Based on the compounds of group 15 elements, the correct statement(s) is (are)

Match the compounds in List-I with the appropriate observations in List-II and choose the correct option.

List - I	List - II
(P)	(1) Reaction with phenyl diazonium salt gives #ff0 dye.
(Q)	(2) Reaction with ninhydrin gives purple color and it also reacts with \(FeCl _3\) to give violet color.
(R)	(3) Reaction with glucose will give corresponding hydrazone.
(S)	(4) Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous \(FeCl _3\) gives blood red color.
	(5) After complete hydrolysis,it will give ninhydrin test and it DOES NOT give positive phthalein dye test.

LIST-$\mathrm{I}$ contains metal species and LIST-$\mathrm{II}$ contains their properties.

List - I	List - II
(I) \(\left[ Cr ( CN )_6\right]^{4-}\)	(P) \(t _{2 g}\) orbitals contain 4 electrons
(II) \(\left[ RuCl _6\right]^{2-}\)	(Q) \(\mu\) spin - only \(=4.9\) BM
(III) \(\left[ Cr \left( H _2 O \right)_6\right]^{2+}\)	(R) low spin complex ion
(IV) \(\left[ Fe \left( H _2 O \right)_6\right]^{2+}\)	(S) metal ion in 4 + oxidation state
	(T) \(d ^4\) species

[Given: Atomic number of $\mathrm{Cr}=24,\mathrm{Ru}=44,\mathrm{Fe}=26$]
Match each metal species in LIST-$\mathrm{I}$ with their properties in LIST-$\mathrm{II}$, and choose the correct option

For the following reaction scheme, percentage yields are given along the arrow:

\(\mathbf{x} g\) and \(\mathbf{y} g\) are mass of \(\mathbf{R}\) and \(\mathbf{U}\), respectively.
(Use: Molar mass (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of \(\mathrm{H}, \mathrm{C}\) and \(\mathrm{O}\) as 1,12 and 16 , respectively)
The value of $\mathrm{x}$ is ___.

The work function ( \(\Phi\) ) of some metals is listed below. The number of metals which will show photoelectric effect when light of \(300 \mathrm{~nm}\) wavelength falls on the metal is

The $1^{\mathrm{st}}$, $2^{\mathrm{nd}}$ and the $3^{\mathrm{rd}}$ ionization enthalpies, ${\mathrm{I}}_1, {\mathrm{I}}_2$ and ${\mathrm{I}}_3$, of four atoms with atomic numbers $\mathrm{n}, \mathrm{n}+1, \mathrm{n}+2,$ and $\mathrm{n}+3,$ where $\mathrm{n}<10,$ are tabulated below. What is the value of $\mathrm{n}$?

Atomic number	Ionization Enthalpy (kJ/mol)
	${\mathrm{I}}_1$	${\mathrm{I}}_2$	${\mathrm{I}}_3$
$\mathrm{n}$	$1681$	$3374$	$6050$
$\mathrm{n}+1$	$2081$	$3952$	$6122$
$\mathrm{n}+2$	$496$	$4562$	$6910$
$\mathrm{n}+3$	$738$	$1451$	$7733$

Paragraph:
A fixed mass $\text{'}\mathrm{m}\text{'}$ of a gas is subjected to transformation of states from $\mathrm{K}$ to $\mathrm{L}$ to $\mathrm{M}$ to $\mathrm{N}$ and back to $\mathrm{K}$ as shown in the figure

Question :
The succeeding operations that enable this transformation of states are

A factory has a total of three manufacturing units, \(M_1, M_2\), and \(M_3\), which produce bulbs independent of each other. The units \(M_1, M_2\), and \(M_3\) produce bulbs in the proportions of 2:2:1, respectively. It is known that \(20 \%\) of the bulbs produced in the factory are defective. It is also known that, of all the bulbs produced by \(M_1, 15 \%\) are defective. Suppose that, if a randomly chosen bulb produced in the factory is found to be defective, the probability that it was produced by \(M_2\) is \(\frac{2}{5}\).
If a bulb is chosen randomly from the bulbs produced by \(M_3\), then the probability that it is defective is ____.

Oxidation states of the metal in the minerals haematite and magnetite, respectively, are

Let \(f\) and \(g\) be real valued functions defined on interval \((-1,1)\) such that \(g^{\prime \prime}(x)\) is continuous, \(g(0) \neq 0, g^{\prime}(0)=0, g^{\prime \prime}(0) \neq 0\) and \(f(x)=g(x) \sin x\).
Statement \(1 \lim _{x \rightarrow 0}[g(x) \cos x-g(0) \operatorname{cosec} x]=f^{\prime \prime}(0)\).
Statement \(2 f^{\prime}(0)=g(0)\).

A circular disc with a groove along its diameter is placed horizontally. A block of mass \(1 \mathrm{~kg}\) is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is \(\mu=2 / 5\). The disc has an acceleration of \(25 \mathrm{~m} / \mathrm{s}^2\). Find the acceleration of the block with respect to disc.

Atoms of metals $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ form face-centred cubic (fcc) unit cell of edge length ${\mathrm{L}}_{\mathrm{x}}$, body-centred cubic (bcc) unit cell of edge length ${\mathrm{L}}_{\mathrm{y}}$, and simple cubic unit cell of edge length ${\mathrm{L}}_{\mathrm{z}}$, respectively. If ${\mathrm{r}}_{\mathrm{z}}=\frac{\sqrt{3}}{2}{\mathrm{r}}_{\mathrm{y}};{\mathrm{r}}_{\mathrm{y}}=\frac{8}{\sqrt{3}}{\mathrm{r}}_{\mathrm{x}};{\mathrm{M}}_{\mathrm{z}}=\frac{3}{2}{\mathrm{M}}_{\mathrm{y}}$ and ${\mathrm{M}}_{\mathrm{z}}=3{\mathrm{M}}_{\mathrm{x}}$, then the correct statement(s) is(are)
[Given: ${\mathrm{M}}_{\mathrm{x}},{\mathrm{M}}_{\mathrm{y}}$, and ${\mathrm{M}}_{\mathrm{z}}$ are molar masses of metals $\mathrm{x}, \mathrm{y}$, and $z$, respectively. ${\mathrm{r}}_{\mathrm{x}},{\mathrm{r}}_{\mathrm{y}}$, and ${\mathrm{r}}_{\mathrm{z}}$ are atomic radii of metals $\mathrm{x},\mathrm{y}$, and $\mathrm{z}$, respectively.]

Let \(S\) denote the locus of the mid-points of those chords of the parabola \(y^2=x\), such that the area of the region enclosed between the parabola and the chord is \(\frac{4}{3}\). Let \(R\) denote the region lying in the first quadrant, enclosed by the parabola \(y^2=x\), the curve \(S\), and the lines \(x=1\) and \(x=4\).
Then which of the following statements is (are) TRUE?