frac{\pi}{4}$
✓
$\frac{\pi}{4}-\frac{1}{2}$
D
$\frac{\pi^2}{2}$

Answer: C.

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Q 2MCQ1 Mark

The area bounded by the curve $\text{y}=\log_{\text{e}}\text{x}$ and $x-$axis and the straight line $x = e$ is:

A
$\text{e sq. units}$
✓
$1\text{ sq. units}$
C
$1-\frac{1}{\text{e}}\text{ sq. units}$
D
$1+\frac{1}{\text{e}}\text{ sq. units}$

Answer: B.

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Q 3MCQ1 Mark

Area bounded by the curve $y = x^3$, the x-axis and the ordinates $x = -2$ and $x = 1$ is:

A
$-9$
B
$\frac{-15}{4}$
C
$\frac{15}{4}$
✓
$\frac{17}{4}$

Answer: D.

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Q 4MCQ1 Mark

Area bounded by parabola $y^2 = x$ and straight line $2y = x$ is:

✓
$43$
B
$1$
C
$23$
D
$13$

Answer: A.

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Q 5MCQ1 Mark

The area bounded by the curve $y^2= 8x$ and $x^2 = 8y$ is:

✓
$\frac{16}{3}\text{ sq. units}$
B
$\frac{3}{16}\text{ sq. units}$
C
$\frac{14}{3}\text{ sq. units}$
D
$\frac{3}{14}\text{ sq. units}$

Answer: A.

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Q 6Solve the Following Question.(5 Marks)5 Marks

Find the area of the region bounded by the parabola $y^2 = 2x + 1$ and the line $x - y - 1 = 0.$

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Q 7Solve the Following Question.(5 Marks)5 Marks

Find the area of the region $\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\leq4,\text{x}+\text{y}\geq2\}$

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Q 8Solve the Following Question.(5 Marks)5 Marks

Find the area of the region bounded by the paraola $y^2 = 4ax$ and line$ x = a.$

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Q 9Solve the Following Question.(5 Marks)5 Marks

Draw a rough sketch of the graph of the function $\text{y}=2\sqrt{1-\text{x}^{2}}, \text{x}\in [0, 1] $ and evaluate the area enclosed between the curve and the x-axis.

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Q 10Solve the Following Question.(5 Marks)5 Marks

Sketch the region bounded by the curves $y = x^2 + 2, y = x, x = 0$ and $x = 1$. Also find the area of this region.

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