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Recent questions tagged geometry

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61
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$$\mid y \mid \leq x$
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62
ISI2015-DCG-38
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2), (3,-4)$ and $(5,6)$ is $12$ $14$ $16$ $18$
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2), (3,-4)$ and $(5,6)$ is$12$$14$$16$$18$
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63
ISI2015-DCG-39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if $b=\sqrt{2}a$ $b=\pm \sqrt{2}b$ $b= – \sqrt{2}a$ $b=a$
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$b=\pm \sqrt{2}b$$b= – \sqrt{2}a$$b=a$...
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64
ISI2015-DCG-40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent a circle a parabola an ellipse a hyperbola
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) representa circlea ...
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65
ISI2015-DCG-41
A straight line touches the circle $x^2 +y^2=2a^2$ and also the parabola $y^2=8ax$. Then the equation of the straight line is $y=\pm x$ $y=\pm (x+a)$ $y=\pm (x+2a)$ $y=\pm (x-21)$
A straight line touches the circle $x^2 +y^2=2a^2$ and also the parabola $y^2=8ax$. Then the equation of the straight line is$y=\pm x$$y=\pm (x+a)$$y=\pm (x+2a)$$y=\pm (x...
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66
ISI2015-DCG-42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8$. hen its eccentricity is $\frac{4}{5}$ $\frac{1}{\sqrt{52}}$ $\frac{3}{5}$ $\frac{1}{2}$
In an ellipse, the distance between its foci is $6$ and its minor axis is $8$. hen its eccentricity is$\frac{4}{5}$$\frac{1}{\sqrt{52}}$$\frac{3}{5}$$\frac{1}{2}$
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67
ISI2015-DCG-43
Four tangents are drawn to the ellipse $\displaystyle{}\frac{x^2}{9} + \frac{y^2}{5} =1$ at the ends of its latera recta. The area of the quadrilateral so formed is $27$ $\frac{13}{2}$ $\frac{15}{4}$ $45$
Four tangents are drawn to the ellipse $\displaystyle{}\frac{x^2}{9} + \frac{y^2}{5} =1$ at the ends of its latera recta. The area of the quadrilateral so formed is$27$$\...
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68
ISI2015-DCG-44
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2}$, then the equation of the hyperbola is $y^2-x^2=32$ $x^2-y^2=16$ $y^2-x^2=16$ $x^2-y^2=32$
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2}$, then the equation of the hyperbola is$y^2-x^2=32$$x^2-y^2=16$$y^2-x^2=16$$x^2-...
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70
ISI2015-DCG-59
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in $[\:- \sqrt{3}, \sqrt{3}\:]$ $(\: – \sqrt{3}, \sqrt{3}\:]$ $(\:\frac{3}{2}, \sqrt{3}\:)$ $(\:\frac{3}{2}, \sqrt{3}\:]$
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in$[\:- \sqrt{3}, \sqrt{3}\:]$$(\: – \sqrt{3}, \sqrt{3}\:]$$(\:\frac{3}{2}, \sqrt{3}\:)$...
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71
ISI2015-DCG-60
Which of the following relations is true for the following figure? $b^2 = c(c+a)$ $c^2 = a(a+b)$ $a^2=b(b+c)$ All of these
Which of the following relations is true for the following figure?$b^2 = c(c+a)$$c^2 = a(a+b)$$a^2=b(b+c)$All of these
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73
ISI2016-DCG-59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in $\left[\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\frac{3}{2},\sqrt{3}\:\right)$ $\left(\:\frac{3}{2},\sqrt{3}\:\right]$
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in$\left[\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:\frac{3}{...
