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Recent questions and answers in Geometry
0
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1
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1
ISI2018DCG23
Let $A$ be the point of intersection of the lines $3xy=1$ 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 $3xy=1$, is $3x3y=2$ $2x+3=0$ $3x+2=0$ $3y2=0$
answered
Mar 15
in
Geometry
by
haralk10
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isi2018dcg
lines
triangles
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0
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1
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2
ISI2016DCG44
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2},$ then the equation of the hyperbola is $y^{2}x^{2}=32$ $x^{2}y^{2}=16$ $y^{2}x^{2}=16$ $x^{2}y^{2}=32$
answered
Mar 15
in
Geometry
by
haralk10
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1.2k
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13
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isi2016dcg
hyperbola
curves
nongate
0
votes
1
answer
3
ISI2015MMA46
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
answered
Mar 14
in
Geometry
by
haralk10
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42
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isi2015mma
lines
nongate
0
votes
1
answer
4
ISI2016DCG43
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 $27$ $\frac{13}{2}$ $\frac{15}{4}$ $45$
answered
Mar 11
in
Geometry
by
haralk10
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29
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isi2016dcg
ellipses
quadrilateral
area
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0
votes
1
answer
5
ISI2016DCG52
The area bounded by $y=x^{2}4,y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
answered
Mar 2
in
Geometry
by
haralk10
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1.2k
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25
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isi2016dcg
curves
area
nongate
0
votes
1
answer
6
ISI2014DCG52
The area under the curve $x^2+3x4$ in the positive quadrant and bounded by the line $x=5$ is equal to $59 \frac{1}{6}$ $61 \frac{1}{3}$ $40 \frac{2}{3}$ $72$
answered
Mar 2
in
Geometry
by
haralk10
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1.2k
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24
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isi2014dcg
curves
area
+1
vote
2
answers
7
ISI2016DCG65
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
answered
Feb 1
in
Geometry
by
Lakshman Patel RJIT
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61.3k
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38
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isi2016dcg
trigonometry
nongate
0
votes
1
answer
8
ISI2018DCG26
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$axis in the first quadrant is $9$ $\frac{27}{4}$ $36$ $18$
answered
Nov 29, 2019
in
Geometry
by
techbd123
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3.7k
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71
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isi2018dcg
curves
area
nongate
+1
vote
1
answer
9
ISI2018DCG18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
answered
Nov 28, 2019
in
Geometry
by
Lakshman Patel RJIT
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61.3k
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isi2018dcg
trigonometry
nongate
+2
votes
1
answer
10
ISI2018DCG20
The value of $\tan \left(\sin^{1}\left(\frac{3}{5}\right)+\cot^{1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$
answered
Nov 28, 2019
in
Geometry
by
Lakshman Patel RJIT
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61.3k
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41
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isi2018dcg
trigonometry
inverse
nongate
0
votes
1
answer
11
ISI2018DCG22
Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+bc)=ab,$ then the angle $C$ is $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2\pi}{3}$
answered
Nov 21, 2019
in
Geometry
by
`JEET
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19.7k
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21
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isi2018dcg
triangles
nongate
0
votes
1
answer
12
ISI2015MMA86
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 coordinates is $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x1$
answered
Nov 19, 2019
in
Geometry
by
`JEET
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19.7k
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23
views
isi2015mma
trigonometry
curves
nongate
0
votes
1
answer
13
ISI2017DCG29
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 $2$ $4$ $6$ $8$
answered
Nov 18, 2019
in
Geometry
by
imShreyas
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447
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37
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isi2017dcg
nongate
geometry
area
0
votes
1
answer
14
ISI2016DCG63
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 $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\sin^{1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
answered
Oct 20, 2019
in
Geometry
by
`JEET
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19.7k
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47
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isi2016dcg
trigonometry
nongate
0
votes
2
answers
15
ISI2016DCG5
If $\tan\: x=p+1$ and $\tan\; y=p1,$ then the value of $2\:\cot\:(xy)$ is $2p$ $p^{2}$ $(p+1)(p1)$ $\frac{2p}{p^{2}1}$
answered
Oct 13, 2019
in
Geometry
by
techbd123
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3.7k
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31
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isi2016dcg
trigonometry
nongate
+1
vote
1
answer
16
ISI2015MMA79
Let $g(x,y) = \text{max}\{12x, 8y\}$. Then the minimum value of $g(x,y)$ $ $ as $(x,y)$ varies over the line $x+y =10$ is $5$ $7$ $1$ $3$
answered
Oct 4, 2019
in
Geometry
by
`JEET
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19.7k
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24
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isi2015mma
lines
nongate
0
votes
1
answer
17
ISI2016DCG61
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
answered
Oct 2, 2019
in
Geometry
by
`JEET
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24
views
isi2016dcg
trigonometry
nongate
0
votes
1
answer
18
ISI2016DCG64
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
answered
Oct 2, 2019
in
Geometry
by
`JEET
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21
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isi2016dcg
trigonometry
nongate
0
votes
1
answer
19
ISI2014DCG20
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 $0$ $1$ $2$ $4$
answered
Oct 1, 2019
in
Geometry
by
techbd123
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3.7k
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43
views
isi2014dcg
calculus
definiteintegrals
area
0
votes
1
answer
20
ISI2016DCG66
If $\sin(\sin^{1}\frac{2}{5}+\cos^{1}x)=1,$ then $x$ is $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
answered
Sep 30, 2019
in
Geometry
by
`JEET
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19.7k
