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Questions without answers in Geometry
0
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1
Game Theory(SELF DOUBT)
legacy
asked
in
Geometry
Apr 20, 2023
by
legacy
87
views
game-theory
0
votes
0
answers
2
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
324
views
isi2014-dcg
curves
0
votes
0
answers
3
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
424
views
isi2015-mma
trigonometry
non-gate
0
votes
0
answers
4
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
439
views
isi2015-mma
trigonometry
curves
non-gate
0
votes
0
answers
5
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
402
views
isi2015-mma
area
non-gate
0
votes
0
answers
6
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
365
views
isi2016-dcg
area
curves
non-gate
0
votes
0
answers
7
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
189
views
isi2016-dcg
lines
non-gate
0
votes
0
answers
8
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
282
views
isi2016-dcg
trigonometry
curves
non-gate
0
votes
0
answers
9
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
182
views
isi2016-dcg
lines
parabola
non-gate
0
votes
0
answers
10
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
167
views
isi2016-dcg
ellipse
non-gate
0
votes
0
answers
11
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
343
views
isi2016-dcg
geometry
triangles
trigonometry
non-gate
0
votes
0
answers
12
ISI2016-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
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
370
views
isi2016-dcg
triangles
non-gate
0
votes
0
answers
13
ISI2016-DCG-62
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$ $2$ $3$ more than $3$
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
182
views
isi2016-dcg
trigonometry
non-gate
0
votes
0
answers
14
ISI2018-DCG-21
A box with a square base of length $x$ and height $y$ has an open top and its volume is $32$ cubic centimetres, as shown in the figure below. The values of $x$ and $y$ that minimize the surface area of the box are $x=4$ cm $\&$ $y=2 $ cm $x=3$ cm $\&$ $y=\frac{32}{9} $ cm $x=2$ cm $\&$ $y=8 $ cm none of these.
gatecse
asked
in
Geometry
Sep 18, 2019
by
gatecse
248
views
isi2018-dcg
cubes
non-gate
2
votes
0
answers
15
ISI2011-PCB-A-1
Let $D = \{d_1, d_2, \dots, d_k\}$ be the set of distinct divisors of a positive integer $n$ ($D$ includes 1 and $n$). Then show that $\Sigma_{i=1}^k \sin^{-1} \sqrt{\log_nd_i}=\frac{\pi}{4} \times k$. hint: $\sin^{−1} x + \sin^{−1} \sqrt{1-x^2} = \frac{\pi}{2}$
go_editor
asked
in
Geometry
Jun 3, 2016
by
go_editor
302
views
isi2011
descriptive
proof
trigonometry
non-gate
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