List of practice Questions

Look at several examples of rational numbers in the form \(\frac{p}{q}\) (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of \(\frac{1}{17}\)? Perform the division to check your answer
Express 0.99999 .... in the form \(\frac{p}{q}\) . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

You know that \(\frac{1}{7}\) = 0142857_ . . Can you predict what the decimal expansions of \(\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}\) are, without actually doing the long division? If so, how? [Hint : Study the remainders while finding the value of 1/7 carefully.]

0.3780 g of an organic chloro compound gave 0.5740 g of silver chloride in Carius estimation. Calculate the percentage of chlorine present in the compound.
Find the capacity in liters of a conical vessel with
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm
A sample of 0.50 g of an organic compound was treated according to Kjeldahl’s method. The ammonia evolved was absorbed in 50 ml of 0.5 M H2SO4. The residual acid required 60 mL of 0.5 M solution of NaOH for neutralization. Find the percentage composition of nitrogen in the compound.
Explain why alkyl groups act as electron donors when attached to a \(\pi\) system.
Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm 
(ii) radius 3.5 cm, height 12 cm
Identify the functional groups in the following compounds.
Listed Compounds with Functioning Groups
A right circular cylinder just encloses a sphere of radius r (see given figure). Find
right circular cylinder
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).
Show how √5 can be represented on the number line.
Give condensed and bond line structural formulas and identify the functional group(s) present, if any, for, 
  1. 2,2,4-Trimethylpentane, 
  2. 2-Hydroxy-1,2,3-propanetricarboxylic acid, 
  3.  Hexanedial.
Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

State whether the following statements are true or false. Justify your answers. 

(i) Every irrational number is a real number. 

(ii) Every point on the number line is of the form √m , where m is a natural number. 

(iii) Every real number is an irrational number

State whether the following statements are true or false. Give reasons for your answers. 

(i) Every natural number is a whole number. 

(ii) Every integer is a whole number. 

(iii) Every rational number is a whole number

Find five rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\).
An organic compound contains 69% carbon and 4.8% hydrogen, the remainder being oxygen. Calculate the masses of carbon dioxide and water produced when 0.20 g of this substance is subjected to complete combustion.
Find six rational numbers between 3 and 4.
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
The reaction, \(CO(g) + 3H_2(g) \leftrightarrow CH_4(g) + H_2O(g)\) is at equilibrium at 1300 K in a 1L flask. It also contain 0.30 mol of CO, 0.10 mol of \(H_2\) and 0.02 mol of \(H_2O\) and an unknown amount of \(CH_4\) in the flask. Determine the concentration of \(CH_4\) in the mixture. The equilibrium constant, \(K_c\) for the reaction at the given temperature is 3.90.
Why is it necessary to use acetic acid and not sulphuric acid for acidification of sodium extract for testing sulphur by lead acetate test?
Find the radius of a sphere whose surface area is 154 cm2
Why is a solution of potassium hydroxide used to absorb carbon dioxide evolved during the estimation of carbon present in an organic compound?
The value of \(K_c\) for the reaction  \(3O_2 \,(g) \leftrightarrow 2O_3 \,(g)\) is \(2.0 ×10^{–50}\) at 25°C. If the equilibrium concentration of \(O_2\) in air at 25°C is \(1.6 ×10^{–2}\), what is the concentration of \(O_3\)?