The density $($in $g cm ^{-3} )$ of the metal which forms a cubic close packed $(ccp)$ lattice with an axial distance $($edge length$)$ equal to $400 \ pm$ is $....$
Use: Atomic mass of metal $=105.6 \ amu$ and Avogadro's constant $=6 \times 10^{23} mol^{-1}$

Which of the following representations correctly explains the function of a mitochondrion?

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

If $a_1, a_2, \dots, a_n$ are positive real numbers whose product is a fixed number $c$,then the minimum value of $a_1 + a_2 + \dots + a_{n-1} + 2a_n$ is

$A$ bullet of mass $10\,g$ moving horizontally with a velocity of $400\,m/s$ strikes a wooden block of mass $2\,kg$ which is suspended by a light inextensible string of length $5\,m$. As a result,the centre of gravity of the block is found to rise a vertical distance of $10\,cm$. The speed of the bullet after it emerges out horizontally from the block will be ............... $m/s$.

The same current is flowing in two alternating circuits. The first circuit contains only an inductor and the second contains only a capacitor. If the frequency of the $e.m.f.$ of the $ac$ source is increased,what will be the effect on the value of the current in these circuits?