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2 answers
74
ISI2017-DCG-2
The area of the shaded region in the following figure (all the arcs are circular) is $\pi$ $2 \pi$ $3 \pi$ $\frac{9}{8} \pi$
The area of the shaded region in the following figure (all the arcs are circular) is$\pi$$2 \pi$$3 \pi$$\frac{9}{8} \pi$
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75
ISI2017-DCG-14
If $a,b,c$ are the sides of a triangle such that $a:b:c=1: \sqrt{3}:2$, then $A:B:C$ (where $A,B,C$ are the angles opposite to the sides of $a,b,c$ respectively) is $3:2:1$ $3:1:2$ $1:2:3$ $1:3:2$
If $a,b,c$ are the sides of a triangle such that $a:b:c=1: \sqrt{3}:2$, then $A:B:C$ (where $A,B,C$ are the angles opposite to the sides of $a,b,c$ respectively) is$3:2:1...
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76
ISI2017-DCG-18
If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{B-C}{2} \tan \frac{A}{2}$ is equal to $\frac{b+c}{b-c}$ $\frac{b-c}{b+c}$ $\frac{c-b}{c+b}$ none of these
If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{B-C}{2} \tan \frac{A}{2}$ is equal to$\frac{b+c}{b-c}$$\frac{b-c}{b+c}$$\frac{c-b}{c+b}$none of these
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77
ISI2017-DCG-19
The angle between the tangents drawn from the point $(-1, 7)$ to the circle $x^2+y^2=25$ is $\tan^{-1} (\frac{1}{2})$ $\tan^{-1} (\frac{2}{3})$ $\frac{\pi}{2}$ $\frac{\pi}{3}$
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}$$\frac{\pi}{3...
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78
ISI2017-DCG-20
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes are $(3,2)$, then the equation of the straight line is $2x+3y=12$ $3x+2y=0$ $2x+3y=0$ $3x+2y=12$
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes are $(3,2)$, then the equation of the straight line is$2x+3y=12$$3...
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79
ISI2017-DCG-21
If $a,b,c$ are in $A.P.$ , then the straight line $ax+by+c=0$ will always pass through the point whose coordinates are $(1,-2)$ $(1,2)$ $(-1,2)$ $(-1,-2)$
If $a,b,c$ are in $A.P.$ , then the straight line $ax+by+c=0$ will always pass through the point whose coordinates are$(1,-2)$$(1,2)$$(-1,2)$$(-1,-2)$
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1 answer
80
ISI2017-DCG-29
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is $2$ $4$ $6$ $8$
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is$2$$4$$6$$8$
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1 votes
1 answer
81
ISI2018-DCG-15
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is $6$ $9$ $12$ $18$
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is$6$$9$$12$$18$
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1 votes
2 answers
82
ISI2019-MMA-17
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is $(3,6)$ $(6,3)$ $(5,10)$ $(10,5)$
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is$(3,6)$$(6,3)$$(5,10)$$(10,5)$
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1 votes
1 answer
83
ISI2019-MMA-16
If $S$ and $S’$ are the foci of the ellipse $3x^2 + 4y^2=12$ and $P$ is a point on the ellipse, then the perimeter of the triangle $PSS’$ is $4$ $6$ $8$ dependent on the coordinates of $P$
If $S$ and $S’$ are the foci of the ellipse $3x^2 + 4y^2=12$ and $P$ is a point on the ellipse, then the perimeter of the triangle $PSS’$ is$4$$6$$8$dependent on the ...
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1 votes
1 answer
85
GATE2019 CE-1: GA-9
A square has side $5$ cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is _______ cm. $18.50$ $15.10$ $10.00$ $8.50$
A square has side $5$ cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger squ...
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3 votes
1 answer
88
GATE2019 IN: GA-3
The radius as well as the height of a circular cone increases by $10\%.$ The percentage increase in its volume is ________. $17.1$ $21.0$ $33.1$ $72.8$
The radius as well as the height of a circular cone increases by $10\%.$ The percentage increase in its volume is ________.$17.1$$21.0$$33.1$$72.8$
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1 votes
1 answer
89
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 solutions No solution $2$ solutions $1$ solution
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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