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18
views
isi2016dcg
trigonometry
inverse
nongate
0
votes
1
answer
21
ISI2016DCG39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if $b=\sqrt{2}a$ $a=\pm\sqrt{2}b$ $b=\sqrt{2}a$ $b=a$
answered
Sep 27, 2019
in
Geometry
by
`JEET
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19.7k
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17
views
isi2016dcg
triangles
nongate
0
votes
1
answer
22
ISI2015MMA49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
answered
Sep 24, 2019
in
Geometry
by
`JEET
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19.7k
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25
views
isi2015mma
trigonometry
nongate
0
votes
1
answer
23
ISI2015MMA32
If a square of side $a$ and an equilateral triangle of side $b$ are inscribed in a circle then $a/b$ equals $\sqrt{2/3}$ $\sqrt{3/2}$ $3/ \sqrt{2}$ $\sqrt{2}/3$
answered
Sep 24, 2019
in
Geometry
by
`JEET
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19.7k
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23
views
isi2015mma
triangles
nongate
0
votes
0
answers
24
ISI2014DCG27
Let $y^24ax+4a=0$ and $x^2+y^22(1+a)x+1+2a3a^2=0$ 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
asked
Sep 23, 2019
in
Geometry
by
Arjun
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34
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isi2014dcg
curves
0
votes
0
answers
25
ISI2015MMA35
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
asked
Sep 23, 2019
in
Geometry
by
Arjun
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436k
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40
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isi2015mma
trigonometry
nongate
0
votes
0
answers
26
ISI2015MMA45
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
asked
Sep 23, 2019
in
Geometry
by
Arjun
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436k
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31
views
isi2015mma
cubes
nongate
0
votes
0
answers
27
ISI2015MMA47
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 $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2y^2+2yk=k^2$
asked
Sep 23, 2019
in
Geometry
by
Arjun
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436k
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22
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isi2015mma
curves
0
votes
0
answers
28
ISI2015MMA48
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 $\{0\}$ $(4a,4a)$ $(a,a)$ $( \infty, \infty)$
asked
Sep 23, 2019
in
Geometry
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Arjun
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24
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isi2015mma
circle
parabola
nongate
0
votes
0
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29
ISI2015MMA64
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
asked
Sep 23, 2019
in
Geometry
by
Arjun
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436k
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19
views
isi2015mma
trigonometry
curves
nongate
0
votes
0
answers
30
ISI2015MMA75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}1$ $8(5 \sqrt{5}1)$
asked
Sep 23, 2019
in
Geometry
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Arjun
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31
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isi2015mma
curves
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0
votes
0
answers
31
ISI2015MMA82
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
asked
Sep 23, 2019
in
Geometry
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Arjun
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436k
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16
views
isi2015mma
area
nongate
0
votes
1
answer
32
ISI2016DCG16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
answered
Sep 19, 2019
in
Geometry
by
Bharat Makhija
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51
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16
views
isi2016dcg
curves
area
nongate
0
votes
1
answer
33
ISI2018DCG25
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
answered
Sep 19, 2019
in
Geometry
by
ankitgupta.1729
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18.1k
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37
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isi2018dcg
circle
lines
nongate
0
votes
0
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34
ISI2016DCG15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
asked
Sep 18, 2019
in
Geometry
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gatecse
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18
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isi2016dcg
area
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0
votes
0
answers
35
ISI2016DCG38
The length of the chord on the straight line $3x4y+5=0$ intercepted by the circle passing through the points $(1,2),(3,4)$ and $(5,6)$ is $12$ $14$ $16$ $18$
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Sep 18, 2019
in
Geometry
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gatecse
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19
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isi2016dcg
lines
nongate
0
votes
0
answers
36
ISI2016DCG40
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
asked
Sep 18, 2019
in
Geometry
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gatecse
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17.7k
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20
views
isi2016dcg
trigonometry
curves
nongate
0
votes
0
answers
37
ISI2016DCG41
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 $y=\pm x$ $y=\pm(x+a)$ $y=\pm(x+2a)$ $y=\pm(x21)$
asked
Sep 18, 2019
in
Geometry
by
gatecse
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17.7k
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13
views
isi2016dcg
lines
parabola
nongate
0
votes
0
answers
38
ISI2016DCG42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8.$ Then its eccentricity is $\frac{4}{5}$ $\frac{1}{\sqrt{52}}$ $\frac{3}{5}$ $\frac{1}{2}$
asked
Sep 18, 2019
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Geometry
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gatecse
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12
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isi2016dcg
ellipses
nongate
0
votes
0
answers
39
ISI2016DCG59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in $\left[\:\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\frac{3}{2},\sqrt{3}\:\right)$ $\left(\:\frac{3}{2},\sqrt{3}\:\right]$
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Sep 18, 2019
in
Geometry
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gatecse
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isi2016dcg
geometry
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trigonometry
nongate
0
votes
0
answers
40
ISI2016DCG60
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
asked
Sep 18, 2019
in
Geometry
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gatecse
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33
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isi2016dcg
triangles
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