$4 \ g$ of a hydrocarbon on complete combustion gave $12.571 \ g$ of $CO_2$ and $5.143 \ g$ of water. What is the empirical formula of the hydrocarbon?

Two identical piano wires have a fundamental frequency of $600 \text{ Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $6 \text{ beats per second}$ when both wires vibrate simultaneously?

In the structure of $B_2H_6$,the number of $BH_2$ groups present in one plane,and the number of $B-H$ terminal bonds,$B-B$ bonds,and $B-H-B$ bridge bonds are respectively:

Which of the following is an example of a ketohexose?

The area of the triangle formed by the points $(a, b + c)$,$(b, c + a)$,and $(c, a + b)$ is equal to:

Match the $\frac{C_P}{C_V}$ ratio for ideal gases with different types of molecules.

Molecule type	$\frac{C_P}{C_V}$
$A$. Monoatomic	$I$. $\frac{7}{5}$
$B$. Diatomic rigid molecules	$II$. $\frac{9}{7}$
$C$. Diatomic non-rigid molecules	$III$. $\frac{4}{3}$
$D$. Triatomic rigid molecules	$IV$. $\frac{5}{3}$