Identify the crystal system in which primitive unit cell has edge lengths \(a=b=200 \mathrm{pm}\) and \(\mathrm{c}=300 \mathrm{pm}\) and all axial angles are same

A body centred cubic lattice is made up of two different types of atoms X and Y. Atom X occupies the body centre and atoms \(\mathrm{Y}\) occupy the corner positions. One of the corners is left unoccupied per unit cell. The empirical formula of it is

Identify the alkyne in the following sequence of reactions,

Match the following


The correct answer is

Which of the following carbonyl compounds will exhibit enolization?
(i) 
(ii)
(iii) 
(iv) 
(v) 

With reference to the redox properties of hydrogen peroxide \(\left(\mathrm{H}_2 \mathrm{O}_2\right)\), which of these reactions are feasible? (i) \(2 \mathrm{Fe}^{2+} 2 \mathrm{H}^{+}+\mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{Fe}^{3+}+2 \mathrm{H}_2 \mathrm{O}\) (ii) \(2 \mathrm{MnO}_4^{-}+6 \mathrm{H}^{+}+5 \mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{Mn}^{2+}\) \(+8 \mathrm{H}_2 \mathrm{O}+5 \mathrm{O}_2\) (iii) \(2 \mathrm{Fe}^{2+}+\mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{Fe}^{3+}+2 \mathrm{OH}^{-}\) (iv)\(2 \mathrm{MnO}_4^{-}+3 \mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{MnO}_2+2 \mathrm{H}_2 \mathrm{O}\) \(+3 \mathrm{O}_2+2 \mathrm{OH}^{-}\)

Statement I: Aldehyde on reaction with \(\mathrm{HCN}\) gives Cyanohydrin. Statement II: Cyanohydrin is a compound which consists of hydroxy and cyano groups on the same carbon. Choose the correct answer from the following with reference to above statements.

If a normal chord of a parabola \(y^2=4 a x\) subtends a right angle at the origin, then the slope of that normal chord is

Gravitational forces operate among which of the following?

The focal distance of a point \((5,5)\) on the parabola \(x^2-2 x-4 y+5=0\) is

\(\int \frac{d x}{x\left(x^4+1\right)}=\)

For the reaction \(\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g)\), the correct relation between degree of dissociation \((\alpha)\) of \(\mathrm{N}_2 \mathrm{O}_4(g)\) and equilibrium constant, \(\mathrm{K}_{\mathrm{p}}\) is \((\mathrm{P}=\) total pressure of mixture \()\)

Suppose \(\overrightarrow{\mathbf{a}}=\lambda \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\lambda \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \lambda \hat{\mathbf{k}}\). If the angle between \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\) is greater than \(90^{\circ}\), then \(\lambda\) satisfies the inequality