List of practice Questions

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by:

From the v - t graph shown, the ratio of distance to displacement in 25 s of motion is:

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

The free space inside a current carrying toroid is filled with a material of susceptibility \( 2 \times 10^3 \). The percentage increase in the value of magnetic field inside the toroid will be:

The critical angle for a denser refractive index is 45°. The speed of light in water medium is \( 3 \times 10^8 \) m/s. The speed of light in the denser medium is:

Given below are two statements:
Statements 1: Astronomical unit (AU), Parsec (pc) and Light year (ly) are units for measuring astronomical distances.
Statement 2: The light of the above distances, choose the most appropriate answer from the options given below:

1 kg of water at 100°C is converted into steam at 100°C by boiling at atmospheric pressure. The volume of water changes from \(1.00 \times 10^{-3}\, \text{m}^3\) as a liquid to \(1.671 \times 10^{-3}\, \text{m}^3\) as steam. The change in internal energy of the system during the process will be:

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be:

The magnetic field B crossing normally a square metallic plate of area \( 4 \, \text{m}^2 \) is changing with time as shown in the figure. The magnitude of induced emf in the plate during \( t = 2 \, \text{s} \) to \( t = 4 \, \text{s} \) is _______ mV.

The length of a wire becomes \( l_1 \) and \( l_2 \) when 100 N and 120 N tensions are applied respectively. If \( l_1 = 11 \, \text{l}_0 \), the natural length of the wire will be \( \frac{1}{x} \, l_1 \). Here the value of \( x \) is _____

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is \( x \times 10^{15} \, \text{Hz} \). The value of \( x \) is_______

A force \( \mathbf{F} = (2 + 3x) \hat{i})\) acts on a particle in the \( x \)-direction where \( F \) is in newton and \( x \) is in meter. The work done by this force during a displacement from \( x = 0 \) to \( x = 4 \, \text{m} \) is _____ J.

As shown in the figure, a configuration of two equal point charges (q₀ = + 2 \(\mu\)C) is placed on an inclined plane. Mass of each point charge is 20g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \( h = x \times 10^{-3} \, \text{m} \). The value of \( x \) is _____

A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular speed of 10 rad/s. If the moment of inertia of the sphere about its tangent is \( x \times 10^2 \) times its angular momentum about the diameter. Then the value of \( x \) will be_____

The equation of wave is given by \( Y = 10^2 \sin 2 \pi \left( (60t - 0.5x + \frac{\pi}{4}) \right) \) where \( x \) and \( Y \) are in m and t in s. The speed of the wave is _____ km h\(^{-1}\).

A projectile fired at \(30^{\circ}\) to the ground is observed to be at the same height at time 3s and 5s after projection, during its flight. The speed of projection of the projectile is_____ ms\(^{-1}\).

Which of the following complex has a possibility to exist as meridional isomer?

L-isomer of tetrose X (\(C_4H_8O_4\)) gives positive Schiff’s test and has two chiral carbons. On acetylation, ‘X’ yields triacetate. ‘X’ undergoes following reactions

Chiral compound ‘X’ is

Match list I with list II:

List I		List II
A	K	I	Thermonuclear reactions
B	KCl	II	Fertilizer
C	KOH	III	Sodium potassium pump
D	Li	IV	Absorbent of CO2

Choose the correct answer from the options given below:

For compound having the formula GaCl\(_3\), the correct option from the following is:

Thin layer chromatography of a mixture shows the following observation:

The correct order of elution in the silica gel column chromatography is .

When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a dark brown ferric ion was formed when treated with ferric chloride. It gave deep red colour which disappeared on boiling and a brown red ppt was formed. The mixture contains:

The polymer X consists of linear molecules and is closely packed. It is prepared in the presence of triethylaluminium and titanium tetrachloride under low pressure. The polymer X is:

Match list I with list II:

List I	Species	List II	Geometry/ Shape
A	H3 O+	I	Tetrahedral
B	Acetylide anion	II	Linera
C	NH4 +	III	Pyramidal
D	ClO2–	IV	Bent

Choose correct answer from the options given below:

Given below are two statements:
Statement I: Methane and steam passed over a heated Ni catalyst produces hydrogen gas.
Statement II: Sodium nitrate reacts with NH\(_4\)Cl to give H\(_2\)O and NaCl.