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Most viewed questions in Geometry
3
votes
2
answers
1
ISRO2014-65
A cube of side $1$ unit is placed in such a way that the origin coincides with one of its top vertices and the three axes along three of its edges. What are the co-ordinates of the vertex which is diagonally opposite to the vertex whose co-ordinates are $(1, 0, 1)?$ $(0, 0, 0)$ $(0, -1, 0)$ $(0, 1, 0)$ $(1, 1, 1)$
A cube of side $1$ unit is placed in such a way that the origin coincides with one of its top vertices and the three axes along three of its edges. What are the co-ordina...
go_editor
6.9k
views
go_editor
asked
Jul 1, 2016
Geometry
isro2014
geometry
non-gate
+
–
7
votes
2
answers
2
ISRO2014-54
The conic section that is obtained when a right circular cone is cut through a plane that is parallel to the side of the cone is called _____ parabola hyperpola circle ellipse
The conic section that is obtained when a right circular cone is cut through a plane that is parallel to the side of the cone is called _____parabolahyperpolacircleellips...
go_editor
6.4k
views
go_editor
asked
Jul 1, 2016
Geometry
isro2014
non-gate
geometry
+
–
4
votes
1
answer
3
UGC NET CSE | December 2015 | Part 3 | Question: 32
The end points of a given line are $(0,0)$ and $(6,18)$. Compute each value of y as x steps from $0$ to $3$, by using equation of straight line: For $x=0, y=0; x=1, y=3; x=2, y=6; x=3, y=9$ For $x=0, y=1; x=1, y=3; x=2, y=4; x=3, y=9$ For $x=0, y=2; x=1, y=3; x=2, y=6; x=3, y=9$ For $x=0, y=0; x=1, y=3; x=2, y=4; x=3, y=6$
The end points of a given line are $(0,0)$ and $(6,18)$. Compute each value of y as x steps from $0$ to $3$, by using equation of straight line:For $x=0, y=0; x=1, y=3; x...
go_editor
4.8k
views
go_editor
asked
Aug 10, 2016
Geometry
ugcnetcse-dec2015-paper3
geometry
lines-curves
+
–
4
votes
1
answer
4
ISRO2014-9
Let $\text{R}$ be the radius of the circle. What is the angle subtended by an arc of length $\text{R}$ at the center of the circle? $1$ degree $1$ radian $90$ degrees $\pi$ radians
Let $\text{R}$ be the radius of the circle. What is the angle subtended by an arc of length $\text{R}$ at the center of the circle?$1$ degree $1$ radian $90$ degrees$...
Anuanu
4.4k
views
Anuanu
asked
Jun 24, 2016
Geometry
isro2014
circle
geometry
+
–
3
votes
3
answers
5
ISRO2011-76
What is the matrix that represents rotation of an object by $\theta^0$ about the origin in $\text{2D}?$ $\cos \theta$ $- \sin \theta$ $\sin \theta$ $\cos \theta$ $\sin \theta$ $- \cos \theta$ $\cos \theta$ $\sin \theta$ $\cos \theta$ $- \sin \theta$ $\cos \theta$ $\sin \theta$ $\sin \theta$ $- \cos \theta$ $\cos \theta$ $\sin \theta$
What is the matrix that represents rotation of an object by $\theta^0$ about the origin in $\text{2D}?$$\cos \theta$$- \sin \theta$$\sin \theta$$\cos \theta$$\sin \theta$...
asu
3.8k
views
asu
asked
Jun 18, 2016
Geometry
isro2011
geometry
+
–
2
votes
1
answer
6
UGC NET CSE | December 2014 | Part 3 | Question: 16
Consider a triangle represented by $A(0, 0), B(1, 1), C(5, 2)$. The triangle is rotated by $45$ degrees about a point $P(-1, -1)$ ...
Consider a triangle represented by $A(0, 0), B(1, 1), C(5, 2)$. The triangle is rotated by $45$ degrees about a point $P(-1, -1)$. The co ordinates of the new triangle ob...
makhdoom ghaya
1.6k
views
makhdoom ghaya
asked
Jul 25, 2016
Geometry
ugcnetcse-dec2014-paper3
geometry
non-gate
+
–
1
votes
2
answers
7
ISI2019-MMA-17
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is $(3,6)$ $(6,3)$ $(5,10)$ $(10,5)$
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is$(3,6)$$(6,3)$$(5,10)$$(10,5)$
Sayan Bose
1.3k
views
Sayan Bose
asked
May 6, 2019
Geometry
isi2019-mma
non-gate
geometry
+
–
1
votes
1
answer
8
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 ...
Sayan Bose
860
views
Sayan Bose
asked
May 6, 2019
Geometry
isi2019-mma
non-gate
geometry
+
–
0
votes
1
answer
9
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 points, then the set of possible values of $d$ is $\{0\}$ $(-4a,4a)$ $(-a,a)$ $(- \infty, \infty)$
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 fou...
