If the radius of the \(3^{\text {rd }}\) Bohr's orbit of hydrogen atom is \(r_{3}\) and the radius of \(4^{\text {th }}\) Bohr's orbit is \(r_{4}\). Then ....

A solution containing \(10 \mathrm{~g}\) of an electrolyte \(\mathrm{AB}_2\) in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The degree of ionization of the electrolyte \((\alpha)\) is _______ \(\times 10^{-1}\). (nearest integer) [Given : Molar mass of \(\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1} \cdot \mathrm{K}_{\mathrm{b}}\) (molal boiling point elevation const. of water) \(=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\), boiling point of water \(=100^{\circ} \mathrm{C}\); \(\mathrm{AB}_2\) ionises as \(\left.\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}\right]\)

Number of \(\mathrm{Cl}=\mathrm{O}\) bonds in chlorous acid, chloric acid and perchloric acid respectively are :

The reduction reaction known as:

A molecule (X) with following structure under mild acidic condition is hydrolysed to produce (Y) and (Z). Identify the correct statements about (Y) and (Z).

A. Both (Y) and (Z) have same molar mass.
B. (Y) and (Z) can be distinguished from each other by \(NaHCO_3\).
C. (Y) and (Z) react with HCN with same rates.
D. (Y) and (Z) undergo addition reaction with \(2,4\)-DNP.
Choose the correct answer from the options given below:

An ether \((A)\), \(C_5H_{12}O\), when heated with excess of hot concentrated \(HI\) produced two alkyl halides which when treated with \(NaOH\) yielded compounds \((B)\) and \((C)\). Oxidation of \((B)\) and \((C)\) gave a propanone and an ethanoic acid respectively. The \(IUPAC\) name of the ether \((A)\) is 

\(20\,mL\) of \(0.1\,M\,NaOH\) is added to \(50\,mL\) of \(0.1\,M\) acetic acid solution. The \(pH\) of the resulting solution is \(.......\times 10^{-2}\) (Nearest integer) \(\text { Given : pKa }\left( CH _3 COOH \right)=4.76\) \(\log 2=0.30\) \(\log 3=0.48\)

A coil of negligible resistance is connected in series with \(90 \Omega\) resistor across \(120 \mathrm{~V}, 60 \mathrm{~Hz}\) supply. A voltmeter reads \(36 \mathrm{~V}\) across resistance. Inductance of the coil is _______.

Match List-I with List-\(II\)

List-\(I\) (Complexion)	List-\(II\) (Spin only magnetic moment in B.M.)
\((A)\) \({\left[\mathrm{Cr}\left(\mathrm{NH}_5\right)_0\right]^{3+}}\)	\((I)\) \(4.90\)
\((B)\) \({\left[\mathrm{NiCl}_4\right]^{2-}}\)	\((II)\) \(3.87\)
\((C)\) \({\left[\mathrm{CoF}_6\right]^{3-}}\)	\((III)\) \(0.0\)
\((D)\) \({\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}}\)	\((IV)\) \(2.83\)

Choose the correct answer from the options given below:

Which one of the following sets of ions represents a collection of isoelectronic species? (Given : Atomic Number: F :9, \(Cl : 17, Na =11\), \(Mg =12, Al =13, K =19, Ca =20, Sc =21\) )

In an arithmetic progression, if \(S_{40}=1030 \text { and } S_{12}=57 \text {, then } S_{30}-S_{10} \text { is equal to : }\)

Let a point A lie between the parallel lines \( L_{1} \) and \( L_{2} \) such that its distances from \( L_{1} \) and \( L_{2} \) are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines \( L_{1} \) and \( L_{2} \) respectively, is:

An electric bulb of \(500 \,watt\) at \(100\, volt\) is used in a circuit having a \(200\, {V}\) supply. Calculate the resistance \({R}\) to be connected in series with the bulb so that the power delivered by the bulb is \(500\, {W}\). (in \(\Omega\))