IAT (IISER) 2020 | IAT (IISER) Year Wise Previous Years Questions

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?

$(1+x) y$ can never be a solution

$y^2$ can never be a solution

$y^{\prime}$ can never be a solution

$x y$ can never be a solution

IAT (IISER) 2020

MCQ (Single Correct Answer)

-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 $x=\frac{A}{B}$ ?

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

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

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

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

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

Two identical containers kept at the same temperature carry the same gas with different molecular mean free paths $l_1$ and $l_2$. The gas from the first container is completely transferred into the second at the same temperature. What is the molecular mean free path of the resultant mixture in the second container?

$\frac{l_1 l_2}{l_1+l_2}$

$\sqrt{l_1 l_2}$

$l_1+l_2$

$\sqrt{l_1^2+l_2^2}$

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