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Recent questions tagged area

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GATE Mechanical 2023 | Question: 22
A linear transformation maps a point $(x, y)$ in the plane to the point $(\hat{x}, \hat{y})$ according to the rule$$\hat{x}=3 y, \quad \hat{y}=2 x .$$Then, the disc $x^2+...
9 9 votes
2 2 answers
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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 $x$ – a...
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4 4 votes
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GATE Mechanical 2022 Set 2 | GA | Question: 10
Equal sized circular regions are shaded in a square sheet of paper of $1$ cm side length. Two cases, case $\text{M}$ and case $\text{N}$, are considered as shown in the f...
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7 7 votes
4 answers 4 answers
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GATE Mechanical 2021 Set 2 | GA | Question: 8
The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is ___________$\frac{1}{8}$$\frac{1}{6}$$\frac{1}{4}$$\fr...
15 15 votes
4 answers 4 answers
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GATE Mechanical 2021 Set 2 | GA | Question: 9
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded s...
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GATE Mechanical 2021 Set 1 | GA | Question: 3
In the above figure, $\textsf{O}$ is the center of the circle and, $\textsf{M}$ and $\textsf{N}$ lie on the circle. The area of the right triangle $\textsf{MON}$ is $50\;...
7 7 votes
1 answers 1 answer
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GATE Mechanical 2018 Set 1 | GA | Question: 4
A rectangle becomes a square when its length and breadth are reduced by $10$ m and $5$ m, respectively. During this process, the rectangle loses $650 m^2$ of area. What i...
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15 15 votes
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GATE Mechanical 2017 Set 1 | GA | Question: 8
Let $S_{1}$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x - 1 \mid \leq 2$ and $ \mid y+2 \mid \leq 3$. Let $S_{2}$ be the plan...
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GATE Mechanical 2016 Set 3 | GA | Question: 10
A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$...
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12 12 votes
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GATE Mechanical 2016 Set 2 | GA | Question: 5
A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If t...
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