Consider the following four compounds I, II, III, and IV.

Choose the correct statement(s).

The number of neutrons emitted when \({ }_{92}^{235} \mathrm{U}\) undergoes controlled nuclear fission to \({ }_{54}^{142} \mathrm{Xe}\) and \({ }_{38}^{90} \mathrm{Sr}\) is

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Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately \(6.023 \times 10^{23}\) ) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A \(4.0\) molar aqueous solution of \(\mathrm{NaCl}\) is prepared and \(500 \mathrm{~mL}\) of this solution is electrolysed. This leads to the evolution of chlorine gas at one of electrodes (atomic mass: \(\mathrm{Na}=23, \mathrm{Hg}=200 ; 1\) faraday \(=96500\) coulombs).
Question:
The total number of moles of chlorine gas evolved is

Which of the given statement(s) about \(\mathbf{N}, \mathbf{O}, \mathbf{P}\) and \(\mathbf{Q}\) with respect to \(\mathbf{M}\) is (are) correct?

The number of aldol reaction(s) that occurs in the given transformation is :

A reversible cyclic process for an ideal gas is shown below. Here, $P,V,\mathrm{a}\mathrm{n}\mathrm{d}T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q,w,H\mathrm{a}\mathrm{n}\mathrm{d}U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)

Match the specified conditions in solids listed in Column I with their properties in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

Column I	Column II
A. Simple cubic and face-centered cubic	p. Have these cell parameters \(a=b=c \text { and } \alpha=\beta=\gamma\)
B. Cubic and rhombohedral	q. Are two crystal systems
C. Cubic and tetragonal	r. Have only two crystallographic angles of \(90^{\circ}\)
D. Hexagonal and monoclinic	s. Belong to same crystal system

Let \(O(0,0), P(3,4)\) and \(Q(6,0)\) be the vertices of the \(\triangle O P Q\). The point \(R\) inside the \(\triangle O P Q\) is such that the \(\triangle O P R, \triangle P Q R, \triangle O Q R\) are of equal area. The coordinates of \(R\) are

Let \(S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.\) and \(\left.3 y+\sqrt{8} x \leq 5 \sqrt{8}\right\}\). If the area of the region \(S\) is \(\alpha \sqrt{2}\), then \(\alpha\) is equal to

The value of  $I={\displaystyle \sum }_{k=1}^{98}\underset{k}{\overset{k+1}{{\displaystyle \int }}}\frac{k+1}{x(x+1)}dx,$ then

Let $f:\left(0,1\right)\to \mathrm{ℝ}$ be the function defined as $f\left(x\right)=\left[4x\right]{\left(x-\frac{1}{4}\right)}^2\left(x-\frac{1}{2}\right)$, where $\left[x\right]$ denotes the greatest integer less than or equal to $x$. Then which of the following is(are) true?

Considering the following reaction sequence,

the correct option(s) is(are)

In a $∆XYZ$ let $x,y,z$,  be the lengths of sides opposite to the angles, $X, Y, Z$, respectively and $2s=x+y+z.$ If $\frac{s-x}{4}=\frac{s-y}{3}=\frac{s-z}{2}$ and area of incircle of the triangle XYZ is $\frac{8\pi }{3},$ then