CBSE Class 11 Mathematics Set Theory Assignment Set 01

Assertion-Reasoning MCQs

Directions Each of these questions contains two statements 
Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of the which is the correct answer. You have to select one of the codes (a), (b), (c) and
(d) given below.
(a) A is true, R is true; R is a correct explanation of A.
(b) A is true, R is true; R is not a correct explanation of A.
(c) A is true; R is false.
(d) A is false; R is true.

Question. Assertion (A) ‘The collection of all natural numbers less than 100’ is a set.
Reason (R) A set is a well-defined collection of the distinct objects.
Answer : A

Question. Assertion (A) The set D = {x : x is a prime number which is a divisor of 60} in roster form is {1, 2, 3, 4, 5}.
Reason (R) The set E = the set of all letters in the word ‘TRIGONOMETRY’, in the roster form is {T, R, I, G, O, N, M, E, Y}.
Answer : D

Question. Assertion (A) The set {1, 4, 9, ... 100} in the set-builder form is {x : x = n 2 , where n ÎN and 1 ≤ n ≤ 10}.
Reason (R) In roster form, the order in which the elements are listed is, immaterial.
Answer : B

Question. Assertion (A) The set {x : x is a month of a year not having 31 days} in roster form is {February, April, June, September, November}.
Reason (R) The set F = {x : x is a consonant in the English alphabet which precedes k } in roster form is F = {b, c , d, f , g , h, j }.
Answer : B

Question. Assertion (A) The set A = {x : x is an even prime number greater than 2} is the empty set.
Reason (R) The set B = {x : x² = 4, x is odd} is not an empty set.
Answer : C

Question. Assertion (A) The set A = {a, b, c , d, e, g } is finite set.
Reason (R) The set B = {men living presently in different parts of the world} is finite set.
Answer : B

Question. Assertion (A) The set of positive integers greater than 100 is infinite.
Reason (R) The set of prime numbers less than 99 is finite.
Answer : B

Case Based MCQs

In a library, 25 students read physics, chemistry and mathematics books. It was found that 15 students read mathematics, 12 students read physics while 11 students read chemistry. 5 students read bothmathematics and chemistry, 9 students read physics and mathematics. 4 students read physics and chemistry and 3 students read all three subject books.

Based on the above information, answer the following questions.

Question. The number of students who reading only chemistry is
(a) 5
(b) 4
(c) 2
(d) 1
Answer : A

Question. The number of students who reading only mathematics is
(a) 4
(b) 3
(c) 5
(d) 11
Answer : A

Question. The number of students who reading only one of the subjects is
(a) 5
(b) 8
(c) 11
(d) 6
Answer : C

Question. The number of students who reading atleast one of the subject is
(a) 20
(b) 22
(c) 23
(d) 21
Answer : C

Question. The number of students who reading none of the subject is
(a) 2
(b) 4
(c) 3
(d) 5
Answer : A

In an University, out of 100 students 15 students offered Mathematics only, 12 students offered Statistics only, 8 students offered only Physics, 40 students offered Physics and Mathematics, 20 students offered Physics and Statistics, 10 students offered Mathematics and Statistics, 65 students offered Physics.
Based on the above information answer the following questions

Question. The number of students who offered all the three subjects is
(a) 4
(b) 3
(c) 2
(d) 5
Answer : B

Question. The number of students who offered Mathematics is
(a) 62
(b) 65
(c) 55
(d) 60
Answer : A

Question. The number of students who offered statistics is
(a) 31
(b) 35
(c) 39
(d) 34
Answer : C

Question. The number of students who offered mathematics and statistics but not physics is
(a) 7
(b) 6
(c) 5
(d) 4
Answer : A

Question. The number of students who did not offer any of the above three subjects is
(a) 4
(b) 1
(c) 5
(d) 3
Answer : B