The number of hexagonal faces that are present in a truncated octahedron is

Paragraph I: An organic compound \(\mathrm{P}\) with molecular formula \(\mathrm{C}_5 \mathrm{H}_{18} \mathrm{O}_2\) decolorizes bromine water and also shows positive iodoform test. \(\mathrm{P}\) on ozonolysis followed by treatment with \(\mathrm{H}_2 \mathrm{O}_2\) gives \(\mathrm{Q}\) and \(\mathrm{R}\). While compound \(\mathrm{Q}\) shows positive iodoform test, compound \(\mathrm{R}\) does not give positive iodoform test. \(\mathrm{Q}\) and \(\mathrm{R}\) on oxidation with pyridinium chlorochromate (PCC) followed by heating give \(\mathrm{S}\) and \(\mathrm{T}\), respectively. Both \(\mathrm{S}\) and \(\mathrm{T}\) show positive iodoform test.
Complete copolymerization of 500 moles of \(\mathrm{Q}\) and 500 moles of \(\mathrm{R}\) gives one mole of a single acyclic copolymer \(\mathrm{U}\).
[Given, atomic mass: \(\mathrm{H}=1, \mathrm{C}=12, \mathrm{O}=16\)]
Question: The molecular weight of \(\mathbf{U}\) is

Paragraph:
Tollen's reagent is used for the detection of aldehyde when a solution of \(\mathrm{AgNO}_3\) is added to glucose with \(\mathrm{NH}_4 \mathrm{OH}\) then gluconic acid is formed
\(\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \)
\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)\) \(+~2 \mathrm{H}^{+}+2 e^{-} ; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \)
\( \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ;\) \(E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\)
[Use \(2.303 \times \frac{R T}{F}=0.0592\) and \(\frac{F}{R T}=38.92\) at \(298 \mathrm{~K}\) ]
Question:
When ammonia is added to the solution, \(\mathrm{pH}\) is raised to 11 . Which half-cell reaction is affected by \(\mathrm{pH}\) and by how much?

The Henry's law constant for the solubility of \(\mathrm{N}_2\) gas in water at \(298 \mathrm{~K}\) is \(1.0 \times 105 \mathrm{~atm}\). The mole fraction of \(\mathrm{N}_2\) in air is \(0.8\). The number of moles of \(\mathrm{N}_2\) from air dissolved in 10 moles of water of \(298 \mathrm{~K}\) and \(5 \mathrm{~atm}\) pressure is

According to kinetic theory of gases

Among \(H_2, H e_2^{+}, L i_2, B e_2, B_2, C_2, N_2, O_2^{-}\), and \(F_2\), the number of diamagnetic species is -
(Atomic number : \(H=1, H e=2, L i=3, B e=4, B=5,\) \(C=6, N =7, O=8, F=9\) )

The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in list II. match List I with List II and select the correct answer using the code given below the lists :

List - I	List - II
A. \(PbO _2+ H _2 SO _4 \xrightarrow{?}\) \(PbSO _4 + O _2+\) other product	P. \(\text{NO}\)
B. \(Na _2 S_2 O _3+ H _2 O \xrightarrow{?}\) \(NaHSO _4~+\) other product	Q. \(\text{I}_2\)
C. \(N _2 H _4 \xrightarrow{?} N_2 +\) other product	R. Warm
D. \(XeF _2 \xrightarrow{?} Xe ~+\) other product	S. \(\text{Cl}_2\)

Let $T$ be the line passing through the points $P\left(-2,7\right)$ and $Q\left(2,-5\right)$. Let $F_1$ be the set of all pairs of circles $\left(S_1,S_2\right)$ such that $T$ is tangents to $S_1$ at $P$ and tangent to $S_2$ at $Q$, and also such that $S_1$ and $S_2$ touch each other at a point, say, $M$. Let $E_1$ be the set representing the locus of $M$ as the pair $\left(S_1, S_2\right)$ varies in $F_1$. Let the set of all straight line segments joining a pair of distinct points of $E_1$ and passing through the point $R\left(\mathrm{1,1}\right)$ be $F_2$ . Let $E_2$ be the set of the mid-points of the line segments in the set $F_2$ . Then, which of the following statement(s) is (are) TRUE?

For 3 x 3 matrices M and N, which of the following statement(s) is (are) not correct?

\[
\text { Match the conics in Column I with the statements/expressions in Column II. }
\]

Which of the following statement is correct in Infinitely long wire kept perpendicula to the paper carrying current inwards the given figure?

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers $R_c<\frac{R}{2},$ which of the following statement(s) about any one of the galvanometers
is(are) true ?

A stationary source is emitting sound at a fixed frequency \(f_0\), which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is \(1.2 \%\) of \(f_0\). What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is \(330 \mathrm{~ms}^{-1}\).