LIST-I | LIST-II | ||
---|---|---|---|
I | \(\text{H}_2\text{O}_2\) | P | \(\text{Mg(HCO}_3\text{)}_2 + \text{Ca(OH)}_2 \rightarrow \) |
II | \(\mathrm{Mg(OH)_2}\) | Q | \(\text{BaO}_2 + \text{H}_2\text{SO}_4 \rightarrow \) |
III | \(\text{BaCl}_2\) | R | \(\text{Ca(OH)}_2 + \text{MgCl}_2 \) |
IV | \(\text{CaCO}_3\) | S | \(\text{BaO}_2 + 2\text{HCl} \rightarrow\) |
T | \(\text{Ca(HCO}_3\text{)}_2 + 2\text{Ca(OH)}_2 \rightarrow \) |
I → Q; II → P; III → S; IV → R
I → T; II → P; III → Q; IV → R
I → T; II → R; III → Q; IV → P
I → Q; II → R; III → S; IV → P
The formation of hydrogen peroxide (\( \text{H}_2\text{O}_2 \)) happens by the reaction between \( \text{BaO}_2 \) and \( \text{H}_2\text{SO}_4 \).
This corresponds to reaction Q.
The formation of magnesium hydroxide (\( \text{Mg(OH)}_2 \)) occurs when \( \text{Ca(OH)}_2 \) reacts with \( \text{MgCl}_2 \).
This corresponds to reaction R.
Barium chloride (\( \text{BaCl}_2 \)) reacts with hydrochloric acid to form barium peroxide (\( \text{BaO}_2 \)), which corresponds to reaction S.
Calcium carbonate (\( \text{CaCO}_3 \)) is formed when \( \text{Mg(HCO}_3\text{)}_2 \) reacts with \( \text{Ca(OH)}_2 \), corresponding to reaction P.
The correct matches are:
The correct option is A: I → Q; II → R; III → S; IV → P.
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.