List of practice Questions

The equation of projectile motion is given by $ y = 3x - 0.8x^2 $. The time of flight of the projectile is (Acceleration due to gravity $ g = 10 $ m/s²):

A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $ g = 10 $ ms$^{-2}$):

The average power generated by a 90 kg mountain climber who climbs a summit of height 600 m in 90 minutes is (Acceleration due to gravity $ g = 10 $ m/s$^2$):

A boy weighing 50 kg finished a long jump at a distance of 8 m. Considering that he moved along a parabolic path and his angle of jump is $ 45^\circ $, his initial kinetic energy is:

A uniform rod of length $ 2L $ is placed with one end in contact with the earth and is then inclined at an angle $ \alpha $ to the horizontal and allowed to fall without slipping at the contact point. When it becomes horizontal, its angular velocity will be:

Two simple harmonic motions are represented by $y_1 = 5 \left[ \sin 2\pi t + \sqrt{3} \cos 2\pi t \right] $ and $y_2 = 5 \sin \left[ 2\pi t + \frac{\pi}{4} \right] $. The ratio of their amplitudes is:

When a mass $ m $ is connected individually to the springs $ s_1 $ and $ s_2 $, the oscillation frequencies are $ v_1 $ and $ v_2 $. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be:

A satellite moving around the Earth in a circular orbit has kinetic energy $ E $. Then, the minimum amount of energy to be added so that it escapes from the Earth is:

The elongation of a copper wire of cross-sectional area $3.5 \text{ mm}^2$, in the figure shown, is $$ Y_{\text{copper}} = 10 \times 10^{10} \, \text{Nm}^{-2} \quad \text{and} \quad g = 10 \, \text{m/s}^2 $$

‘X’ is a protecting colloid. The following data is obtained for preventing the coagulation of 10 mL of gold sol to which 1 mL of 10% NaCl is added. What is the gold number of ‘X’?

Water is flowing in a streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $ 10 $ cm$^2$ and velocity $ 1 $ m/s is $ 2000 $ Pa, then the pressure of water at another point where the cross-sectional area is $ 5 $ cm$^2$ is:

A metal ball of mass 100 g at $ 20^\circ C $ is dropped in 200 ml of water at $ 80^\circ C $. If the resultant temperature is $ 70^\circ C $, then the ratio of specific heat of the metal to that of water is:

The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincide and Kelvin-Fahrenheit scales coincide is (approximately):

Initially the pressure of 1 mole of an ideal gas is $ 10^5 $ Nm$^2$ and its volume is 16 liters. When it is adiabatically compressed, its final volume is 2 liters. Work done on the gas is (molar specific heat at constant volume $ C_V = \frac{3R}{2} $):

An ideal gas is taken around ABCA as shown in the P-V diagram. The work done during a cycle is:

Which sol is used as an intramuscular injection?

The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is:

The reactions which occur in blast furnace at 500 – 800 K during extraction of iron from haematite are
i. $3Fe_2O_3 + CO \rightarrow 2Fe_3O_4 + CO_2$
ii. $Fe_2O_3 + 3C \rightarrow 2Fe + 3CO$
iii. $FeO + 4CO \rightarrow 3Fe + 4CO_2$
iv. $FeO + CO \rightarrow 2FeO + CO_2$

Which of the following reactions give phosphine?
i. Reaction of calcium phosphide with water
ii. Heating white phosphorus with concentrated NaOH solution in an inert atmosphere
iii. Heating red phosphorus with alkali

The vibrations of four air columns are shown below. The ratio of frequencies is:

The paramagnetic complex ion which has no unpaired electrons in $ t_{2g} $ orbitals is

Which of the following is an example for fibre?

When glucose is oxidized with nitric acid, the compound formed is

The number of essential and non-essential amino acids from the following list respectively is Given amino acids: Val, Gly, Leu, Lys, Pro, Ser