Paragraph: When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex \(\mathbf{P}\) is formed. In a strong acidic medium, the equilibrium shifts completely towards \(\mathbf{P}\). Addition of zinc chloride to \(\mathbf{P}\) in a slightly acidic medium results in a sparingly soluble complex Q.
Question: The number of zinc ions present in the molecular formula of \(\mathbf{Q}\) is

Columns 1, 2 and 3 contain starting materials, reaction conditions and type of reactions respectively.

Column 1	Column 2	Column 3
(I) Toulene	(i) \(NaOH\) \( /Br _2\)	(P) Condensation
(II) Acetophenone	(ii) \(B r_2 / h v\)	(Q) Carboxylation
(III) Benzaldehyde	(iii) \(\left( CH _3 CO \right)_2\) \(O / CH _3\) \(COOK\)	(R) Substitution
(IV) Phenol	(iv) \(NaOH\) \(/CO _2\)	(S) Haloform

The only CORRECT combination in which the reaction proceeds through radical mechanism is

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is _____
Use: Universal gas constant \((\mathrm{R})=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\); Atomic mass (in amu): \(\mathrm{H}=1, \mathrm{O}=16\) (mark absolute value as answer)

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, \(\left.\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)

Among \(\left[ Ni ( CO )_4\right],\left[ NiCl _4\right]^{2-},\left[ Co \left( NH _3\right)_4 Cl _2\right] Cl , Na _3\) \(\left[ CoF _6\right], Na _2 O _2\) and \(CsO _2\), the total number of paramagnetic compounds is

Paragraph:
The coordination number of \(\mathrm{Ni}^{2+}\) is 4 .
\(\mathrm{NiCl}_2+\mathrm{KCN}\) (excess) \(\rightarrow A\) (cyano complex)
\(\mathrm{NiCl}_2+\) conc. \(\mathrm{HCl}\) (excess) \(\rightarrow B\) (chloro complex)
Question:
The IUPAC name of \(A\) and \(B\) are

Reaction of \(\mathbf{x}\) g of \(\mathrm{Sn}\) with \(\mathrm{HCl}\) quantitatively produced a salt. Entire amount of the salt reacted with \(\mathbf{y} g\) of nitrobenzene in the presence of required amount of \(\mathrm{HCl}\) to produce \(1.29 \mathrm{~g}\) of an organic salt (quantitatively).
(Use Molar masses (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of \(\mathrm{H}, \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{Cl}\) and \(\mathrm{Sn}\) as \(1,12,14,16,35\) and 119 , respectively).
The value of $\mathrm{x}$ is _______ .

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8:15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are:

A point charge $q$ of mass $m$ is suspended vertically by a string of length $l.$ A point dipole of dipole moment $\overrightarrow{p}$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N\times \left(mgh\right)$, where $g$ is the acceleration due to gravity, then the value of $N$ is ____________ (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{\mathrm{F}}{\sin \theta }$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)

The value(s) of \(\int_0^1 \frac{x^4(1-x)^4}{1+x^2} d x\) is (are)

Paragraph:

A small block of mass \(1 \mathrm{~kg}\) is released from rest at the top of a rough track. The track is a circular arc of radius \(40 \mathrm{~m}\). The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point \(Q\), as shown in the figure below, is \(150 \mathrm{~J}\). (Take the acceleration due to gravity, \(g=10 \mathrm{~m} \mathrm{~s}^{-2}\) ).


Question :
The magnitude of the normal reaction that acts on the block at the point \(Q\) is

Let $P$ and $Q$ be distinct points on the parabola $y^2=2x\mathrm{ }$ such that a circle with $PQ$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the first quadrant and the area of the triangle $\mathrm{\Delta }OPQ$ is $3\sqrt{2},\mathrm{ }$then which of the following is (are) the coordinates of $P$?

Statement I The formula connecting \(u, v\) and \(f\) for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Statement II Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.