ISI2018-DCG-25

gatecse asked in Geometry Sep 18, 2019 recategorized Nov 20, 2019 by Lakshman Bhaiya

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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 $C$ and cuts the second circle at the points $A$ and $B$ as shown in the figure.Then the length of the line segment $AB$ is

$6$ units
$7$ units
$8$ units
$9$ units

isi2018-dcg
circle
lines
non-gate

gatecse asked in Geometry Sep 18, 2019 recategorized Nov 20, 2019 by Lakshman Bhaiya

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Answer : (C)

ankitgupta.1729 answered Sep 18, 2019

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gatecse asked in Geometry Sep 18, 2019

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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 $3x-3y=2$ $2x+3=0$ $3x+2=0$ $3y-2=0$

gatecse asked in Geometry Sep 18, 2019

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isi2018-dcg
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gatecse asked in Geometry Sep 18, 2019

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ISI2018-DCG-18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$

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isi2018-dcg
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gatecse asked in Geometry Sep 18, 2019

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ISI2018-DCG-20
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$

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266 views

isi2018-dcg
trigonometry
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gatecse asked in Geometry Sep 18, 2019

248 views

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

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