1
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
2
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
$13 / 28$
3
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
4
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

The potential energy of a point particle of mass $m$ undergoing rectilinear motion along the $x$-axis is given by

$$ V(x)=A x+B x^2 $$

What is the maximum speed attained by the particle if it starts from rest at $x=\frac{A}{B}$ ?

A

$\frac{3 A}{\sqrt{2 B m}}$

B

$\frac{A}{\sqrt{2 B m}}$

C

$\frac{2 A}{\sqrt{B m}}$

D

$A \sqrt{\frac{2}{B m}}$

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