1
IAT (IISER) 2023
MCQ (Single Correct Answer)
+4
-1
What is the locus of the center of circles passing through the origin $(0,0)$ with fixed radius?
A
Line
B
Hyperbola
C
Parabola
D
Circle
2
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1
Consider the tangent lines to the circle $x^2+y^2=1$ at points $P=(1,0)$ and $Q=\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$. If $R$ is the point of intersection of these two tangent lines, then $\angle P R Q$ is:
A
$\frac{\pi}{4}$
B
$\frac{3 \pi}{4}$
C
$\frac{5 \pi}{6}$
D
$\frac{\pi}{6}$
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

Let $C$ be a circle which passes through $(-2,1)$ and $(0,3)$ and whose centre lies on the line $y-x=1$. Then which of the following points lies on $C$ ?

A
$(\sqrt{2}+1,1)$
B
$(1, \sqrt{2}+1)$
C
$(1, \sqrt{3}+1)$
D
$(1, \sqrt{3}-1)$
IAT (IISER) Subjects
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