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Recent questions tagged geometry

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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. In the case $\text{M}$, four circles are shaded in the square sheet and in the case $\text{N}$, nine circles are ... of unshaded regions of case $\text{M}$ to that of case $\text{N}$? $2 : 3$ $1 : 1$ $3 : 2$ $2 : 1$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
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1 answer
A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus? $\dfrac{1}{\sqrt{2}}$ $\dfrac{1}{2\sqrt{2}}$ $\sqrt{2}$ $2 \sqrt{2}$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
1 vote
1 answer
An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle? $3\sqrt{3} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 4 : 2\sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : 2\sqrt{\pi}$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
1 vote
2 answers
The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is ___________ $\frac{1}{8}$ $\frac{1}{6}$ $\frac{1}{4}$ $\frac{1}{2}$
asked Mar 1, 2021 in Quantitative Aptitude go_editor 5.0k points
1 vote
1 answer
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 $50\;\text{cm}^{2}$. What is the area of the circle in $\text{cm}^{2}?$ $2\pi$ $50\pi$ $75\pi$ $100\pi$
asked Feb 22, 2021 in Quantitative Aptitude gatecse 1.6k points
1 vote
1 answer
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y=2x-0.1x^2$ where $y$ is the height of the arch in meters. The maximum possible height of the arch is $8$ meters $10$ meters $12$ meters $14$ meters
asked Mar 20, 2018 in Quantitative Aptitude Andrijana3306 1.5k points
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A wire would enclose an area of $1936 \: m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters? $1096$ $1111$ $1243$ $2486$
asked Feb 17, 2018 in Quantitative Aptitude Arjun 27.4k points
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The perimeters of a circle, a square, and an equilateral triangle are equal. Which one of the following statements is true? The circle has the largest area The square has the largest area The equilateral triangle has the largest area All the three shapes have the same area
asked Feb 17, 2018 in Quantitative Aptitude Arjun 27.4k points
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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 is the area of the original rectangle in square meters? $1125$ $2250$ $2924$ $4500$
asked Feb 17, 2018 in Quantitative Aptitude Arjun 27.4k points
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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 plane figure given by the inequalities $x-y \geq -2, y \geq 1$, and $x \leq 3$. Let $S$ be the union of $S_{1}$ and $S_{2}$. The area of $S$ is. $26$ $28$ $32$ $34$
asked Feb 27, 2017 in Quantitative Aptitude Arjun 27.4k points
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A right-angled cone (with base radius $5$ cm and height $12$ cm), as shown in the figure below, is rolled on the ground keeping the point $P$ fixed until the point $Q$ (at the base of the cone, as shown) touches the ground again. By what angle (in radians) about $P$ does the cone travel? $\dfrac{5\pi}{12} \\$ $\dfrac{5\pi}{24} \\$ $\dfrac{24\pi}{5} \\$ $\dfrac{10\pi}{13}$
asked Feb 27, 2017 in Quantitative Aptitude Arjun 27.4k points
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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 $1:2$. What is the length of the side of the square (in $mm$) such that the combined area of the square and the rectangle is a $\textbf{MINIMUM}$? $30$ $40$ $120$ $180$
asked Feb 24, 2017 in Quantitative Aptitude Arjun 27.4k points
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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 the perimeter of the window is $6$ $m$, the area of the window in $m^2$ is ___________. $1.43$ $2.06$ $2.68$ $2.88$
asked Feb 24, 2017 in Quantitative Aptitude Arjun 27.4k points
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Right triangle $PQR$ is to be constructed in $xy$-plane so that the right angle is at $P$ and line $PR$ is parallel to $x$-axis.The $x$ and $y$ coordinates of $P$, $Q$ and $R$ are to be integers that satisfies the inequalities: $-4\leq x\leq 5$ and $6\leq y\leq 16$. How many different triangles could be constructed with these properties? $110$ $1100$ $9900$ $10000$
asked Feb 24, 2017 in Quantitative Aptitude Arjun 27.4k points
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In the given figure $Q$ is a right triangle, $PS:QS = 3:1$ $RT:QT = 5:2$ $PU:UR = 1:1$ If area of triangle $QTS$ is $20$ $cm^2$, then the area of triangle $PQR$ in $cm^2$ is_____
asked Feb 24, 2017 in Quantitative Aptitude Arjun 27.4k points
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From a circular sheet of paper of radius $30$ $cm$, a sector of $10\%$ area is removed. If the remaining part is used to make a conical surface, then the ratio of radius and height of cone is_____
asked Feb 24, 2017 in Quantitative Aptitude Arjun 27.4k points
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