A hydroxy compound (X) with molar mass 122 g \( mol^{-1} \) is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of 290 g \( mol^{-1} \). The number of hydroxyl groups present in compound (X) is :

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

In \(3 d\) series, the metal having the highest \(M ^{2+} / M\) standard electrode potential is .... .

How many different stereoisomers are possible for the given molecule?

The number of subshells associated with \(n=4\) and \(m =-2\) quantum numbers is :

An inorganic Compound \('\mathrm{X}^{\prime}\) on treatment with concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) produces brown fumes and gives dark brown ring with \(\mathrm{FeSO}_{4}\) in presence of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) Also Compound \('\mathrm{X}'\) gives precipitate \('Y',\) when its solution in dilute \(\mathrm{HCI}\) is treated with \(\mathrm{H}_{2} \mathrm{~S}\) gas. The precipitate \('Y'\) on treatment with concentrated \(\mathrm{HNO}_{3}\) followed by excess of \(\mathrm{NH}_{4} \mathrm{OH}\) further gives deep blue coloured solution, Compound \('X'\) is :

The incorrect statements regarding geometrical isomerism are :
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene shows two geometrical isomers.
(E) Trans-isomer has lower melting point than cis isomer.
Choose the correct answer from the options given below :

Water fall from a \(40\,m\) high dam at the rate of \(9 \times 10^{4}\,kg\) per \(hour\). Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of \(100\,W\) lamps, that can be lit, is (Take \(\left.g=10\,ms ^{-2}\right)\)

Let \(A=\left[\begin{array}{ccc}2 & 2+p & 2+p+q \\ 4 & 6+2 p & 8+3 p+2 q \\ 6 & 12+3 p & 20+6 p+3 q\end{array}\right]\).
If \(\operatorname{det}(\operatorname{adj}(\operatorname{adj}(3 \mathrm{~A})))=2^{\mathrm{m}} \cdot 3^{\mathrm{n}}, \mathrm{m}, \mathrm{n} \in \mathrm{N}\), then \(\mathrm{m}+\mathrm{n}\) is equal to

Let \(p_n\) denote the total number of triangles formed by joining the vertices of an \(n\)-side regular polygon. If \(p_{n+1} - p_n = 66\), then the sum of all distinct prime divisors of \(n\) is:

During the qualitative analysis of salt with cation \(y ^{2+}\), addition of a reagent \(( X )\) to alkaline solution of the salt gives a bright red precipitate. The reagent \(( X )\) and the cation \(\left( y ^{2+}\right)\) present respectively are .... .

In the following nuclear rection, \(D \stackrel{\alpha}{\longrightarrow} D _{1} \stackrel{\beta-}{\longrightarrow} D _{2} \stackrel{\alpha}{\longrightarrow} D _{3} \stackrel{\gamma}{\longrightarrow} D _{4}\) Mass number of \(D\) is \(182\) and atomic number is \(74\) . Mass number and atomic number of \(D _{4}\) respectively will be

Two point dipoles of dipole moment \({\vec P_1}\) and \({\vec P_2}\) are at a distance \(x\) from each other and  \({\vec P_1}\) || \({\vec P_2}\). The force between the dipoles is