List of practice Questions

Show that for any sets A and B, \(A = (A ∩ B) ∪ (A – B)\) and \(A ∪ (B – A) = (A ∪ B)\)
Using properties of sets show that (i) \(A ∪ (A ∩ B) = A \) (ii) \(A ∩ (A ∪ B) = A.\)

How many neutrons and protons are there in the following nuclei? \(_{6}^{13}\textrm{C}\), \(_{8}^{16}\textrm{O}\), \(_{12}^{24}\textrm{Mg}\), \(_{26}^{56}\textrm{Fe}\), \(_{38}^{88}\textrm{Sr}\).

Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A) 
(i) Z = 17, A = 35
(ii) Z = 92, A = 233
(iii) Z = 4, A = 9

Calculate the molarity of a solution of ethanol in water, in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

Draw the Lewis structures for the following molecules and ions: \(H_2S\), \(SiCl_4\), \(BeF_2\), \(CO_3^{2-}\) , \(HCOOH\)

Match the following (column I with column II) Column I Column II (a) Chlamydomonas (i) Moss (b) Cycas (ii) Pteridophyte (c) Selaginella (iii) Algae (d) Sphagnum (iv) Gymnosperm

Find the energy of each of the photons which (i) corresponds to light of frequency 3×1015 Hz. (ii) have a wavelength of 0.50 Å

What will be the mass of one \(^{12}C\) atom in g?
How many significant figures should be present in the answer of the following calculations?
  1. \(\frac {0.02856 × 298.15 × 0.112}{0.5785}\)
  2. \(5 × 5.364\)
  3. \(0.0125 + 0.7864 + 0.0215\)
Write the favourable factors for the formation of ionic bond.
Look at the graphs (a) to (d) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle.
 
Graph a to d possibly representing one-dimensional motion of a particle
What is the SI unit of mass? How is it defined?
A 25 watt bulb emits monochromatic yellow light of wavelength of 0.57µm. Calculate the rate of emission of quanta per second.
Use the data given in the following table to calculate the molar mass of naturally occuring argon isotopes:
IsotopeIsotopic molar massAbundance
36Ar35.96755 g mol–1 0.337% 
38Ar37.96272 g mol–1 0.063%
40Ar 39.9624 g mol–1 99.600% 
What do you mean by significant figures?
Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below:
\(1\text{Pa} = 1\text{N m}^{–2} \)
If mass of air at sea level is \(1034\, \text{g cm}^{–2}\), calculate the pressure in pascal.
How do you express the bond strength in terms of bond order?
Figure 2.11shows the x-t plot of one dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t >0 ? If not, suggest a suitable physical context for this graph.
x-t plot of one dimensional motion of a particle
Figure 2.11
Express the following in the scientific notation: 
(i) 0.0048 
(ii) 234,000 
(iii) 8008 
(iv) 500.0 
(v) 6.0012
How many significant figures are present in the following? 
(i) 0.0025 
(ii) 208 
(iii) 5005 
(iv) 126,000 
(v) 500.0 
(vi) 2.0034
If the density of methanol is \(0.793\, \text{kg L}^{–1}\), what is its volume needed for making 2.5 L of its 0.25 M solution?
In three moles of ethane \((\text{C}_2\text{H}_6)\), calculate the following: 
(i) Number of moles of carbon atoms. 
(ii) Number of moles of hydrogen atoms. 
(iii) Number of molecules of ethane.
A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range : α\(_{steel}\)= 1.20 × 10\(^{-5}\) K\(^{-1}\).
Figure 2.15 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest ? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at the points A, B, C and D ?
speed-time graph of a particle in motion along a constant direction