| List i | List II | ||
|---|---|---|---|
| A. | ![]() | i | Dishwashing power |
| B. | ![]() | ii | Toothpaste |
| C. | \(C_{17}H_{35}COO^–Na^++Na_2CO_3+Rosinate\) | iii | Laundry soap |
| D. | \(CH_3(CH_2)_{16}COO(CH_2CH_2O)CH_2CH_2OH\) | iv | Hair conditional |
| List i | List II | ||
|---|---|---|---|
| A. | ![]() | iv | Hair conditional |
| B. | ![]() | ii | Toothpaste |
| C. | \(C_{17}H_{35}COO^–Na^++Na_2CO_3+Rosinate\) | iii | Laundry soap |
| D. | \(CH_3(CH_2)_{16}COO(CH_2CH_2O)CH_2CH_2OH\) | i | Dishwashing powder |
Hence, the correct option is (B): (A) –(IV) (B) – (II), (C) – (III), (D) – (I)


Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to:
A square loop of sides \( a = 1 \, {m} \) is held normally in front of a point charge \( q = 1 \, {C} \). The flux of the electric field through the shaded region is \( \frac{5}{p} \times \frac{1}{\varepsilon_0} \, {Nm}^2/{C} \), where the value of \( p \) is:
The scientific study of matter’s properties and behaviour is known as chemistry. It is a natural science that studies the elements that makeup matter, as well as the compounds, made up of atoms, molecules, and ions: their composition, structure, qualities, and behaviour, as well as the changes that occur when they mix with other things.