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Recent questions and answers 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 $\text{2D}?$ $\cos \theta$ $- \sin \theta$ $\sin \theta$ $\cos \theta$ $\sin \theta$ $- \cos \theta$ $\cos \theta$ $\sin \theta$ $\cos \theta$ $- \sin \theta$ $\cos \theta$ $\sin \theta$ $\sin \theta$ $- \cos \theta$ $\cos \theta$ $\sin \theta$
Nagasaikanmatha
answered
in
Geometry
Aug 2, 2021
by
Nagasaikanmatha
2.7k
views
isro2011
geometry
0
votes
1
answer
2
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
rishabhjain18
answered
in
Geometry
Jul 2, 2021
by
rishabhjain18
316
views
isi2015-mma
cubes
non-gate
0
votes
1
answer
3
ISI2015-MMA-75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}-1$ $8(5 \sqrt{5}-1)$
NastyBall
answered
in
Geometry
Jun 20, 2021
by
NastyBall
281
views
isi2015-mma
curves
non-gate
0
votes
1
answer
4
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 $\{0\}$ $(-4a,4a)$ $(-a,a)$ $(- \infty, \infty)$
Amartya
answered
in
Geometry
May 18, 2020
by
Amartya
426
views
isi2015-mma
circle
parabola
non-gate
0
votes
1
answer
5
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 $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2-y^2+2yk=k^2$
Amartya
answered
in
Geometry
May 18, 2020
by
Amartya
328
views
isi2015-mma
curves
0
votes
1
answer
6
ISI2018-DCG-23
Let $A$ be the point of intersection of the lines $3x-y=1$ and $y=1$. Let $B$ be the point of reflection of the point $A$ with respect to the $y$-axis. Then the equation of the straight line through $B$ that produces a right angled triangle $ABC$ with $\angle ABC=90^{\circ}$, and $C$ lies on the line $3x-y=1$, is $3x-3y=2$ $2x+3=0$ $3x+2=0$ $3y-2=0$
haralk10
answered
in
Geometry
Mar 15, 2020
by
haralk10
178
views
isi2018-dcg
lines
triangle
non-gate
0
votes
1
answer
7
ISI2016-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 $y^{2}-x^{2}=32$ $x^{2}-y^{2}=16$ $y^{2}-x^{2}=16$ $x^{2}-y^{2}=32$
haralk10
answered
in
Geometry
Mar 15, 2020
by
haralk10
144
views
isi2016-dcg
hyperbola
curves
non-gate
0
votes
1
answer
8
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
haralk10
answered
in
Geometry
Mar 14, 2020
by
haralk10
307
views
isi2015-mma
lines
non-gate
0
votes
1
answer
9
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 $27$ $\frac{13}{2}$ $\frac{15}{4}$ $45$
haralk10
answered
in
Geometry
Mar 11, 2020
by
haralk10
224
views
isi2016-dcg
ellipse
quadrilateral
area
non-gate
0
votes
1
answer
10
ISI2016-DCG-52
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
haralk10
answered
in
Geometry
Mar 2, 2020
by
haralk10
183
views
isi2016-dcg
curves
area
non-gate
0
votes
1
answer
11
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 $59 \frac{1}{6}$ $61 \frac{1}{3}$ $40 \frac{2}{3}$ $72$
haralk10
answered
in
Geometry
Mar 2, 2020
by
haralk10
165
views
isi2014-dcg
curves
area
1
vote
2
answers
12
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
Lakshman Patel RJIT
answered
in
Geometry
Feb 1, 2020
by
Lakshman Patel RJIT
183
views
isi2016-dcg
trigonometry
non-gate
0
votes
1
answer
13
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 $9$ $\frac{27}{4}$ $36$ $18$
techbd123
answered
in
Geometry
Nov 29, 2019
by
techbd123
288
views
isi2018-dcg
curves
area
non-gate
1
vote
1
answer
14
ISI2018-DCG-18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
Lakshman Patel RJIT
answered
in
Geometry
Nov 28, 2019
by
Lakshman Patel RJIT
187
views
isi2018-dcg
trigonometry
non-gate
2
votes
1
answer
15
ISI2018-DCG-20
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$
Lakshman Patel RJIT
answered
in
Geometry
Nov 28, 2019
by
Lakshman Patel RJIT
176
views
isi2018-dcg
trigonometry
inverse
non-gate
0
votes
1
answer
16
ISI2018-DCG-22
Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+b-c)=ab,$ then the angle $C$ is $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2\pi}{3}$
`JEET
answered
in
Geometry
Nov 21, 2019
by
`JEET
199
views
isi2018-dcg
triangle
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 $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x-1$
`JEET
answered
in
Geometry
Nov 19, 2019
by
`JEET
285
views
isi2015-mma
trigonometry
curves
non-gate
0
votes
1
answer
18
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 $2$ $4$ $6$ $8$
imShreyas
answered
in
Geometry
Nov 18, 2019
by
imShreyas
240
views
isi2017-dcg
non-gate
geometry
area
0
votes
1
answer
19
ISI2016-DCG-63
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\sin^{-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
`JEET
answered
in
Geometry
Oct 20, 2019
by
`JEET
204
views
isi2016-dcg
trigonometry
non-gate
0
votes
2
answers
20
ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$
techbd123
answered
in
Geometry
Oct 13, 2019
by
techbd123
215
views
isi2016-dcg
trigonometry
non-gate
1
vote
1
answer
21
