The surface of sodium metal is irradiated with radiation of wavelength \(x\) nm. The kinetic energy of ejected electrons is \(2.8 \times 10^{-20}\) J. The work function of sodium is \(2.3\) eV. The value of \(x\) is _____ \(\times 10^2\) nm. (Nearest integer)
(Given: \(h = 6.6 \times 10^{-34}\) J s; \(1\) eV \(= 1.6 \times 10^{-19}\) J; \(c = 3.0 \times 10^8\) m s\(^{-1}\))

The number of chiral carbon\((s)\) present in peptide, Ile\(-\)Arg\(-\)Pro, is......

The energy of an electron in first Bohr orbit of H -atom is -13.6 eV. The magnitude of energy value of electron in the first excited state of \(\mathrm{Be}^{3+}\) is ________ eV. (nearest integer value)

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\) Assertion \((A) :\) At \(10^{\circ} C\), the density of a \(5\, M\) solution of \(KCl\) [atomic masses of \(K\) and \(Cl\) are \(39\) and \(35.5\, g \,mol ^{-1}\) ]. The solution is cooled to \(-21^{\circ} C\). The molality of the solution will remain unchanged. Reason \((R):\) The molality of a solution does not change with temperature as mass remains unaffected with temperature. In the light of the above statements, choose the correct answer from the options given below

For a cell, \(Cu ( s ) \mid Cu ^{2+}\left(0.001 M || Ag ^{+}(0.01\,M ) \mid Ag ( s )\right.\) the cell potential is found to be \(0.43\,V\) at \(298 K\). The magnitude of standard electrode potential for \(Cu ^{2+} / Cu\) \(.........\times 10^{-2}\,V\) \(\left[\text { Given }: E _{ Ag ^{+} / Ag }^{\Theta}=0.80 V \text { and } \frac{2.303 \,RT }{ F }=0.06\,V \right]\)

The hybridisations of the atomic orbitals of nitrogen in \(\mathrm{NO}_{2}^{-}, \mathrm{NO}^{+} _2\) and \(\mathrm{NH}_{4}{ }^{+}\)respectively are.

The number of moles of methane required to produce \(11 \mathrm{~g} \mathrm{CO}_2(\mathrm{~g})\) after complete combustion is _______. (Given molar mass of methane in \(\mathrm{g} \mathrm{mol}^{-1}: 16\) )

A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

If the set \(R=\{(a, b) ; a+5 b=42, a, b \in \mathbb{N}\}\) has \(m\) elements and \(\sum_{n=1}^m\left(1-i^{n !}\right)=x+i y\), where \(I=\sqrt{-1}\), then the value of \(m+x+y\) is :

The \(71^{st}\) electron of an element \(X\) with an atomic number of \(71\) enters into the orbital:

Let the point \((p, p+1)\) lie inside the region \(E=\left\{(x, y): 3-x \leq y \leq \sqrt{9-x^2}, 0 \leq x \leq 3\right\}\) If the set of all values of \(p\) is the interval \((a, b)\). then \(b^2+b-a^2\) is equal to \(.................\).

If an optical medium possesses a relative permeability of \(\frac{10}{\pi}\) and relative permittivity of \(\frac{1}{0.0885}\), then the velocity of light is greater in vacuum than that in this medium by ________ times.
\(\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right.\)
\(\left.\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)\)

Statement \(-1\) : The system of linear equations \(x + \left( {\sin \,\alpha } \right)y + \left( {\cos \,\alpha } \right)z = 0\) \(x + \left( {\cos \,\alpha } \right)y + \left( {\sin \alpha } \right)z = 0\) \(x - \left( {\sin \,\alpha } \right)y - \left( {\cos \alpha } \right)z = 0\) has a non-trivial solution for only one value of \(\alpha \) lying in the interval \(\left( {0\,,\,\frac{\pi }{2}} \right)\)  Statement \(-2\) : The equation in \(\alpha \) \(\left| {\begin{array}{*{20}{c}}
  {\cos {\mkern 1mu} \alpha }&{\sin {\mkern 1mu} \alpha }&{\cos {\mkern 1mu} \alpha } \\ 
  {\sin {\mkern 1mu} \alpha }&{\cos {\mkern 1mu} \alpha }&{\sin {\mkern 1mu} \alpha } \\ 
  {\cos {\mkern 1mu} \alpha }&{ - \sin {\mkern 1mu} \alpha }&{ - \cos {\mkern 1mu} \alpha } 
\end{array}} \right| = 0\) has only one solution lying in the interval \(\left( {0\,,\,\frac{\pi }{2}} \right)\)