JEE Advanced Practice Quiz

Question 1

A particle of mass $m$ moves in one dimension under the potential $V(x)=\frac{k}{2}x^2+\frac{\lambda}{4}x^4$, where $k>0$ and $\lambda>0$. For small oscillations with amplitude $A$, which statement is correct about the time period $T$?

Accepted Answer

$T$ increases as $A$ increases

Question 2

For the reaction $2NO(g)+O_2(g)\rightarrow 2NO_2(g)$, the experimentally observed rate law is $r=k[NO]^2[O_2]$. If the volume of the vessel is suddenly reduced to one-third at constant temperature, the initial rate immediately after compression becomes

Accepted Answer

$27$ times the original rate

Question 3

Let $f(x)=x^3-3x+1$. The number of real roots of the equation $f(f(x))=0$ is

Accepted Answer

$7$

Question 4

A uniform thin rod of length $L$ and mass $M$ is hinged at one end and released from rest from the horizontal position. The angular speed of the rod when it becomes vertical is

Accepted Answer

$\sqrt{\frac{3g}{L}}$

Question 5

For the complex number $z$, suppose $|z-1|=|z+1|=|z-i|$. Then $z$ is

Accepted Answer

$0$

JEE Advanced

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