For the reaction, \(2 \mathrm{CO}+\mathrm{O}_2 \rightarrow 2 \mathrm{CO}_2 ; \Delta H=-560 \mathrm{~kJ}\). Two moles of \(\mathrm{CO}\) and one mole of \(\mathrm{O}_2\) are taken in a container of volume \(1 \mathrm{~L}\). They completely form two moles of \(\mathrm{CO}_2\), the gases deviate appreciably from ideal behaviour. If the pressure in the vessel changes from 70 to \(40 \mathrm{~atm}\), find the magnitude (absolute value) of \(\Delta U\) at \(500 \mathrm{~K} .(1 \mathrm{~L}-\mathrm{atm}=0.1 \mathrm{~kJ})\)

Silver (atomic weight \(=108 \mathrm{~g} \mathrm{~mol}^{-1}\) ) has a density of \(10.5 \mathrm{~g} \mathrm{~cm}^{-3}\). The number of silver atoms on a surface of area \(10^{-12} \mathrm{~m}^2\) can be expressed in scientific notation as \(y \times 10^x\). The value of \(x\) is

Among the following compounds, the most acidic is

The order of the oxidation state of the phosphorus atom in $H_{3}P{O}_2, H_{3}P{O}_4, H_{3}P{O}_3$ and $H_4{P}_2{O}_6$ is

The number of geometric isomers possible for the complex ${\left[\text{C}\text{o}{\text{L}}_2\text{C}{\text{l}}_2\right]}^{-}\left(\text{L}={\text{H}}_2\text{N}\text{C}{\text{H}}_2\text{C}{\text{H}}_2{\text{O}}^{-}\right)$ is
 

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A fixed mass $\text{'}\mathrm{m}\text{'}$ of a gas is subjected to transformation of states from $\mathrm{K}$ to $\mathrm{L}$ to $\mathrm{M}$ to $\mathrm{N}$ and back to $\mathrm{K}$ as shown in the figure

Question :
The pair of isochoric processes among the transformation of states is

An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II. Match List I with List II and select the correct using answer the code given below the lists :

List - I	List - II
a. \(\underset{\quad\quad~~ X }{( C _2 H _5)_3 N}+\underset{ Y }{CH _3 COOH}\)	p. Conductivity decreases and then increases
b. \(\underset{\quad\quad~~ X }{KI (0.1 M )}+\underset{ Y }{AgNO _3(0.01 M )}\)	q. Conductivity decreases and then does not change much
c. \(\underset{\text X }{CH _3 COOH}+\underset{\text Y }{KOH}\)	r. Conductivity increases and then does not change much
d. \(\underset{\text X }{NaOH}+\underset{\text Y }{HI}\)	s. Conductivity does not change much and then increases

In the following reaction sequence, the major product \(\mathbf{P}\) is formed.

Glycerol reacts completely with excess \(\mathbf{P}\) in the presence of an acid catalyst to form \(\mathbf{Q}\). Reaction of \(\mathbf{Q}\) with excess \(\mathrm{NaOH}\) followed by the treatment with \(\mathrm{CaCl}_2\) yields Ca-soap \(\mathbf{R}\), quantitatively. Starting with one mole of \(\mathbf{Q}\), the amount of \(\mathbf{R}\) produced in gram is ________.
[Given, atomic weight: \(\mathrm{H}=1, \mathrm{C}=12,\) \(\mathrm{~N}=14, \mathrm{O}=16, \mathrm{Na}=23, \mathrm{Cl}=35,\) \(\mathrm{Ca}=40\)]

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Tangents are drawn from the point \(P(3,4)\) to the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) touching the ellipse at points \(A\) and \(B\).Question:
The coordinates of \(A\) and \(B\) are

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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:
\(2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Ag}(\mathrm{s})\) \(+~\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_4+2 \mathrm{H}^{+}\). Find \(\ln \mathrm{K}\) of this reaction.

A container has a base of $50\mathrm{cm}\times 5\mathrm{cm}$ and height $50\mathrm{cm}$, as shown in the figure. It has two parallel electrically conducting walls each of area $50\mathrm{cm}\times 50\mathrm{cm}$. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant $3$at a uniform rate of $250{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. What is the value of the capacitance of the container after $10$seconds?
[Given: Permittivity of free space ${\epsilon }_0=9\times {10}^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$, the effects of the non-conducting walls on the capacitance are negligible]

Let \(E^c\) denotes the complement of an event \(E\). Let \(E, F, G\) be pairwise independent events with \(P(G)>0\) and \(P(E \cap F \cap G)=0\). Then, \(P\left(E^c \cap F^c \mid G\right)\) equals

Statement 1 There is a natural asymmetry between converting work to heat and converting heat to work.
Statement 2 No process is possible in which the sole result in the absorption of heat from a reservoir and its complete conversion into work.