Dissolving \(120 \mathrm{~g}\) of urea (molecular weight 60) in \(1000 \mathrm{~g}\) of water gave a solution of density \(1.15 \mathrm{~g} / \mathrm{mL}\). The molarity of the solution is

Total number of cis $\mathrm{N}-\mathrm{M}\mathrm{n}-\mathrm{C}\mathrm{l}$ bond angles (that is, $\mathrm{M}\mathrm{n}-\mathrm{N}$ and $\mathrm{M}\mathrm{n}-\mathrm{C}\mathrm{l}$ bonds in cis positions) present in a molecule of cis- $\left[\mathrm{M}\mathrm{n}{\left(\mathrm{e}\mathrm{n}\right)}_2{\mathrm{C}\mathrm{l}}_2\right]$ complex is _________ $\left(en={\mathrm{N}\mathrm{H}}_2{\mathrm{C}\mathrm{H}}_2{\mathrm{C}\mathrm{H}}_2{\mathrm{N}\mathrm{H}}_2\right)$

The standard reduction potential data at $25°C$ is given below.
\(E ^o\left( Fe ^{3+}, Fe ^{2+}\right)=+0.77 V ; \)
\( E ^o\left( Fe ^{2+}, Fe \right)=-0 . 44 V \)
\( E ^o\left( Cu ^{2+}, Cu \right)=+0.34 V ; \)
\( E ^o\left( Cu ^{+}, Cu \right)=+0.52 V \)
\( E ^o\left[ O _2(g)+4 H ^{+}+4 e ^{-} \rightarrow 2 H _2 O \right]=\) \(+1.23~V \)
\( E ^o\left[ O _2(g)+2 H _2 O +4 e^{-} \longrightarrow \text { 4OH}^{-}\right]=\) \(+0.40~V \)
\( E ^o\left( Cr ^{3+}, Cr \right)=-0.74 V ; \)
\( E ^o\left( Cr ^{2+}, Cr \right)=-0.91 V\)
Match E^o of the redox pair in List I with the values given in List II and select the correct answer using the code given below the lists :
 

	List I		List II
A.	$E^o\left({\mathit{\text{Fe}}}^{3+},\mathit{\text{Fe}}\right)$	P.	$-0.18V$
B.	$E^o\left(4{\text{H}}_2\text{O}\rightleftharpoons 4H^{+}+4{\mathit{\text{OH}}}^{-}\right)$	Q.	$-0.4V$
C	$E^o\left({\mathit{\text{Cu}}}^{2+}+\mathit{\text{Cu}}\to 2{\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{Cu}}^{+}\right)$	R.	$-0.04V$
D.	$E^o\left({\mathit{\text{Cr}}}^{3+},{\mathit{\text{Cr}}}^{2+}\right)$	S.	$-0.83V$

The given graph represent the variations of compressibility factor \((Z)=\frac{P V}{n R T}\) versus \(P\), for three real gases \(A, B\) and \(C\). Identify the only incorrect statement

The boiling point of water in a \(0.1\) molal silver nitrate solution (solution \(\mathbf{A}\) ) is \(\mathbf{x}^{\circ} \mathrm{C}\). To this solution \(\mathbf{A}\), an equal volume of \(0.1\) molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions \(\mathbf{A}\) and \(\mathbf{B}\) is \(\mathbf{y} \times 10^{-2}{ }^{\circ} \mathrm{C}\).
(Assume: Densities of the solutions \(\mathbf{A}\) and \(\mathbf{B}\) are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), \(K_{b}=0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\); Boiling point of pure water as \(100^{\circ} \mathrm{C}\).)
The value of $\left|\mathrm{y}\right|$ is ___.

Statement 1 For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
Statement 2 At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

A positron is emitted from \({ }_{11}^{23} \mathrm{Na}\). The ratio of the atomic mass and atomic number of the resulting nuclide is

A particle of mass $m$ is attached to one end of a massless spring of force constant $k$, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5u_0$, it collides elastically with a rigid wall. After this collision :

In the scheme given below, the total number of intramolecular aldol condensation products formed from ' \(Y\) ' is

A plot of the number of neutrons $(\text{N})$ against the number of protons $(\text{P})$ of the stable nuclei exhibits upwards deviation from linearity for atomic number, $\text{Z}>20$. For an unstable nucleus having $\frac{\text{N}}{\text{P}}$ ratio less than $1$, the possible mode(s) of decay is (are):

The compound(s) formed upon combustion of sodium metal in excess air is (are)

A block of mass \(2 \mathrm{~kg}\) is free to move along the \(x\)-axis. It is at rest and from \(t\) \(=0\) onwards it is subjected to a time-dependent force \(F(t)\) in the \(x\) direction. The force \(F(t)\) varies with \(t\) as shown in the figure. The kinetic energy of the block after \(4.5 \mathrm{~s}\) is

Let the point $\mathrm{B}$ be the reflection of the point $\mathrm{A}\left(2,\mathrm{ }3\right)$ with respect to the line $8\mathrm{x}-6\mathrm{y}-23=0.$ Let ${\mathrm{T}}_{\mathrm{A}}$ and ${\mathrm{T}}_{\mathrm{B}}$ be circle of radii $2$ and $1$ with centres $\mathrm{A}$ and $\mathrm{B}$ respectively. Let $\mathrm{T}$ be a common tangent to the circle ${\mathrm{T}}_{\mathrm{A}}$ and ${\mathrm{T}}_{\mathrm{B}}$ such that both the circle are on the same side of $\mathrm{T}.$ If $\mathrm{C}$ is the point of intersection of $\mathrm{T}$ and the line passing through $\mathrm{A}$ and $\mathrm{B},$ then the length of the line segment $\mathrm{A}\mathrm{C}$ is ___________.