The compound(s) with two lone pairs of electrons on the central atom is (are)

For the cell $\mathrm{Zn} \left(\mathrm{s}\right)\left|{\mathrm{ZnSO}}_4 \left(\mathrm{aq}\right)\right|\left|{\mathrm{CuSO}}_4 \left(\mathrm{aq}\right)\right|\mathrm{Cu} \left(\mathrm{s}\right)$, when the concentration of ${\mathrm{Zn}}^{2+}$ is $10$ times the concentration of ${\mathrm{Cu}}^{2+}$, the expression for $\mathrm{\Delta G} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ is
$[\mathrm{F}=$Faraday's constant, $\mathrm{R}=$universal gas constant, $\mathrm{T}=$temperature, ${\mathrm{E}}^{\mathrm{o}}\mathrm{cell}=1.1\mathrm{V}]$

The cubic unit cell structure of a compound containing cation $\mathrm{M}$ and anion $\mathrm{X}$ is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

The heating of \(\mathrm{NH}_4 \mathrm{NO}_2\) at \(60-70^{\circ} \mathrm{C}\) and \(\mathrm{NH}_4 \mathrm{NO}_3\) at \(200-250^{\circ} \mathrm{C}\) is associated with the formation of nitrogen containing compounds \(\mathbf{X}\) and \(\mathbf{Y}\), respectively. \(\mathbf{X}\) and \(\mathbf{Y}\), respectively, are

Match each set of hybrid orbitals from LIST-I with complex (es) given in LIST-II.

	LIST -I		LIST -II
A)	$ds{p}^2$	P)	${\left[Fe{F}_6\right]}^{4-}$
B)	$s{p}^3$	Q)	$\left[Ti{\left(H_{2}O\right)}_{3}C{l}_3\right]$
C)	$s{p}^3{d}^2$	R)	${\left[Cr{\left(N{H}_3\right)}_6\right]}^{3+}$
D)	$d^{2}s{p}^3$	S)	${\left[FeC{l}_4\right]}^{2-}$
		T)	$Ni{\left(CO\right)}_4$
		U)	${\left[Ni{\left(CN\right)}_4\right]}^{2-}$

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The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.
The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2,+4\) and \(+6 . \mathrm{XeF}_4\) reacts violently with water to give \(\mathrm{XeO}_3\). The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.
Question:
The structure of \(\mathrm{XeO}_3\) is

For a double strand DNA, one strand is given below:

The amount of energy required to split the double strand DNA into two single strands is _______ kcal \(\mathrm{mol}^{-1}.\)
[Given: Average energy per \(\mathrm{H}\)-bond for A-T base pair \(=1.0 \mathrm{kcal} \mathrm{mol}^{-1}, \mathrm{G}-\mathrm{C}\) base pair \(=1.5 \mathrm{kcal}\) \(\mathrm{mol}^{-1}\), and A-U base pair \(=1.25 \mathrm{kcal} \mathrm{mol}^{-1}.\) Ignore electrostatic repulsion between the phosphate groups.]

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Two plane harmonic sound waves are expressed by the equations.
\(\begin{aligned}
& y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\
& y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)
\end{aligned}\)
(All parameters are in MKS)
Question:
At \(x=0\) how many times the amplitude of \(y_1+y_2\) is zero in one second at \(x=0\) ?

A \(20 \mathrm{~cm}\) long string, having a mass of \(1.0 \mathrm{~g}\), is fixed at both the ends. The tension in the string is \(0.5 \mathrm{~N}\). The string is set into vibration using an external vibrator of frequency 100 \(\mathrm{Hz}\). Find the separation (in \(\mathrm{cm}\) ) between the successive nodes on the string.

If the reaction sequence given below is carried out with $15$ moles of acetylene, the amount of the product $\mathrm{D}$ formed (in $\mathrm{g}$) is The yields of $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ are given in parentheses. [Given: Atomic mass of $\mathrm{H}=1,\mathrm{C}=12,\mathrm{O}=16,\mathrm{Cl}=35$]

A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $xy$ plane with its center at the origin. The Coulomb potential along the $z$-axis is
$V\left(z\right)=\frac{\sigma }{2{ϵ}_0}\left(\sqrt{R^2+z^2}-z\right)$ A particle of positive charge $q$ is placed initially at rest at a point on the $z$-axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\overrightarrow{F}=-c\hat{k}$ with $c>0$. Let $\beta =\frac{2c{\epsilon }_0}{q\sigma }$. Which of the following statement(s) is(are) correct?

A container with $1 \mathrm{kg}$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 \mathrm{W} {\mathrm{m}}^{-2}$ and it is absorbed by the water over an effective area of $0.05 {\mathrm{m}}^2.$ Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${}^{\circ }\mathrm{C}$) in the temperature of water and the surroundings after a long time will be_________. (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 {\mathrm{s}}^{-1},$ Heat capacity of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

Of the three independent events ${\text{E}}_1$, ${\text{E}}_2$ and ${\text{E}}_3$, the probability that only ${\text{E}}_1$ occurs is $\alpha$, only ${\text{E}}_2$ occurs is $\beta$ and only  ${\text{E}}_3$ occurs is $\gamma$. Let the probability $p$ that none of events ${\text{E}}_1$, ${\text{E}}_2$ or ${\text{E}}_3$ occurs satisfy the equations $\left(\alpha -2\beta \right)p=\alpha \beta$ and $\left(\beta -3\gamma \right)p = 2\beta \gamma$. All the given probabilities are assumed to lie in the interval $\left(\text{0, 1}\right)$.
Then   $\frac{{\text{Probability of occurrence of E}}_1}{{\text{Probability of occurrence of E}}_3}=$ ​