1
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
$t=-1$
2
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
3
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
$13 / 28$
4
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
Consider the differential equation $f^{\prime \prime}+p f^{\prime}+q f=0$ where $p$ and $q$ are constants, $p^2=4 q$ and $q \neq 0$. If y is a nonzero solution of the equation, then which of the following statements is correct?
A
$(1+x) y$ can never be a solution
B
$y^2$ can never be a solution
C
$y^{\prime}$ can never be a solution
D
$x y$ can never be a solution
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