The species in which the \(N\) atom is in a state of \(sp\) hybridization is :

\(600\,mL\) of \(0.01\,M\,HCl\) is mixed with \(400\,mL\) of \(0.01\,M\,H _2 SO _4\). The \(pH\) of the mixture is \(.......\times 10^{-2}\). (Nearest integer) [Given \(\log 2=0.30, \quad \log 3=0.48\) \(\log 5=0.69 \quad \log 7=0.84\) \(\log 11=1.04]\)

In the estimation of bromine, \(0.5\, g\) of an organic compound gave \(0.40\, g\) of silver bromide. The percentage of bromine in the given compound is \(.....\,\%\) (nearest integer) (Relative atomic masses of \(Ag\) and \(Br\) are \(108\, u\) and \(80\, u\), respectively).

Consider the following reactions. From these reactions which reaction will give carboxylic acid
as a major product ?
(A) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \mathrm{H}^{+} / \mathrm{H}_2 \mathrm{O}}\)
(B) \(\mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}\)
(C) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}\)
(D) \(\mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}\)
(E)

Choose the correct answer from the options given below:

For a reaction \(A \rightarrow P\) at \(T\text{ K}\), the half life \((t_{1/2})\) is plotted as a function of initial concentration \([A]_0\) of \(A\) as given below.

The value of \(x\) in the given figure is _______ s (Nearest integer)

A proton and a \(Li ^{3+}\) nucleus are accelerated by the same potential. If \(\lambda_{L i}\) and \(\lambda_{P}\) denote the de Broglie wavelengths of \(Li ^{3+}\) and proton respectively, then the value of \(\frac{\lambda_{ Li }}{\lambda_{ P }}\) is \(x \times 10^{-1}\).The value of \(x\) is ............ (Rounded off to the nearest integer) (Mass of \(Li ^{3+}=8.3\) mass of proton)

The number of structural isomers for \(C_6H_{14}\) is

Light source having wavelength \(331\) nm is used to generate photo-electrons whose stopping potential is \(0.2\) V. The work function of the used metal in the experiment is \(\alpha \times 10^{-19}\) J. The value of \(\alpha\) is _____.
(\(h = 6.62 \times 10^{-34}\) J s, \(e = 1.6 \times 10^{-19}\) C and \(c = 3 \times 10^8\) m/s)

Let \(S\) be the set of values of \(\lambda\), for which the system of equations \(6 \lambda x-3 y+3 z=4 \lambda^2\) \(2 x+6 \lambda y+4 z=1\) \(3 x+2 y+3 \lambda z=\lambda \text { has no solution. Then } 12 \sum_{\lambda \in S}|\lambda|\) is equal to \(...........\).

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from \(300\, nm\) to \(400\, nm\). The decrease in the stopping potential is close to ................ \(V\) \(\left( {\frac {{hc}}{e} = 1240\,nm - V} \right)\)

The period of oscillation of a simple pendulum is \(T =2 \pi \sqrt{\frac{ L }{ g }} .\) Measured value of \( L \) is \(1.0\, m\) from meter scale having a minimum division of \(1 \,mm\) and time of one complete oscillation is \(1.95\, s\) measured from stopwatch of \(0.01 \,s\) resolution. The percentage error in the determination of \(g\) will be ..... \(\%.\)

The dipole moment of a circular loop carrying a current \(I\), is \(m\) and the magnetic field at the centre of the loop is \(B_1\) . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is \(B_2\) . The ratio \(\frac{{{B_1}}}{{{B_2}}}\) is

The magnetic field inside a 200 turns solenoid of radius 10 cm is \(2.9 \times 10^{-4} \mathrm{Tesla}\). If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ \(\pi \mathrm{cm}\).