Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) Dipole-dipole interactions are the only non-covalent interactions, resulting in hydrogen bond formation. Reason \(R\) : Fluorine is the most electronegative element and hydrogen bonds in \(HF\) are symmetrical. In the light of the above statements, choose the most appropriate answer from the options given below.

Consider the following cases of standard enthalpy of reaction \(\left(\Delta \mathrm{H}_{\mathrm{r}}^{\circ}\right.\) in \(\left.\mathrm{kJ} \mathrm{mol}{ }^{-1}\right)\)
\(\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \Delta \mathrm{H}_1^{\circ}=-1550 \)
\( \mathrm{C} \text { (graphite) }+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \quad \Delta \mathrm{H}_2^{\circ}=-393.5 \)
\( \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \quad \Delta \mathrm{H}_3^{\circ}=-286\)
The magnitude of \(\Delta \mathrm{H}_{f \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})}^{\circ}\) is _______ \(\mathrm{kJ} \mathrm{mol}{ }^{-1}\) (Nearest integer).

Consider the following reaction \(MnO _{4}^{-}+8 H ^{+}+5 e ^{-} \rightarrow Mn ^{2+}+4 H _{2} O , E ^{\circ}=1.51 V\) The quantity of electricity required in Faraday to reduce five moles of \(MnO _{4}^{-}\) is ..... .

For the following Friedel Craft's alkylation reaction, which of the statements are correct?

A. Major product is n-propyl benzene.
B. iso-propyl carbocation intermediate is also generated.
C. Multiple substitution is inevitable.
D. Introducing electron-donating substituent on benzene will not produce any alkyl benzene.
Choose the correct answer from the options given below:

Which of the following reagent is suitable for the preparation of the product in the above reaction?

Identify the name reaction.

Given below are two statements:
Statement-I: The correct order in terms of atomic/ionic radii is \(Al > Mg > Mg^{2+} > Al^{3+}\).
Statement-II: The correct order in terms of the magnitude of electron gain enthalpy is \(Cl > Br > S > O\).
In the light of the above statements, choose the correct answer from the options given below :

Let the solution curve of the differential equation \(x \frac{d y}{d x}-y=\sqrt{y^{2}+16 x^{2}}, y(1)=3\) be \(y=y(x)\). Then \(y (2)\) is equal to

Let \(A=\{-2,-1,0,1,2,3\}\). let R be a relation on A defined by \(x R y\) if and only if \(y=\max \{x, 1\}\). Let \(l\) be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then \(l+\mathrm{m}+\mathrm{n}\) is equal to

The angle of elevation of the top of a vertical tower from a point \(P\) on the horizontal ground was observed to be \(\alpha \). After moving a distance \(2\, metres\) from \(P\) towards the foot of the tower, the angle of elevation changes to \(\beta \). Then the height (in metres) of the tower is

A capacitor is made of a tlat plate of area \(A\) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is \(\mathrm{d}\), the capacitance of the arrangement is _______.

The explosive in a Hydrogen bomb is a mixture of \({ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3\) and \({ }_3 \mathrm{Li}^6\) in some condensed form. The chain reaction is given by \( { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \) \( { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1\) During the explosion the energy released is approximately [Given : \(\mathrm{M}(\mathrm{Li})=6.01690\  \mathrm{amu} . \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \  amu.\) \(\mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388\  \mathrm{amu}\),\( and\ \)\(1 \ \mathrm{amu}=931.5\) \(\mathrm{MeV}]\)

A \(1 \,kg\) block attached to a spring vibrates with a frequency of \(1\, Hz\) on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an \(8\, kg\) block placed on the same table. So, the frequency of vibration of the \(8\, kg\) block is ..... \(Hz\)