

Reaction:
\[\text{Aniline (C}_6\text{H}_5\text{NH}_2) + \text{CH}_3\text{COCl} \rightarrow \text{Acetanilide (C}_6\text{H}_5\text{NHCOCH}_3\text{)}\]
From stoichiometry, 93 g of aniline gives 135 g of acetanilide.
So, for 6.55 g of aniline:
\[\text{Amount of acetanilide} = \frac{135}{93} \times 6.55 = 9.5 \, \text{g}\]
In scientific notation: \( 9.5 = 95 \times 10^{-1} \, \text{g}. \)
Given below are two statements: 
Statement I: Vanillin will react with NaOH and also with Tollen’s reagent.  
 
Statement II: Vanillin will undergo self-aldol condensation very easily. 
In the light of the above statements, choose the most appropriate answer from the options given below:
Chlorobenzene to biphenyl
Match the LIST-I with LIST-II

Choose the correct answer from the options given below:
Let \( y = y(x) \) be the solution of the differential equation \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] such that \( y(0) = \frac{5}{4} \). Then \[ 12 \left( y\left( \frac{\pi}{4} \right) - e^{-2} \right) \] is equal to _____.
Let \( A \) be a \( 3 \times 3 \) real matrix such that \[ A^{2}(A - 2I) - 4(A - I) = O, \] where \( I \) and \( O \) are the identity and null matrices, respectively. 
If \[ A^{5} = \alpha A^{2} + \beta A + \gamma I, \] where \( \alpha, \beta, \gamma \) are real constants, then \( \alpha + \beta + \gamma \) is equal to:
Let \( \vec{a} = 2\hat{i} - 3\hat{j} + \hat{k} \), \( \vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k} \) and a vector \( \vec{c} \) be such that \[ (\vec{a} - \vec{c}) \times \vec{b} = -18\hat{i} - 3\hat{j} + 12\hat{k} \] and \[ \vec{a} \cdot \vec{c} = 3. \] If \( \vec{b} \times \vec{c} = \vec{d} \), then find \( |\vec{a} \cdot \vec{d}| \).