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Recent questions tagged area

3 votes
1 answer
4
GATE Mechanical 2022 Set 2 | GA Question: 3
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ – axis? $\frac{1}{2}$ $1$ $2$ $4$
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ –...
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1 votes
1 answer
6
GATE ECE 2022 | GA Question: 8
Four points $\text{P(0, 1), Q(0, – 3), R( – 2, – 1),}$ and $\text{S(2, – 1)}$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral? $4$ $4 \sqrt{2}$ $8$ $8 \sqrt{2}$
Four points $\text{P(0, 1), Q(0, – 3), R( – 2, – 1),}$ and $\text{S(2, – 1)}$ represent the vertices of a quadrilateral.What is the area enclosed by the quadrilat...
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13 votes
2 answers
7
GATE CSE 2022 | GA Question: 2
A function $y(x)$ is defined in the interval $[0, 1]$ on the $x - $ ... the curve for the interval $[0, 1]$ on the $x - $ axis? $\frac{5}{6}$ $\frac{6}{5}$ $\frac{13}{6}$ $\frac{6}{13}$
A function $y(x)$ is defined in the interval $[0, 1]$ on the $x – $ axis as$$y(x) = \left\{\begin{matrix} 2& \text{if} & 0 \leq x < \frac{1}{3} \\ 3& \text{if}& \frac{1...
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3 votes
1 answer
10
GATE Electrical 2021 | GA Question: 7
In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $\text{cm}^{2}$ is: $12.50$ $6.25$ $3.125$ $1.5625$
In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown...
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0 votes
1 answer
14
ISI2014-DCG-20
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(t)$ equals $0$ $1$ $2$ $4$
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(...
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0 votes
1 answer
15
ISI2014-DCG-52
The area under the curve $x^2+3x-4$ in the positive quadrant and bounded by the line $x=5$ is equal to $59 \frac{1}{6}$ $61 \frac{1}{3}$ $40 \frac{2}{3}$ $72$
The area under the curve $x^2+3x-4$ in the positive quadrant and bounded by the line $x=5$ is equal to$59 \frac{1}{6}$$61 \frac{1}{3}$$40 \frac{2}{3}$$72$
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0 votes
0 answers
16
ISI2015-MMA-82
The volume of the solid, generated by revolving about the horizontal line $y=2$ the region bounded by $y^2 \leq 2x$, $x \leq 8$ and $y \geq 2$, is $2 \sqrt{2\pi}$ $28 \pi/3$ $84 \pi$ none of the above
The volume of the solid, generated by revolving about the horizontal line $y=2$ the region bounded by $y^2 \leq 2x$, $x \leq 8$ and $y \geq 2$, is$2 \sqrt{2\pi}$$28 \pi/3...
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0 votes
2 answers
17
ISI2015-DCG-16
The shaded region in the following diagram represents the relation $y \leq x$ $\mid y \mid \leq \mid x \mid$ $y \leq \mid x \mid$ $\mid y \mid \leq x$
The shaded region in the following diagram represents the relation$y \leq x$$\mid y \mid \leq \mid x \mid$$y \leq \mid x \mid$$\mid y \mid \leq x$
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0 votes
0 answers
18
ISI2016-DCG-15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
The shaded region in the following diagram represents the relation$y\:\leq\: x$$\mid \:y\mid \:\leq\: \mid x\:\mid $$y\:\leq\: \mid x\:\mid$$\mid \:y\mid\: \leq\: x$
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0 votes
1 answer
19
ISI2016-DCG-16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
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0 votes
1 answer
20
ISI2016-DCG-43
Four tangents are drawn to the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ at the ends of its latera recta. The area of the quadrilateral so formed is $27$ $\frac{13}{2}$ $\frac{15}{4}$ $45$
Four tangents are drawn to the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ at the ends of its latera recta. The area of the quadrilateral so formed is$27$$\frac{13}{2}$...
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0 votes
1 answer
21
ISI2016-DCG-52
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is$\frac{64}{3}$$6$$\frac{16}{3}$$\frac{32}{3}$
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0 votes
2 answers
22
ISI2017-DCG-2
The area of the shaded region in the following figure (all the arcs are circular) is $\pi$ $2 \pi$ $3 \pi$ $\frac{9}{8} \pi$
The area of the shaded region in the following figure (all the arcs are circular) is$\pi$$2 \pi$$3 \pi$$\frac{9}{8} \pi$
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0 votes
1 answer
23
ISI2017-DCG-29
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is $2$ $4$ $6$ $8$
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is$2$$4$$6$$8$
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0 votes
1 answer
24
ISI2018-DCG-26
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$-axis in the first quadrant is $9$ $\frac{27}{4}$ $36$ $18$
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$-axis in the first quadrant is$9$$\frac{27}{4}$$36$$18$
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0 votes
1 answer
25
ISI2017-MMA-1
The area lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and lines $x=0 \text{ and } x=1$ is given by $\frac{\pi}{3}+\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$ $\frac{\pi}{3}-\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{2}$
The area lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and lines $x=0 \text{ and } x=1$ is given by$\frac{\pi}{3}+\frac{\sqrt{3}}{2}$$\frac{\pi}{6}+\f...
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1 votes
1 answer
26
ISRO2012-ECE: Engineering Mathematics
The area bounded by the curves $y^2 =x, y=x $ is given by $2/3$ $1/2$ $1/6$ $1/3$
The area bounded by the curves $y^2 =x, y=x $ is given by$2/3$$1/2$$1/6$$1/3$
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