1
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
$(1, \sqrt{3}-1)$
2
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
For what value of $t$ does $f(x)=x^3+t x^2+(2-t) x-3$ have only real roots?
A
$t=0$.
B
$t=4$.
C
$t=2$.
D
$t=-1$
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
If $f(x)=a x^2+b x+c$ and $f\left(\frac{1}{n}\right)=\frac{n+1}{n^2}$ for all $n \in N$, then what is the value of $\lim \limits_{x \rightarrow 0} f^{\prime}(x)$ ?
A
2
B
0
C
1
D
-1
4
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

A bag contains 8 balls, of which 5 are green and 3 are red. The probability that two balls chosen at random are of the same colour is :

A
$12 / 28$
B
$14 / 28$
C
$15 / 28$
D
$13 / 28$
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