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 $5$ $7$ $1$ $3$
`JEET
answered
in
Geometry
Oct 4, 2019
by
`JEET
296
views
isi2015-mma
lines
non-gate
0
votes
1
answer
22
ISI2016-DCG-61
The value of $\sin^{6}\frac{\pi}{81}+\cos^{6}\frac{\pi}{81}-1+3\sin^{2}\frac{\pi}{81}\:\cos^{2}\frac{\pi}{81}$ is $\tan^{6}\frac{\pi}{81}$ $0$ $-1$ None of these
`JEET
answered
in
Geometry
Oct 2, 2019
by
`JEET
181
views
isi2016-dcg
trigonometry
non-gate
0
votes
1
answer
23
ISI2016-DCG-64
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$ None of these
`JEET
answered
in
Geometry
Oct 2, 2019
by
`JEET
179
views
isi2016-dcg
trigonometry
non-gate
0
votes
1
answer
24
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 $0$ $1$ $2$ $4$
techbd123
answered
in
Geometry
Oct 1, 2019
by
techbd123
217
views
isi2014-dcg
calculus
definite-integral
area
0
votes
1
answer
25
ISI2016-DCG-66
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
`JEET
answered
in
Geometry
Sep 30, 2019
by
`JEET
180
views
isi2016-dcg
trigonometry
inverse
non-gate
0
votes
1
answer
26
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 $b=\sqrt{2}a$ $a=\pm\sqrt{2}b$ $b=-\sqrt{2}a$ $b=a$
`JEET
answered
in
Geometry
Sep 27, 2019
by
`JEET
199
views
isi2016-dcg
triangle
non-gate
0
votes
1
answer
27
ISI2015-MMA-49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
`JEET
answered
in
Geometry
Sep 24, 2019
by
`JEET
272
views
isi2015-mma
trigonometry
non-gate
0
votes
1
answer
28
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 $\sqrt{2/3}$ $\sqrt{3/2}$ $3/ \sqrt{2}$ $\sqrt{2}/3$
`JEET
answered
in
Geometry
Sep 24, 2019
by
`JEET
391
views
isi2015-mma
triangle
non-gate
0
votes
0
answers
29
ISI2014-DCG-27
Let $y^2-4ax+4a=0$ and $x^2+y^2-2(1+a)x+1+2a-3a^2=0$ be two curves. State which one of the following statements is true. These two curves intersect at two points These two curves are tangent to each other These two curves intersect orthogonally at one point These two curves do not intersect
Arjun
asked
in
Geometry
Sep 23, 2019
by
Arjun
203
views
isi2014-dcg
curves
0
votes
0
answers
30
ISI2015-MMA-35
If $f(x)=x^2$ and $g(x)= x \sin x + \cos x$ then $f$ and $g$ agree at no points $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two points $f$ and $g$ agree at more than two points
Arjun
asked
in
Geometry
Sep 23, 2019
by
Arjun
298
views
isi2015-mma
trigonometry
non-gate
0
votes
0
answers
31
ISI2015-MMA-64
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $t=0$ and $t=2 \pi$ is $2 \pi$ $2 \sqrt{2 \pi}$ $\sqrt{2 \pi}$ none of the above
Arjun
asked
in
Geometry
Sep 23, 2019
by
Arjun
268
views
isi2015-mma
trigonometry
curves
non-gate
0
votes
0
answers
32
ISI2015-MMA-82
The volume of the solid, generated by revolving about the horizontal line $y=2$ the region bounded by $y^2 \leq 2x$, $x \leq 8$ and $y \geq 2$, is $2 \sqrt{2\pi}$ $28 \pi/3$ $84 \pi$ none of the above
Arjun
asked
in
Geometry
Sep 23, 2019
by
Arjun
271
views
isi2015-mma
area
non-gate
0
votes
1
answer
33
ISI2016-DCG-16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
Bharat Makhija
answered
in
Geometry
Sep 19, 2019
by
Bharat Makhija
191
views
isi2016-dcg
curves
area
non-gate
0
votes
1
answer
34
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
ankitgupta.1729
answered
in
Geometry
Sep 19, 2019
by
ankitgupta.1729
286
views
isi2018-dcg
circle
lines
non-gate
0
votes
0
answers
35
ISI2016-DCG-15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
159
views
isi2016-dcg
area
curves
non-gate
0
votes
0
answers
36
ISI2016-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 $12$ $14$ $16$ $18$
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
115
views
isi2016-dcg
lines
non-gate
0
votes
0
answers
37
ISI2016-DCG-40
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ represent a circle a parabola an ellipse a hyperbola
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
176
views
isi2016-dcg
trigonometry
curves
non-gate
0
votes
0
answers
38
ISI2016-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 $y=\pm x$ $y=\pm(x+a)$ $y=\pm(x+2a)$ $y=\pm(x-21)$
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
105
views
isi2016-dcg
lines
parabola
non-gate
0
votes
0
answers
39
ISI2016-DCG-42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8.$ Then its eccentricity is $\frac{4}{5}$ $\frac{1}{\sqrt{52}}$ $\frac{3}{5}$ $\frac{1}{2}$
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
106
views
isi2016-dcg
ellipse
non-gate
0
votes
0
answers
40
ISI2016-DCG-59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in $\left[\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\frac{3}{2},\sqrt{3}\:\right)$ $\left(\:\frac{3}{2},\sqrt{3}\:\right]$
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
139
views
isi2016-dcg
geometry
triangle
trigonometry
non-gate
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