Q1. Which of the following are sets? Justify our answer.

(i) The collection of all months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.
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Q2.  If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

Q3. Find the radian measures corresponding to the following degree measures:
(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°.

Q4. Prove the following by using the principle of mathematical induction for all n ∈ N:

Q5. Express of the complex number given in the form a + ib.
(5i) (-3/5i)

Q6. Solve 24x < 100, when

(i) x is a natural number.
(ii) x is an integer.

Q7. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) Repetition of the digits is allowed?
(ii) Repetition of the digits is not allowed?

Q8. Expand the expressions.
(1 – 2x)5

Q9. Write the first five terms of the sequences, whose nth terms are:
an = n (n + 2) .

Q10. Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.