From the vitamins \(\mathrm{A}, \mathrm{B}_1, \mathrm{~B}_6, \mathrm{~B}_{12}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and \(\mathrm{K}\), the number vitamins that can be stored in our body is _______.

The minimum volume of water required to dissolve \(0.1\,g\) lead \((II)\) chloride to get a saturated solution (\(K_{SP}\) of \(PbCl_2 = 3.2 \times 10^{-8}\); atomic mass of \(Pb= 207\, u\)) is......\(L\)

The major products from the following reaction sequence are product \(\mathrm{A}\) and product \(\mathrm{B}\). The total sum of \(\pi\) electrons in product \(A\) and product \(B\) are _______. (nearest integer)

Wavenumber for a radiation having \(5800 \mathring A\) wavelength is \(x \times 10 \mathrm{~cm}^{-1}\). The value of \(x\) is _______.

Given below are two statements :
Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test.
Statement (II) : The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test.
In the light of the above statements, choose the correct anower from the options given below :

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

List \(- I\) Electronic configuration of elements	List \(- II\) \(\Delta_{ i }\) in \(kJ\, mol-1\)
\((a)\) \(1 s ^{2} 2 s ^{2}\)	\((i)\) \(801\)
\((b)\) \(1 s ^{2} 2 s ^{2} 2 p ^{4}\)	\((ii)\) \(899\)
\((c)\) \(1 s^{2} 2 s^{2} 2 p^{3}\)	\((iii)\) \(1314\)
\((d)\) \(1 s ^{2} 2 s ^{2} 2 p ^{1}\)	\((iv)\) \(1402\)

Choose the most appropriate answer from the options given below

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

A circular loop ofradius \(0.3\ cm\) lies parallel to amuch bigger circular loop ofradius \(20\ cm\). The centre of the small loop is on the axis of the bigger loop. The distance between their centres is \(15\ cm\). If a current of \(2.0\ A\) flows through the smaller loop, then the flux linked with bigger loop is

Let \(\mathrm{A}=\{\mathrm{n} \in[100,700] \cap \mathrm{N}: \mathrm{n}\) is neither a multiple of \(3\) nor a multiple of 4\(\}\). Then the number of elements in \(\mathrm{A}\) is

Number of geometrical isomers possible for the given structure is _______.

Let \(\vec{a}, \vec{b}, \vec{c}\) be three vectors mutually perpendicular to each other and have same magnitude. If a vector \(\overrightarrow{\mathrm{r}}\) satisfies. \(\overrightarrow{\mathrm{a}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{a}}\}+\overrightarrow{\mathrm{b}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{c}}) \times \overrightarrow{\mathrm{b}}\}+\overrightarrow{\mathrm{c}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{a}}) \times \overrightarrow{\mathrm{c}}\}=\overrightarrow{0}\) then \(\overrightarrow{\mathrm{r}}\) is equal to:

A thin uniform rod \(( X )\) of mass M and length L is pivoted at a height \(\left(\frac{ L }{3}\right)\) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is _________ . (g = gravitational acceleration)

Let \(C\) be the circle in the complex plane with centre \(z_0=\frac{1}{2}(1+3 i)\) and radius \(r=1\). Let \(z_1=1+\) \(i\) and the complex number \(z_2\) be outside the circle \(C\) such that \(\left|z_1-z_0\right|\left|z_2-z_0\right|=1\). If \(z_0, z_1\) and \(z_2\) are collinear, then the smaller value of \(\left|z_2\right|^2\) is equal to \(.............\).