Arjun
602
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
circle
parabola
non-gate
+
–
0
votes
1
answer
10
ISI2018-DCG-26
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$-axis in the first quadrant is $9$ $\frac{27}{4}$ $36$ $18$
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$-axis in the first quadrant is$9$$\frac{27}{4}$$36$$18$
gatecse
529
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
curves
area
non-gate
+
–
0
votes
1
answer
11
ISI2015-MMA-32
If a square of side $a$ and an equilateral triangle of side $b$ are inscribed in a circle then $a/b$ equals $\sqrt{2/3}$ $\sqrt{3/2}$ $3/ \sqrt{2}$ $\sqrt{2}/3$
If a square of side $a$ and an equilateral triangle of side $b$ are inscribed in a circle then $a/b$ equals$\sqrt{2/3}$$\sqrt{3/2}$$3/ \sqrt{2}$$\sqrt{2}/3$
Arjun
527
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
triangles
non-gate
+
–
0
votes
1
answer
12
ISI2015-MMA-45
Angles between any pair of $4$ main diagonals of a cube are $\cos^{-1} 1/\sqrt{3}, \pi – \cos ^{-1} 1/\sqrt{3}$ $\cos^{-1} 1/3, \pi – \cos ^{-1} 1/3$ $\pi/2$ none of the above
Angles between any pair of $4$ main diagonals of a cube are$\cos^{-1} 1/\sqrt{3}, \pi – \cos ^{-1} 1/\sqrt{3}$$\cos^{-1} 1/3, \pi – \cos ^{-1} 1/3$$\pi/2$none of the ...
Arjun
521
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
cubes
non-gate
+
–
1
votes
1
answer
13
ISI2015-MMA-79
Let $g(x,y) = \text{max}\{12-x, 8-y\}$. Then the minimum value of $g(x,y)$ $ $ as $(x,y)$ varies over the line $x+y =10$ is $5$ $7$ $1$ $3$
Let $g(x,y) = \text{max}\{12-x, 8-y\}$. Then the minimum value of $g(x,y)$ $ $ as $(x,y)$ varies over the line $x+y =10$ is$5$$7$$1$$3$
Arjun
492
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
lines
non-gate
+
–
0
votes
1
answer
14
ISI2015-MMA-75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}-1$ $8(5 \sqrt{5}-1)$
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is$5 \sqrt{5}+1$$8(5 \sqrt{5}+1)$$5 \sqrt{5}-1$$8(5 \sqrt{5}-1)$
Arjun
477
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
curves
non-gate
+
–
0
votes
1
answer
15
ISI2015-MMA-47
Consider the family $\mathcal{F}$ of curves in the plane given by $x=cy^2$, where $c$ is a real parameter. Let $\mathcal{G}$ be the family of curves having the following property: every member of $\mathcal{G}$ intersect each member of $\mathcal{F}$ orthogonally. Then $\mathcal{G}$ is given by $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2-y^2+2yk=k^2$
Consider the family $\mathcal{F}$ of curves in the plane given by $x=cy^2$, where $c$ is a real parameter. Let $\mathcal{G}$ be the family of curves having the following ...
Arjun
475
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
curves
+
–
0
votes
1
answer
16
ISI2015-MMA-86
The coordinates of a moving point $P$ satisfy the equations $\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=-\sin^2x, \:\:\:\:\: t \geq 0.$ If the curve passes through the point $(\pi/2, 0)$ when $t=0$, then the equation of the curve in rectangular co-ordinates is $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x-1$
The coordinates of a moving point $P$ satisfy the equations $$\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=-\sin^2x, \:\:\:\:\: t \geq 0.$$ If the curve passes through ...
Arjun
444
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
trigonometry
curves
non-gate
+
–
0
votes
1
answer
17
ISI2015-MMA-49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
The polar equation $r=a \cos \theta$ representsa spirala parabolaa circlenone of the above
Arjun
438
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
trigonometry
non-gate
+
–
0
votes
2
answers
18
ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is$2p$$p^{2}$$(p+1)(p-1)$$\frac{2p}{p^{2}-1}$
gatecse
435
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
19
ISI2018-DCG-25
There are three circles of equal diameter ($10$ units each) as shown in the figure below. The straight line $PQ$ passes through the centres of all the three circles. The straight line $PR$ is a tangent to the third circle at $C$ ... $B$ as shown in the figure.Then the length of the line segment $AB$ is $6$ units $7$ units $8$ units $9$ units
There are three circles of equal diameter ($10$ units each) as shown in the figure below. The straight line $PQ$ passes through the centres of all the three circles. The ...
gatecse
434
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
circle
lines
non-gate
+
–
0
votes
1
answer
20
ISI2017-DCG-29
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is $2$ $4$ $6$ $8$
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is$2$$4$$6$$8$
gatecse
431
views
gatecse
asked
Sep 18, 2019
Geometry
isi2017-dcg
non-gate
geometry
area
+
–
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