1.

For a certain reaction at 300 K, \( K = 10 \), then \( \Delta G^\circ \) for the same reaction is \[- \, \_ \times 10^{-1} \, \text{kJ mol}^{-1}.\](Given \( R = 8.314 \, \text{JK}^{-1} \text{mol}^{-1} \))

2.

Solubility of calcium phosphate (molecular mass, \( M \)) in water is \( W_g \) per 100 mL at \( 25^\circ C \). Its solubility product at \( 25^\circ C \) will be approximately:

• \( 10^7 \left( \frac{W}{M} \right)^3 \)
• \( 10^7 \left( \frac{W}{M} \right)^5 \)
• \( 10^3 \left( \frac{W}{M} \right)^5 \)
• \( 10^5 \left( \frac{W}{M} \right)^5 \)

3.

10 mL of gaseous hydrocarbon on combustion gives 40 mL of CO\(_2\)(g) and 50 mL of water vapour. The total number of carbon and hydrogen atoms in the hydrocarbon is ______ .

4.

Match List - I with List - II

Choose the correct answer from the options given below :

• (A)-(I), (B), (II), (C)-(III), (D)-(IV)
• (A)-(III), (B)-(I), (C)-(IV), (D)-( II)
• (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
• (A)-( II), (B)-(III), (C)-(I), (D)-(IV)

5.

The number of tripeptides formed by three different amino acids using each amino acid once is ______.

6.

Let \[\vec{a} = \hat{i} + \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} - 8\hat{j} + 2\hat{k}, \quad \text{and} \quad \vec{c} = 4\hat{i} + c_2\hat{j} + c_3\hat{k} \]be three vectors such that \[\vec{b} \times \vec{a} = \vec{c} \times \vec{a}.\]If the angle between the vector $\vec{c}$ and the vector $3\hat{i} + 4\hat{j} + \hat{k}$ is $\theta$, then the greatest integer less than or equal to $\tan^2 \theta$ is: