The major product of the following reaction is

The number of optically active products obtained from the complete ozonolysis of the given compound is :

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In hexagonal system of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be ' \(r\) '.
Question:
The number of atoms in this HCP unit cell is

All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

A tetrapeptide has -COOH group on alanine. This produces glycine (Gly), Valine (Val), Phenyl alanine (Phe) and Alanine (Ala) on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with -NH₂ group attached to a chiral center is 

In the reaction given below, the total number of atoms having ${\mathrm{sp}}^2$ hybridization in the major product $\mathrm{P}$ is ___.

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
Question:
\(25 \mathrm{~mL}\) of household solution was mixed with \(30 \mathrm{~mL}\) of \(0.50\) M KI and \(10 \mathrm{~mL}\) of \(4 \mathrm{~N}\) acetic acid. In the titration of the liberated iodine, \(48 \mathrm{~mL}\) of \(0.25 \mathrm{~N~} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) was used to reach the end point. The molarity of the household bleach solution is

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The hydrogen-like species \(\mathrm{Li}^{2+}\) is in a spherically symmetric state \(S_1\) with one radial node. Upon absorbing light the ion undergoes transition to a state \(S_2\). The state \(S_2\) has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Question:
The orbtial angular momentum quantum number of the state \(S_2\) is

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.

Let $f :\left[0, 4\pi \right]\to \left[0, \pi \right]$ be defined by $f\left(x\right)={\cos }^{-1}\left(\cos x\right).$ The number of points $x \in \left[0, 4\pi \right]$ satisfying the equation $f\left(x\right)=\frac{10-x}{10}$ is_________

Choose the correct statement(s) among the following.

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PV - diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

	LIST -I		LIST -II
A)	In process $I$	P)	Work done by the gas is zero
B)	In process $II$	Q)	Temperature of the gas remains unchanged
C)	In process $III$	R)	No heat is exchanged between the gas and its surroundings
D)	In process $IV$	S)	Work done by the gas is $6P_0{V}_0$

Let $\widehat{u}=u_1\widehat{i}+u_2\widehat{j}+u_3\widehat{k}$ be a unit vector in ${\mathbb{R}}^3$ and $\widehat{w}=\frac{1}{\sqrt{6}} \left(\widehat{i}+ \widehat{j}+2\widehat{k}\right).$ Given that there exists a vector $\overrightarrow{v}$ in ${\mathbb{R}}^3$ such that $\left|\widehat{u}\times \overrightarrow{v}\right|=1$ and $\widehat{w} . \left(\widehat{u}\times \overrightarrow{v}\right)=1.$ Which of the following statement(s) is (are) correct ?