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Previous GATE
Featured
Most answered questions in Geometry
3
votes
3
answers
1
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$$\sin \theta$...
asu
3.8k
views
asu
asked
Jun 18, 2016
Geometry
isro2011
geometry
+
–
0
votes
2
answers
2
ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is$2p$$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
+
–
1
votes
2
answers
3
ISI2016-DCG-65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is$8$$9$$9.5$None of these
gatecse
320
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
1
votes
2
answers
4
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
+
–
3
votes
2
answers
5
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
6
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
+
–
0
votes
1
answer
7
ISI2014-DCG-20
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(t)$ equals $0$ $1$ $2$ $4$
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(...
Arjun
322
views
Arjun
asked
Sep 23, 2019
Geometry
isi2014-dcg
calculus
definite-integral
area
+
–
0
votes
1
answer
8
ISI2014-DCG-52
The area under the curve $x^2+3x-4$ in the positive quadrant and bounded by the line $x=5$ is equal to $59 \frac{1}{6}$ $61 \frac{1}{3}$ $40 \frac{2}{3}$ $72$
The area under the curve $x^2+3x-4$ in the positive quadrant and bounded by the line $x=5$ is equal to$59 \frac{1}{6}$$61 \frac{1}{3}$$40 \frac{2}{3}$$72$
Arjun
275
views
Arjun
asked
Sep 23, 2019
Geometry
isi2014-dcg
curves
area
+
–
0
votes
1
answer
9
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}$$\sqrt{2}/3$
Arjun
527
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
triangles
non-gate
+
–
0
votes
1
answer
10
ISI2015-MMA-45
Angles between any pair of $4$ main diagonals of a cube are $\cos^{-1} 1/\sqrt{3}, \pi – \cos ^{-1} 1/\sqrt{3}$ $\cos^{-1} 1/3, \pi – \cos ^{-1} 1/3$ $\pi/2$ none of the above
Angles between any pair of $4$ main diagonals of a cube are$\cos^{-1} 1/\sqrt{3}, \pi – \cos ^{-1} 1/\sqrt{3}$$\cos^{-1} 1/3, \pi – \cos ^{-1} 1/3$$\pi/2$none of the ...
Arjun
520
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
cubes
non-gate
+
–
0
votes
1
answer
11
ISI2015-MMA-46
If the tangent at the point $P$ with coordinates $(h,k)$ on the curve $y^2=2x^3$ is perpendicular to the straight line $4x=3y$, then $(h,k) = (0,0)$ $(h,k) = (1/8, -1/16)$ $(h,k) = (0,0) \text{ or } (h,k) = (1/8, -1/16)$ no such point $(h,k)$ exists
If the tangent at the point $P$ with coordinates $(h,k)$ on the curve $y^2=2x^3$ is perpendicular to the straight line $4x=3y$, then$(h,k) = (0,0)$$(h,k) = (1/8, -1/16)$$...
Arjun
427
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
lines
non-gate
+
–
0
votes
1
answer
12
ISI2015-MMA-47
Consider the family $\mathcal{F}$ of curves in the plane given by $x=cy^2$, where $c$ is a real parameter. Let $\mathcal{G}$ be the family of curves having the following property: every member of $\mathcal{G}$ intersect each member of $\mathcal{F}$ orthogonally. Then $\mathcal{G}$ is given by $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2-y^2+2yk=k^2$
Consider the family $\mathcal{F}$ of curves in the plane given by $x=cy^2$, where $c$ is a real parameter. Let $\mathcal{G}$ be the family of curves having the following ...
Arjun
475
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
curves
+
–
0
votes
1
answer
13
ISI2015-MMA-48
Suppose the circle with equation $x^2+y^2+2fx+2gy+c=0$ cuts the parabola $y^2=4ax, \: (a>0)$ at four distinct points. If $d$ denotes the sum of the ordinates of these four points, then the set of possible values of $d$ is $\{0\}$ $(-4a,4a)$ $(-a,a)$ $(- \infty, \infty)$
Suppose the circle with equation $x^2+y^2+2fx+2gy+c=0$ cuts the parabola $y^2=4ax, \: (a>0)$ at four distinct points. If $d$ denotes the sum of the ordinates of these fou...
Arjun
602
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
circle
parabola
non-gate
+
–
0
votes
1
answer
14
ISI2015-MMA-49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
The polar equation $r=a \cos \theta$ representsa spirala parabolaa circlenone of the above
Arjun
438
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
trigonometry
non-gate
+
–
0
votes
1
answer
15
ISI2015-MMA-75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}-1$ $8(5 \sqrt{5}-1)$
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is$5 \sqrt{5}+1$$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
+
–
1
votes
1
answer
16
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$$3$
Arjun
492
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
lines
non-gate
+
–
0
votes
1
answer
17
ISI2015-MMA-86
The coordinates of a moving point $P$ satisfy the equations $\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=-\sin^2x, \:\:\:\:\: t \geq 0.$ If the curve passes through the point $(\pi/2, 0)$ when $t=0$, then the equation of the curve in rectangular co-ordinates is $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x-1$
The coordinates of a moving point $P$ satisfy the equations $$\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=-\sin^2x, \:\:\:\:\: t \geq 0.$$ If the curve passes through ...
Arjun
444
views
Arjun
asked
Sep 23, 2019
Geometry
isi2015-mma
trigonometry
curves
non-gate
+
–
0
votes
1
answer
18
ISI2016-DCG-16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
gatecse
275
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
curves
area
non-gate
+
–
0
votes
1
answer
19
ISI2016-DCG-39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if $b=\sqrt{2}a$ $a=\pm\sqrt{2}b$ $b=-\sqrt{2}a$ $b=a$
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$a=\pm\sqrt{2}b$$b=-\sqrt{2}a$$b=a$
gatecse
302
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
triangles
non-gate
+
–
0
votes
1
answer
20
ISI2016-DCG-43
Four tangents are drawn to the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ 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 $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ at the ends of its latera recta. The area of the quadrilateral so formed is$27$$\frac{13}{2}$...
gatecse
331
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
ellipse
quadrilateral
area
non-gate
+
–
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