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GATE Civil 2023 Set 1 | GA Question: 10
A square of side length $4 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, ... $ $8$4$12$10$
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GATE Electrical 2023 | GA Question: 10
A square with sides of length $6 \mathrm{~cm} $ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, ... of the shaded region is_______ $\mathrm{cm}^2.$6 \pi$18$20$9 \pi$
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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 figures below. ... $? $2 : 3$1 : 1$3 : 2$2 : 1$
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TIFR CSE 2021 | Part A | Question: 2
What is the area of a rectangle with the largest perimeter that can be inscribed in the unit circle (i.e., all the vertices of the rectangle are on the circle with radius $1$)?$1$2$3$4$5$
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GATE Civil 2021 Set 2 | GA Question: 9
In the figure shown above, $\text{PQRS}$ ... }{2}$\frac{1}{2}$\frac{\pi }{2}-1$\frac{\pi }{4}$
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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 $\textsf{MON}$ ... the area of the circle in $\text{cm}^{2}?$2\pi$50\pi$75\pi$100\pi$
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GATE Electrical 2020 | GA Question: 9
Given a semicircle with $\text{O}$ as the centre, as shown in the figure, the ratio $\dfrac{\overline{AC}+\overline{CB}}{\overline{AB}}$ ... overline{CB}$ and $\overline{AB}$ are chords.$\sqrt{2}$\sqrt{3}$2$3$
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GATE ECE 2020 | GA Question: 8
A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$, then the area ... $\pi a^{2}-3a^{2}$
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GATE CSE 2020 | Question: GA-8
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner ... )^{2}]$\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
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TIFR CSE 2020 | Part A | Question: 13
What is the area of the largest rectangle that can be inscribed in a circle of radius $R$?$R^{2}/2$\pi \times R^{2}/2$R^{2}$2R^{2}$None of the above
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ISI2014-DCG-14
$x^4-3x^2+2x^2y^2-3y^2+y^4+2=0$ representsA pair of circles having the same radiusA circle and an ellipseA pair of circles having different radiinone of the above
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ISI2014-DCG-58
Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of one of the ... $(2\sqrt{2}, -2\sqrt{2})$
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ISI2014-DCG-60
The equation of any circle passing through the origin and with its centre on the $X$-axis is given by$x^2+y^2-2ax=0$ where $a$ must be positive$x^2+y^2-2ax=0$ for any ... $b$ must be positive$x^2+y^2-2by=0$ for any given $b \in \mathbb{R}$
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ISI2015-MMA-48
Suppose the circle with equation $x^2+y^2+2fx+2gy+c=0$ cuts the parabola $y^2=4ax, \: (a>0)$ at four distinct points. If $d$ denotes the sum of the ordinates of these four ... $ is$\{0\}$(-4a,4a)$(-a,a)$(- \infty, \infty)$
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ISI2015-DCG-38
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2), (3,-4)$ and $(5,6)$ is$12$14$16$18$
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ISI2017-DCG-19
The angle between the tangents drawn from the point $(-1, 7)$ to the circle $x^2+y^2=25$ is$\tan^{-1} (\frac{1}{2})$\tan^{-1} (\frac{2}{3})$\frac{\pi}{2}$\frac{\pi}{3}$
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ISI2018-DCG-25
There are three circles of equal diameter ($10$ units each) as shown in the figure below. The straight line $PQ$ passes through the centres of all the three circles. The ... of the line segment $AB$ is$6$ units$7$ units$8$ units$9$ units
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UPPCL AE 2018:85
The set of equations $x^{2} + y^{2} = 1$ and $x + y = 0$ has how many real solutions?Infinite number of solutionsNo solution$2$ solutions$1$ solution
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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}+ ... $\frac{\pi}{6}+\frac{\sqrt{3}}{2}$
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ISI-2014-14
The locus of the center of a circle that passes through origin and cuts off a length $2a$ from the line $y=c$ is$x^2+2cx=a^2+c^2$x^2+2cy=a^2+c^2$y^2+cx=a^2+c^2$y^2+2cy=a^2+c^2$
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GATE CSE 2018 | Question: GA-3
The area of a square is $d$. What is the area of the circle which has the diagonal of the square as its diameter?$\large{\pi} d$\large{\pi} d^2$\dfrac{1}{4}\large{\pi} d^2$\dfrac{1}{2}\large{\pi} d$
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TIFR CSE 2018 | Part A | Question: 1
Consider a point $A$ inside a circle $C$ that is at distance $9$ from the centre of a circle. Suppose you told that there is a chord of length $24$ passing ... $ have integer length and pass through $A?$2$6$7$12$14$
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