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Recent questions tagged geometry

1 vote
1 answer
1
In a triangle $\text{ABC}, \angle \text{BCA} = 50^{\circ}. \text{D}$ and $\text{E}$ are points on $\text{AB}$ and $\text{AC},$ respectively, such that $\text{AD = DE}.$ If $\text{F}$ is a point on $\text{BC}$ such that $\text{BD = DF},$ then $\angle \text{FDE, in degrees},$ is equal to $96$ $72$ $80$ $100$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 82 views
1 vote
1 answer
2
Let $\text{ABCD}$ be a parallelogram. The lengths of the side $\text{AD}$ and the diagonal $\text{AC}$ are $10 \; \text{cm}$ and $20 \; \text{cm},$ respectively. If the angle $\angle \text{ADC}$ is equal to $30^{\circ}$ then the area of the parallelogram, in sq. cm, is $\frac{25(\sqrt{5} + \sqrt{15})}{2}$ $25 (\sqrt{5} + \sqrt{15})$ $\frac{25 (\sqrt{3} + \sqrt{15})}{2}$ $25 (\sqrt{3} + \sqrt{15})$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 62 views
1 vote
1 answer
3
The cost of fencing a rectangular plot is $ ₹ \; 200 \; \text{per ft}$ along one side, and $ ₹ \; 100 \; \text{per ft}$ along the three other sides. If the area of the rectangular plot is $60000 \; \text{sq. ft},$ then the lowest possible cost of fencing all four sides, in $\text{INR},$ is $160000$ $100000$ $120000$ $90000$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 77 views
1 vote
1 answer
4
A park is shaped like a rhombus and has area $96 \; \text{sq m}.$ If $40 \; \text{m}$ of fencing is needed to enclose the park, the cost, in $\text{INR},$ of laying electric wires along its two diagonals, at the rate of $ ₹ \; 125 \; \text{per m},$ is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 106 views
1 vote
1 answer
5
If a rhombus has area $12 \; \text{sq cm}$ and side length $5 \; \text{cm},$ then the length, $\text{in cm},$ of its longer diagonal is $\sqrt{13} + \sqrt{12}$ $\sqrt{37} + \sqrt{13}$ $\frac{\sqrt{37} + \sqrt{13}}{2}$ $\frac{\sqrt{13} + \sqrt{12}}{2}$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 85 views
1 vote
1 answer
6
The sides $\text{AB}$ and $\text{CD}$ of a trapezium $\text{ABCD}$ are parallel, with $\text{AB}$ being the smaller side. $\text{P}$ is the midpoint of $\text{CD}$ and $\text{ABPD}$ is a parallelogram. If the difference between the areas of the parallelogram $\text{ABPD}$ and the ... $\text{in sq cm},$ of the trapezium $\text{ABCD}$ is $25$ $30$ $40$ $20$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 73 views
1 vote
1 answer
7
Let $\text{D}$ and $\text{E}$ be points on sides $\text{AB}$ and $\text{AC},$ respectively, of a triangle $\text{ABC},$ such that $\text{AD}$ : $\text{BD} = 2 : 1$ and $\text{AE}$ : $\text{CE} = 2 : 3.$ If the area of the triangle $\text{ADE}$ is $8 \; \text{sq cm},$ then the area of the triangle $\text{ABC, in sq cm},$ is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 84 views
1 vote
1 answer
8
If the area of a regular hexagon is equal to the area of an equilateral triangle of side $12 \; \text{cm},$ then the length, in cm, of each side of the hexagon is $6 \sqrt{6}$ $2 \sqrt{6}$ $4 \sqrt{6}$ $\sqrt{6}$
asked Jan 19 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 83 views
1 vote
1 answer
9
Suppose the length of each side of a regular hexagon $\text{ABCDEF}$ is $2 \; \text{cm}.$ It $\text{T}$ is the mid point of $\text{CD},$ then the length of $\text{AT, in cm},$ is $\sqrt{15}$ $\sqrt{13}$ $\sqrt{12}$ $\sqrt{14}$
asked Jan 19 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 112 views
1 vote
1 answer
10
A circle of diameter $8 \; \text{inches}$ is inscribed in a triangle $\text{ABC}$ where $\angle \text{ABC} = 90^{\circ}.$ If $\text{BC} = 10 \; \text{inches}$ then the area of the triangle in $\text{square inches}$ is
asked Jan 19 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 76 views
0 votes
0 answers
11
The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$ $\frac{12 \pi}{5}$ $\frac{123 \pi}{7}$ $\frac{205 \pi}{9}$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 70 views
0 votes
0 answers
12
The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$ $14$ $13$ $15$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 52 views
0 votes
0 answers
13
