Exercise 1.1 — Sets

1. 1.1.12 marksNCERT Class 11 Mathematics, Sets, Reprint 2026-27

   Which of the following are sets? Justify your answer: (i) months of the year beginning with J, (ii) ten most talented writers of India, (iii) eleven best cricket batsmen of the world, (iv) all boys in your class, (v) natural numbers less than 100, (vi) novels written by Munshi Prem Chand, (vii) all even integers, (viii) questions in this chapter, (ix) most dangerous animals of the world.

   Hint. A collection is a set only if membership can be decided without any dispute -- 'well-defined' rules out anything based on opinion or ranking.

   (i), (iv), (v), (vi), (vii), (viii) are sets, since anyone checking would agree on exactly which objects qualify. (ii), (iii), (ix) are not sets, since 'most talented', 'best', and 'most dangerous' are matters of opinion -- different people would list different members.

   ✦ Working through each part gives: sets: (i),(iv),(v),(vi),(vii),(viii). Not sets: (ii),(iii),(ix), since they rely on subjective judgement.

2. 1.1.21 markNCERT Class 11 Mathematics, Sets, Reprint 2026-27

   Let A = {1, 2, 3, 4, 5, 6}. Insert the correct symbol, epsilon or not-epsilon, in each blank: (i) 5 . A (ii) 8 . A (iii) 0 . A (iv) 4 . A (v) 2 . A (vi) 10 . A.

   Hint. Check each number directly against the listed elements of A.

   A = {1,2,3,4,5,6}. 5 is listed, 8 is not, 0 is not, 4 is listed, 2 is listed, 10 is not.

   ✦ Working through each part gives: (i) in (ii) not in (iii) not in (iv) in (v) in (vi) not in.

3. 1.1.33 marksNCERT Class 11 Mathematics, Sets, Reprint 2026-27

   Write the following sets in roster form: (i) A = {x : x is an integer and -3 <= x < 7}, (ii) B = {x : x is a natural number less than 6}, (iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}, (iv) D = {x : x is a prime number which is a divisor of 60}, (v) E = the set of letters in TRIGONOMETRY, (vi) F = the set of letters in BETTER.

   Hint. List every qualifying element once, in any order, inside braces -- for D, factorise 60 first.

   (i) integers from -3 up to but not including 7. (ii) natural numbers 1 through 5. (iii) two-digit numbers whose digits sum to 8. (iv) 60 = 2^2 x 3 x 5, so its prime divisors are 2, 3, 5. (v) each distinct letter of TRIGONOMETRY, written once. (vi) each distinct letter of BETTER, written once.

   ✦ Working through each part gives: (i) A={-3,-2,-1,0,1,2,3,4,5,6} (ii) B={1,2,3,4,5} (iii) C={17,26,35,44,53,62,71,80} (iv) D={2,3,5} (v) E={T,R,I,G,O,N,M,E,Y} (vi) F={B,E,T,R}.

4. 1.1.42 marksNCERT Class 11 Mathematics, Sets, Reprint 2026-27

   Write the following sets in set-builder form: (i) {3,6,9,12}, (ii) {2,4,8,16,32}, (iii) {5,25,125,625}, (iv) {2,4,6,...}, (v) {1,4,9,...,100}.

   Hint. Look for the pattern connecting position in the list to the value -- multiples, powers, or squares.

   (i) multiples of 3 up to 12. (ii) powers of 2 from 2^1 to 2^5. (iii) powers of 5 from 5^1 to 5^4. (iv) every even natural number, unending. (v) perfect squares of 1 through 10.

   ✦ Working through each part gives: (i) {x:x=3n, n in N, n<=4} (ii) {x:x=2^n, n in N, 1<=n<=5} (iii) {x:x=5^n, n in N, 1<=n<=4} (iv) {x:x is an even natural number} (v) {x:x=n^2, n in N, 1<=n<=10}.

5. 1.1.53 marksNCERT Class 11 Mathematics, Sets, Reprint 2026-27

   List all the elements of: (i) A = odd natural numbers, (ii) B = {x : x is an integer, -1/2 < x < 9/2}, (iii) C = {x : x is an integer, x^2 <= 4}, (iv) D = letters in LOYAL, (v) E = months of a year not having 31 days, (vi) F = consonants in the English alphabet preceding k.

   Hint. For (ii) and (iii), first find which integers actually satisfy the inequality before listing them.

   (i) odd naturals continue without end. (ii) integers strictly between -0.5 and 4.5 are 0,1,2,3,4. (iii) integers whose square is at most 4 are -2,-1,0,1,2. (iv) distinct letters of LOYAL. (v) months with 28,29 or 30 days. (vi) letters before k, excluding vowels a and e.

   ✦ Working through each part gives: (i) F={1,3,5,7,...} (ii) B={0,1,2,3,4} (iii) C={-2,-1,0,1,2} (iv) D={L,O,Y,A} (v) E={February,April,June,September,November} (vi) F={b,c,d,f,g,h,j}.

6. 1.1.62 marksNCERT Class 11 Mathematics, Sets, Reprint 2026-27

   Match each roster-form set on the left with its set-builder description on the right: (i) {1,2,3,6} (ii) {2,3} (iii) {M,A,T,H,E,I,C,S} (iv) {1,3,5,7,9}, against (a) primes dividing 6, (b) odd naturals under 10, (c) naturals dividing 6, (d) letters of MATHEMATICS.

   Hint. Check each roster set against every description until exactly one fits.

   {1,2,3,6} are exactly the divisors of 6, matching (c). {2,3} are exactly the prime divisors of 6, matching (a). {M,A,T,H,E,I,C,S} are the distinct letters of MATHEMATICS, matching (d). {1,3,5,7,9} are the odd naturals below 10, matching (b).

   ✦ Working through each part gives: (i)-(c), (ii)-(a), (iii)-(d), (iv)-(b).

Solutions written by the tuition.in editorial team and checked against the NCERT Class 11 Mathematics textbook, Reprint 2026-27 (kemh101.pdf) — five numbered exercises (1.1-1.5, 39 questions total) plus the chapter's Miscellaneous Exercise (10 questions); every question solved directly from the given sets rather than from memory, including the multi-part true/false and subset-vs-membership questions in Exercise 1.3 Q3 and the Miscellaneous Exercise Q2, which require care to avoid conflating 'element of' with 'subset of'. Questions are referenced from the NCERT textbook for identification.