List of practice Questions

During Manmohan Singh's tenure as the Prime Minister of India (2004–2014), which of the following significant initiatives or events took place?

Who founded the Indian National Congress (INC) party?

Who was the first Chief Election Commissioner of India?

Arrange the following expressions in ascending order: \[ \sqrt{401} - \sqrt{399}, \quad \sqrt{301} - \sqrt{299}, \quad \sqrt{201} - \sqrt{199}. \]

In the following questions, you have to identify the correct statement/s.
For each of the following, find the sentence/s that are correct.

Find the odd one out:

Cricket is the national game of which country?

Find the right word for the pair: Chair: Furniture :: Shoe: ?

Who authored the famous book, Akbar-Nama?

If \( A \) and \( B \) are binomial coefficients of the 30\(^\text{th}\) and 12\(^\text{th}\) terms of the binomial expansion \( (1 + x)^{2n-1} \), and \( 2A = 5B \), then the value of \( n \) is

Consider the following reaction:
\[ \text{S(s)} + \frac{3}{2} \text{O}_2 \text{(g)} \to \text{SO}_3 \text{(g)} + 2x \text{ K} \] \[ \text{SO}_2 \text{(g)} + \frac{1}{2} \text{O}_2 \text{(g)} \to \text{SO}_3 \text{(g)} + y \text{ K} \] Calculate \( \Delta H \) for the following reaction (K):
\[ \text{S(s)} + \text{O}_2 \text{(g)} \to \text{SO}_2 \text{(g)} \]

There is a group A of 5 boys and 3 girls and another group B of 5 boys and 6 girls. How many ways can we invite 4 boys and 4 girls for a party with 5 from group A and 3 from group B?

If the acceleration due to gravity on the surface of Earth is \( g \), then the acceleration due to gravity on a planet whose diameter is \( \frac{1}{3} \) of that of Earth and same mass as that of Earth is \( g' = ng \), where \( n \) is

When ethane-1,2-diamine is progressively added to aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be:

A solid sphere and hollow sphere roll down purely equal distances on the same inclined plane (starting from rest) in time \( t_1 \) and \( t_2 \). Then

A solid sphere rolls without slipping on a horizontal plane. What is the ratio of translational kinetic energy to the rotational kinetic energy of the sphere?

The conditions and consequences that favour the \( t_{2g}^6 e_g^1 \) configuration in a metal complex are

The equation of chord of the ellipse \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \) with (3, 1) as mid-point is

Given that the arithmetic mean \( S_{12} = 57 \), \( S_{40} = 1030 \), find \( S_{30} - S_{10} \)?

In Young's Double Slit Experiment, monochromatic light of wavelength \( \lambda \) is used. The slits are separated by a distance \( d \), and the screen is placed at a distance \( D \) from the slits. If the fringe width is observed to be \( \beta \), and the distance between the slits and the screen is doubled, what will be the new fringe width?

Sulfur undergoes oxidation to form sulfur trioxide (SO$_3$) and sulfur dioxide (SO$_2$) in the following reactions:
1. \( \text{S} + \text{O}_2 \to \text{SO}_2 \)
2. \( 2\text{SO}_2 + \text{O}_2 \to 2\text{SO}_3 \)
Given that sulfur (S) is oxidized to SO$_2$, and SO$_2$ is further oxidized to SO$_3$, calculate the change in oxidation states of sulfur in both reactions.

The temperature in a city is measured to be 30°C. What is the corresponding temperature in Fahrenheit?

Two charges +7 mC and -4 mC at coordinates (-7, 0, 0) and (7, 0, 0), respectively, find the electrostatic potential energy. \[ \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2}. \]