In a trapezium $\text{ABCD},\; \text{AB}$ is parallel to $\text{DC}, \; \text{BC}$ is perpendicular to $\text{DC}$ and $\angle \text{BAD} = 45^{\circ}.$ If $\text{DC} = 5 \; \text{cm}, \; \text{BC} = 4 \; \text{cm},$ the area of the trapezium in $\text{sq. cm}$ is
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 47 views
2 votes
1 answer
14
The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{cm}.$ The area, $\text{T},$ of the triangle and the area, $\text{R},$ of the rectangle, both in $\text{sq cm},$ ... the sides of the rectangle are in the ratio $1:3,$ then the length, in cm, of the longer side of the rectangle, is $24$ $27$ $21$ $18$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 152 views
2 votes
1 answer
15
Let $\text{C}$ be a circle of radius $5 \; \text{meters}$ having center at $\text{O}.$ Let $\text{PQ}$ be a chord of $\text{C}$ that passes through points $\text{A}$ and $\text{B}$ where $\text{A}$ is located $4 \; \text{meters}$ north of $\text{O}$ and $\text{B}$ is located $3 \; \text{meters}$ east of $\text{O}.$ Then, the length of $\text{PQ}$, in meters, is nearest to $7.2$ $7.8$ $6.6$ $8.8$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 145 views
2 votes
1 answer
16
Let $\text{C}1$ and $\text{C}2$ be concentric circles such that the diameter of $\text{C}1$ is $2 \; \text{cm}$ longer than that of $\text{C}2.$ If a chord of $\text{C}1$ has length $6 \; \text{cm}$ and is a tangent to $\text{C}2,$ then the diameter, in $\text{cm},$ of $\text{C}1$ is
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 124 views
1 vote
1 answer
17
From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s.$ Then the area of the triangle is $\frac{\sqrt{3}s^{2}}{2}$ $\frac{s^{2}}{\sqrt{3}}$ $\frac{2s^{2}}{\sqrt{3}}$ $\frac{s^{2}}{2 \sqrt{3}}$
asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 114 views
1 vote
1 answer
18
On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two$-$thirds of the painted area then the perimeter of the rectangle in inches is $5\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$ ... $3\sqrt{\pi }\left ( 5+\frac{12}{\pi} \right )$ $4\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$
asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 207 views
1 vote
1 answer
19
A circle is inscribed in a thombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\frac{3\pi }{25}$ $\frac{2\pi }{15}$
asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 5 88 354 70 views
0 votes
1 answer
20
A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path? $51 \pi$ square feet $60 \pi$ square feet $69 \pi$ square feet $90 \pi$ square feet
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 265 views
0 votes
1 answer
21
What is the area of a semicircle with a diameter of $16$ inches? $32 \pi$ square inches $64 \pi$ square inches $128 \pi$ square inches $256 \pi$ square inches
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 299 views
0 votes
1 answer
22
Which of the following figures has the largest perimeter $(1 \text{ foot} = 12 \text{ inches})$ a square with a diagonal of $5$ feet a rectangle with sides of $3$ feet and $4$ feet an equilateral triangle with a side equal to $48$ inches a regular hexagon whose longest diagonal is $6$ feet
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 238 views
0 votes
1 answer
23
The perimeter of a parallelogram is $50$ cm. The length of the parallelogram is $5$ cm more than the width. Find the length of the parallelogram. $15$ cm $11$ cm $5$ cm $10$ cm
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 297 views
0 votes
1 answer
24
A conical tent is to accommodate $10$ persons. Each person must have $6$ $m$^{2}$ space to sit and $30\;m^{3}$ of air to breath. What will be height of cone ? $37.5$ $m$ $150$ $m$ $75$ $m$ $15$ $m$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 227 views
0 votes
4 answers
25
In a swimming-pool $90$ m by $40$ m, $150$ men take a dip. If the average displacement of water by a man is $8$ cubic metres, what will be rise in water level ? $30$ cm $33.33$ cm $20.33$ cm $25$ cm
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 305 views
0 votes
1 answer
26
If $A$ be the area of a right angled triangle and $b$ be one of the sides containing the right angle, then the length of altitude on the hypotenuse is : $\frac{2Ab}{\sqrt{4b^{4}+A^{2}}}$ $\frac{Ab}{\sqrt{b^{4}+4A^{2}}}$ $\frac{2Ab}{\sqrt{b^{4}+4A^{2}}}$ $\frac{Ab}{\sqrt{4b^{4}+A^{2}}}$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 216 views
