List of practice Questions

Two media A and B are separated by a plane boundary surface. The speed of light in medium A and B are 2 x 108 m/s and 2.5 x 108 m/s respectively. The critical angle for which a ray of light going from A to B will have total internal reflection is A
An object of mass \(10 \, \text{kg}\) is released from rest in a liquid. If the object moves a distance of \(2 \, \text{m}\) while sinking in a time duration of \(1 \, \text{s}\), then the mass of the liquid displaced by the submerged object is (Given: Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \))
A liquid of density \( \rho \) flows steadily. At point 1, area = \( 2A \), speed = \( \sqrt{2}\ \text{m/s} \); at point 2, area = \( A \), height difference = 10 cm, pressure difference = 100 N/m\(^2\). Find \( \rho \).
Aliquidofdensityρflowssteadily
Which of the following methods are not used to refine any metal?
  1. Liquation
  2. Calcination
  3. Electrolysis
  4. Leaching
  5. Distillation
Choose the correct answer from the options given below :
Write the classification of aliphatic ketones with example. What is the action of sodium hypoiodite on acetone?
Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.
An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm–3. The number of atoms present in 180 g of the element is ______× 1023. (Nearest integer)
A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10–5 Nsm–2 and its density is negligible as compared to that of water (106 gm–3). Terminal velocity of the water drop is
(Take acceleration due to gravity = 10 ms–2)

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:

Fig. 
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
Two point charges A and B of magnitude +8 × 10–6 C and –8 × 10–6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 104 NC–1. The distance ‘d’ between the point charges A and B is:
A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is 2.0 mm2 and the resistivity of copper is 1.7 × 10–8 Ω, the force experienced by moving electron in the wire is ___ × 10–23N.
(Charge on electron = 1.6 × 10–19C)
While performing a thermodynamics experiment, a student made the following observations.
HCl + NaOH \(\rightarrow\) NaCl + H2O; ΔH = – 57.3 kJ mol–1
CH3COOH + NaOH \(\rightarrow\) CH3COONa + H2O; ΔH = –55.3 kJ mol–1
The enthalpy of ionization of CH3COOH, as calculated by the student, is ______ kJ mol–1. [nearest integer]
Given below are two statements.
Statement I: Iron (III) catalyst, acidified \(K_2Cr_2O_7\) and neutral \(KMnO_4\) have the ability to oxidise \(I^–\) to \(I_2\) independently.
Statement II: Manganate ion is paramagnetic in nature and involves \(pπ – pπ\) bonding.
In the light of the above statements, choose the correct answer from the options given below.
A long cylindrical volume contains a uniformly distributed charge of density ρ cm–3.
 The electric field inside the cylindrical volume at a distance \(x=\frac{2ε_0}{ρ} m\) from its axis is _______ Vm–1
Fig.
A mass 0.9 kg, attached a horizontal spring, executes SHM with an amplitude A1. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude A2. If the ratio A1/A2 is α/(α – 1), then the value of α will be _____.
A sample of 4.5 mg of an unknown monohydric alcohol, R–OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is___ g/mol. [Nearest integer]
In Young’s double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:
\(\lim_{x\rightarrow \frac{\pi}{4}}\) 8\(\sqrt2\)−(cosx+sinx)\(^{\frac{7}{\sqrt2}}\)−\(\sqrt2\)sin2x is equal to
A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___ m distance.
A square aluminium (shear modulus is 25 × 109 Nm–2) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of 18.0 × 104 N. The lower edge is riveted to the floor. The displacement of the upper edge is ______μm.

Following statements related to radioactivity are given below:

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).
(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.
Choose the most appropriate answer from the options given below:

A pulley of radius 1.5 m is rotated about its axis by a force F = (12t – 3t2) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m2, the number of rotations made by the pulley before its direction of motion is reversed, will be K/π. The value of K is ________.
A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x is _______.

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as
\(v_2=\frac{n}{m^2}v_1\) and \(a_2=\frac{a_1}{mn}\)
respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :