Among the species given below, the total number of diamagnetic species is _____________.
\(H\) atom, \(N O_2\) monomer, \(O_2^{-}\)(superoxide), dimeric sulphur in vapour phase,
\(Mn_3 O_4, \left(NH_4\right)_2\left[FeCl_4\right], \left(NH_4\right)_2\left[NiCl_4\right],\) \(K_2 MnO_4, K_2 CrO_4\)

The reaction of $4$-methyloct-$1$-ene $(\mathrm{P},2.52 \mathrm{g})$ with $\mathrm{HBr}$ in the presence of ${\left({\mathrm{C}}_6{\mathrm{H}}_5\mathrm{CO}\right)}_2{\mathrm{O}}_2$ gives two isomeric bromides in a $9: 1$ ratio, with a combined yield of $50\%$. Of these, the entire amount of the primary alkyl bromide was reacted with an appropriate amount of diethylamine followed by treatment with aq. ${\mathrm{K}}_2{\mathrm{CO}}_3$ to give a non-ionic product $\mathrm{S}$ in $100\%$ Yield. The mass (in $\mathrm{mg}$ ) of $\mathrm{S}$ obtained is
[Use molar mass (in ${\mathrm{gmol}}^{-1}$ ): $\mathrm{H}=1,\mathrm{C}=12, \mathrm{N}=14,\mathrm{Br}=80$ ]

Consider an electrochemical cell: $\text{A}\left(\text{s}\right)\left|{\text{ A}}^{\text{n+}}\left(\text{aq, 2 M}\right)\right|\left|{\text{ B}}^{\text{2n+}}\left(\text{aq, 1 M}\right)\right|\text{ B}\left(\text{s}\right)$. The value of ${\text{ΔH}}^{\text{o}}$ for the cell reaction is twice that of ${\text{ΔG}}^{\text{o}}$ at $\text{300 K}\text{.}$ If the emf of the cell is zero, the magnitude of $\mathrm{\Delta }{\text{S}}^o$ $\left(\text{in} {\text{J}}^{-1}{\text{K}}^{-1} {\text{mol}}^{-1}\right)$ of the cell reaction per mole of $\text{B}$ formed at $\text{300}\text{K}$ is ____
(Given: R $\text{=}\text{8}\text{.3}{\text{JK}}^{-\text{1}}{\text{mol}}^{-1}.$ $\text{H,}\text{S}$ and $\text{G}$ are enthalpy, entropy and Gibbs energy, respectively.)

Consider the following volume-temperature \((\mathrm{V}-\mathrm{T})\) diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence \(\mathbf{X} \rightarrow \mathbf{Y} \rightarrow \mathbf{Z}\) is ________.
[Use the given data: Molar heat capacity of the gas for the given temperature range, \(\mathrm{C}_{\mathrm{V}, \mathrm{m}}=12 \mathrm{~J} \mathrm{~K}^{-1}\) \(\mathrm{mol}^{-1}\) and gas constant, \(\left.\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)

The substituents \(R_{1}\) and \(R_{2}\) for nine peptides are listed in the table given below. How many of these peptides are positively charged at \(\mathrm{pH}=7.0\) ?

\(\begin{array}{|c|c|c|}\hline Peptide & \mathbf{R}_{\mathbf{1}} & \mathbf{R}_{\mathbf{2}} \\\hline I & \mathrm{H} & \mathrm{H} \\\hline II & \mathrm{H} & \mathrm{CH}_{3} \\\hline III & \mathrm{CH}_{2} \mathrm{COOH} & \mathrm{H} \\\hline IV & \mathrm{CH}_{2} \mathrm{CONH}_{2} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\\hline V & \mathrm{CH}_{2} \mathrm{CONH}_{2} & \mathrm{CH}_{2} \mathrm{CONH}_{2} \\\hline VI & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\\hline VII & \mathrm{CH}_{2} \mathrm{COOH} & \mathrm{CH}_{2} \mathrm{CONH}_{2} \\\hline VIII & \mathrm{CH}_{2} \mathrm{OH} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\\hline IX & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} & \mathrm{CH}_{3} \\\hline\end{array}\)

The total number of lone pairs of electrons in ${\mathrm{N}}_2{\mathrm{O}}_3$ is

Consider the following molecules : ${\mathrm{Br}}_3{\mathrm{O}}_8, {\mathrm{F}}_2\mathrm{O},{\mathrm{H}}_2 {\mathrm{S}}_4{\mathrm{O}}_6,{\mathrm{H}}_2 {\mathrm{S}}_5{\mathrm{O}}_6$, and ${\mathrm{C}}_3{\mathrm{O}}_2$. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is

If $2x-y+1=0$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{16}=1$ , then which of the following CANNOT be sides of a right angled triangle?

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

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x=0$ , in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block its position is x and velocity is v. At that instant which of the following options is correct?

The energy of a system as a function of time $\mathrm{t}$ is given as $\mathrm{E}\left(\mathrm{t}\right)={\mathrm{A}}^2\left(-\mathrm{\alpha }\mathrm{t}\right)$ , where $\alpha =0.2\mathrm{ }{\mathrm{s}}^{-1}$ . The measurement of $\mathrm{A}$ has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of $\mathrm{E}\left(\mathrm{t}\right)$ at $\mathrm{t}=5$ s is

For a point P in the plane, let $d_1\left(P\right)$ and $d_2\left(P\right)$ be the distances of the point P from the lines $x-y=0$ and $x+y=0$ respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying $2 \le d_1\left(P\right)+d_2\left(P\right) \le 4,$ is ________

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift's motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the lists.
 

	List I		List II
A.	Lift is accelerating vertically up.	$P.$	$\mathrm{d}=1.2\mathrm{ }\mathrm{m}$
B.	Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.	$Q.$	$\mathrm{d}>1.2\mathrm{ }\mathrm{m}$
C.	Lift is moving vertically up with constant speed.	$R.$	$\mathrm{d}<1.2\mathrm{ }\mathrm{m}$
D.	Lift is falling freely.	$S.$	No water leaks out of the jar