$x$ grams of calcium carbonate was completely burnt in air. The weight of the solid residue formed is $28 \text{ g}$. What is the value of $x$ (in grams)?

Two circular loops $P$ and $Q$ of radii $r$ and $nr$ respectively are made from a uniform wire. The moment of inertia of $Q$ about its axis is four times that of $P$ about its axis. The value of $n$ is

The correct order of increasing $s-$ character (in percentage) in the hybrid orbitals of the following molecules/ions is:
$I. CO_3^{2-}$
$II. XeF_4$
$III. I_3^{-}$
$IV. NCl_3$
$V. BeCl_2$

$A$ block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \, N$,the mass of the block (in $kg$) is: (take $g = 10 \, m/s^2$)

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

The ratio of minimum wavelengths of Lyman and Balmer series will be