List of practice Questions

Write short notes on:

Neutralisation reaction

Write short notes on:
Budding

Write short notes on:
Functions of thyroxine hormone

Write balanced equation:
Barium chloride + Aluminium sulphate → Barium sulphate + Aluminium chloride

Write short notes on :
Double displacement reaction

Write short notes on :
Neutralization reaction

Explain the reason for the following:
(i) On putting a zinc rod in copper sulphate solution, its blue colour vanishes slowly.
(ii) Ionic compounds have high melting points.

Write short notes on the following:
(i) Homologous series
(ii) Versatile nature of Carbon

Write short notes on:
Addition reaction

Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]

Evaluate the integral $$ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. $$

If $|\square + 1| + (\square + 2)^2 = 0$ and $\square\square - 3\square\square = 1$, then the value of $\square$ is:

The data provided in the table were obtained from the following reaction, carried out at 273 𝐾.
𝐴 + 𝐵 → 𝐶

Initial concentration of [𝐴] 𝑚𝑜𝑙 $𝐿 ^{−1}$	Initial concentration of [𝐵] 𝑚𝑜𝑙$𝐿 ^{−1}$	Initial rate of formation of [𝐶] 𝑚𝑜𝑙 $𝐿^{−1} 𝑠 ^{−1}$
0.2	0.2	0.3
0.4	0.2	0.6
0.4	0.4	2.4

The order of the reaction with respect to 𝐴 is _________.

The coefficient of $xy^2z^3$ in the expansion of $(x - 2y + 3z)^6$ is:

A person bought an item for Rs. 1350 and spent Rs.150 towards transportation of the item. Then he sold it for Rs.1800. The profit percentage is

If \[ A = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}, \] show that $ A^2 = A $.

Find the mean for the following probability distribution:

\[ \begin{array}{|c|c|c|c|c|} \hline x_i & 0 & 1 & 2 & 3 \\ \hline p_i & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \\ \hline \end{array} \]

Find $\frac{dy}{dx}$ when \[ (\sin y)^x = (\cos x)^y. \]

Evaluate the determinant \[ \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}. \]

Evaluate: \[ (\vec{i} - 3\vec{j} + 4\vec{k}) \cdot \big[(2\vec{i} - \vec{j}) \times (\vec{j} + \vec{k})\big]. \]

Minimize \[ Z = 2x + y, \] subject to \[ 5x + 10y \le 50, \quad x + y \ge 1, \quad y \le 4, \quad x \ge 0, \quad y \ge 0. \]

In four throws, with a pair of dice, what is the probability of occurrence of doublets at least twice?

If $\vec{a} = \vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = 2\vec{i} + \vec{j} + 3\vec{k}$, then find the value of $|\vec{a} + \vec{b}|$.

Find the direction cosines of the vector $3\vec{i} - 4\vec{j} + 12\vec{k}$.

Find the value of \[ \int_0^{\pi/2} x \cos x \, dx. \]