2 votes
1 answer
27
In an acute angled triangle $ABC$, if $\tan \left(A+B-C \right)=1$ and $\sec \left(B+C-A \right)=2$, Find angle $A$. $60^\circ$ $45^\circ$ $30^\circ$ $90^\circ$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 240 views
0 votes
1 answer
28
What will be area of the rhombus with equations of sides $ax \pm$ $by \pm c$ = $1$ ? $\frac{3c^{2}}{ab}$sq. units $\frac{4c^{2}}{ab}$sq. units $\frac{2c^{2}}{ab}$sq. units $\frac{c^{2}}{ab}$sq. units
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 303 views
0 votes
1 answer
29
If $\left (-4, 0 \right), \left(1, -1 \right)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on : $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 205 views
1 vote
1 answer
30
In a triangle $XYZ$, $P$ and $Q$ are points on ${XY,XZ}$ respectively such that $XP=2PY$, $XQ=2QZ$, then the ratio, of area of $\triangle XPQ$ and area of $\triangle XYZ$ is: $4:9$ $2:3$ $3:2$ $9:4$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 246 views
0 votes
1 answer
31
A conical tent is to accommodate $10$ persons. Each person must have $6m^{2}$ space to sit and $30m^{3}$ of air to breath. What will be height of cone? $37.5$ m $150$ m $75$ m $15$ m
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 185 views
0 votes
1 answer
32
In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with $38$ bangles. If he wanted to increase the size of square by one bangle each side of the square he found that $25$ bangles fall short of in completing the square. The actual number of bangles which he had with him the shop was_________. $1690$ $999$ $538$ $1000$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 174 views
0 votes
0 answers
33
$A,B,C$ are three towns forming a triangle. A man has to walk from one town to next town, then ride to the next town then again drive towards his starting point. He can walk,ride,drive a km in $a,b,c$ minutes respectively. If he starts from $B$, he takes $a-b+c$ ... from $A$ he takes $c+b-a$ hrs. The length of the triangle is: (assume the motion in anticlockwise direction) $60a$ $50a$ $40a$ $65a$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 196 views
0 votes
1 answer
34
A cylindrical box of radius $5$ cm contains $10$ solid spherical balls each of radius $5$ cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is: $\dfrac{2500\pi}{3}$ cubic cm $500\pi$ cubic cm $2500\pi$ cubic cm $\dfrac{5000\pi}{3}$ cubic cm
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 233 views
0 votes
1 answer
35
If $(-4,0),(1,-1)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on: $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 178 views
0 votes
1 answer
36
For a sphere of radius $10$ cm, the numerical value of the surface area is how many percent of the numerical value of its volume? $26.5\%$ $24\%$ $30\%$ $45\%$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 147 views
0 votes
1 answer
37
Line $AB$ is $24$ metres in length and is tangent to the inner one of the two concentric circles at point $C.$ Points $A$ and $B$ lie on the circumference of the outer circle. It is known that the radii of the two circles are integers. The radius of the outer circle is $13$ m $5$ m $7$ m $4$ m
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 499 views
0 votes
1 answer
38
A rectangular field is to be fenced on three sides leaving a side of $20$ feet uncovered. If the area of the field is $680$ sq feet, how many feet of fencing will be required? $34$ $40$ $68$ $88$
asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 275 views
0 votes
2 answers
39
If $10$, $12$ and '$x$' are sides of an acute angled triangle, how many integer values of '$x$' are possible ? $7$ $12$ $9$ $13$
asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 1.0k views
0 votes
1 answer
40
The length of a rope, to which a cow is tied, is increased from $19$ m to $30$ m. How much additional ground will it be able to graze ? Assume that the cow is able to move on all sides with equal ease. Use $\pi = \frac{22}{7}$ in your calculations. $1696$ sq m $1694$ sq m $1594$ sq m $1756$ sq m
asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 119 744 834 375 views
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