Which statements are True?
A. In Hoffmann bromamide degradation, \(4\) moles of NaOH and \(2\) moles of Br\(_2\) are consumed per mole of an amide
B. Hoffmann bromamide reaction is not given by alkyl amides.
C. Primary amines can be synthesized by Hoffmann bromamide degradation.
D. Secondary amide on reaction with Br\(_2\) and NaOH will give secondary amine.
E. The by-products of Hoffmann degradation are Na\(_2\)CO\(_3\), NaBr and H\(_2\)O.
Choose the correct answer from the options given below:

When light of wavelength \(248\, nm\) falls on a metal of threshold energy \(3.0 \,eV\), the de-Broglie wavelength of emitted electrons is ............. \(\mathring A\) (Round off to the Nearest Integer). [Use : \(\sqrt{3}=1.73, h =6.63 \times 10^{-34} Js\) \(m _{ e }=9.1 \times 10^{-31} kg ; c =3.0 \times 10^{8} ms ^{-1}\) \(\left.1 eV =1.6 \times 10^{-19} J \right]\)

Consider the above sequence of reactions. The number of bromine atom(s) in the final product (P) will be:

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

Match \(List-I\) with \(List-II\). 

\(List-I\)	\(List-II\)
\((A)\) \(Cd ( s )+2 Ni ( OH )_{3}( s ) \rightarrow CdO ( s )+2 Ni ( OH )_{2}( s )+ H _{2} O (l)\)	\((I)\) Primary battery
\((B)\)  \(Zn ( Hg )+ HgO ( s ) \rightarrow ZnO ( s )+ Hg (l)\)	\((II)\) Discharging of secondary battery
\((C)\) \(2 PbSO _{4}( s )+2 H _{2} O (l) \rightarrow Pb ( s )+ PbO _{2}( s )+ 2 H _{2} SO _{4}( aq )\)	\((III)\) Fuel cell
\((D)\) \(2 H _{2}( g )+ O _{2}( g ) \quad \rightarrow 2 H _{2} O (l)\)	\((IV)\) Charging of secondary battery

Choose the correct answer from the options given below.

Thyroxine, the hormone has given below structure

The percentage of iodine in thyroxine is ____ \(\%\). (nearest integer)
(Given molar mass in \(\mathrm{g} \mathrm{mol}^{-1} \mathrm{C}: 12. \mathrm{H}: 1, \mathrm{O}: 16\), \(\mathrm{N}: 14, \mathrm{I}: 127)\)

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\): The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction. Reason \(R:\) The wavelengths of waves are different in different media. In the light of the above statements, choose the most appropriate answer from the options given below

If \(\phi(x)=\frac{1}{\sqrt{x}} \frac{\pi}{4} \int \limits_0^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, \quad x > 0\) then \(\phi^{\prime}\left(\frac{\pi}{4}\right)\) is equal to :

If \(\quad A=\left[\begin{array}{cc}\cos \theta & \text { isin } \theta \\ \operatorname{isin} \theta & \cos \theta\end{array}\right], \left(\theta=\frac{\pi}{24}\right)\) and \(A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right],\) where \(i=\sqrt{-1},\) then which one of the following is not true?

A tub is filled with water and a wooden cube \(10\) cm \(\times\) \(10\) cm \(\times\) \(10\) cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \(3.87\) cm. The mass of the metal coin is _______ gram.
(Take water density as \(1\) g/cm\(^3\) and density of wood as \(0.4\) g/cm\(^3\))

Which of the following statement is not true for glucose?

A two point charges \(4 q\) and \(-q\) are fixed on the \(x-\)axis at \(x=-\frac{d}{2}\) and \(x=\frac{d}{2},\) respectively. If a third point charge \('q'\) is taken from the origin to \(x = d\) along the semicircle as shown in the figure, the energy of the charge will