MONTHLY TEST - APRIL (2024-2025)
CLASS: XI SUB: MATHS MAX. MARKS: 25
SECTION A EACH CARRIES 3 MARKS
(i) Represent the set {x:x is a prime number which is divisor of 60} in the roster form. (ii) Represent the set {2,4,6,8,32} in the set builder form.
Write down all the subsets of {1,2,3}.
Draw appropriate venn diagram for (i) A’ B’ (ii) (A B)’
Let U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4}, B ={ 2,4,6,8) and C = { 3,4,5,6). Find A’ and (B-C)’.
If A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = (15,17}. Find (i)( A B) (B C) (ii) A ( B D)
SECTION B EACH CARRIES 5 MARKS
In a group of 65 people, 40 like cricket 10 like both cricket and tennis, How many like tennis only not cricket? How many like tennis?
In class XI there are 200 students out of which 80 have taken Mathematics, 120 have taken Economics and 90 have taken Physical Education. If 50 have taken Mathematics and Economics, 60 have taken Economics and Physical Education, 40 have taken Mathematics and Economics. If 20 students have taken all three subjects then on the basis of above information answer the following:
(1) The number of students who have taken at least one of the subjects
(a) 160 (b ) 40 (c) 290 (d) 200
(ii) The number of students who have taken at most one of the subject.
(a) 60 (b) 90 (c) 40 (d) 70
(iii) The number of students who has taken none of the subject
(a) 60 (b) 90 (c) 40 (d) 160
(iv) The number of students who have taken exactly one subject
(a) 20 (b) 50 (c) 40 (d) 70
(v) The number of students who has taken Mathematics and Economics but not Physical Education
a) 60 (b) 140 (c) 120 (d) 20
Answer key - MONTHLY TEST - APRIL (2024-2025)
CLASS: XI SUB: MATHS MAX. MARKS: 25
SECTION A EACH CARRIES 3 MARKS
(i) Represent the set {x:x is a prime number which is divisor of 60} in the roster form.
Answer: 60=2x2x3x5
A={2,3,5}
(ii) Represent the set {2,4,6,8,32} in the set builder form.
Answer : {x:x = 2n, nN and 1 n 4}
2. Write down all the subsets of {1,2,3}.
Answer : , {1}, {2}, {3}, {1,2}, {2,3}, {1,3},{1,2,3}
3. Draw appropriate venn diagram for (i) A’ B’ (ii) (A B)’
4. Let U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4}, B ={ 2,4,6,8) and C = { 3,4,5,6). Find A’ and (B-C)’.
Answer : A’ = { 5,6,7,8,9}, (B-C)’ = {1,3,4,5,6,7,9}
5. If A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = (15,17}. Find (i)( A B) (B C) (ii) A ( B D)
Answer : (i)( A B) (B C) = {7,9,11} {7,9,11,13,15} = {7,9,11}
(ii) A ( B D) = {7,9,11} U = {7,9,11}
SECTION B EACH CARRIES 5 MARKS
6. In a group of 65 people, 40 like cricket 10 like both cricket and tennis, How many like tennis only not cricket? How many like tennis?
Answer: Let C denote the set the people like cricket, and T denote the set of people who like tennis
∴n(C∪T)=65,n(C)=40,n(C∩T)=10
n(C∪T)=n(C)+n(T)−n(C∩T)
∴65=40+n(T)−10
⇒65=30+n(T)
⇒n(T)=65−30=35
Therefore, 35 people like tennis.
n(T−C)=n(T)−n(T∩C)
⇒n(T−C)=35−10=25
Thus, 25 people like only tennis.
In class XI there are 200 students out of which 80 have taken Mathematics, 120 have taken Economics and 90 have taken Physical Education. If 50 have taken Mathematics and Economics, 60 have taken Economics and Physical Education, 40 have taken Mathematics and Economics. If 20 students have taken all three subjects then on the basis of above information answer the following:
(1) The number of students who have taken at least one of the subjects
(a) 160 (b ) 40 (c) 290 (d) 200
(ii) The number of students who have taken at most one of the subject.
(a) 60 (b) 90 (c) 40 (d) 70
(iii) The number of students who has taken none of the subject
(a) 60 (b) 90 (c) 40 (d) 160
(iv) The number of students who have taken exactly one subject
(a) 20 (b) 50 (c) 40 (d) 70
(v) The number of students who has taken Mathematics and Economics but not Physical Education
a) 60 (b) 140 (c) 120 (d) 20
Answer: 1) a) 2) b 3) c) 4) b 5) d
Let 'M' represent the set of students who have taken Maths. 'E' represent the set of students who have taken Economics, 'PH' represent the set of students who have taken Physical Education.
(i) (a), at least one of the subjects = MUEUPH =10+40+20+40+30+20=160 (at least one subject mean one subject or two subjects or three subjects)
(ii) (b), at most one of the subjects = one subject or none of the subjects =10+40+40+0=90
(iii) (c), None of the subjects = 40
(iv) (b), exactly one subject =10+40+0=50
(v) (d), Mathematics and Economics but not Physical Education = (ME) – PH = 20
OR
In a survey of 800 people it was found that 21% people liked to drink tea, 26% people liked to drink coffee, 29% people liked to drink milk. If 14% people liked both tea and coffee, 12% people liked both tea and milk, 14% people liked both coffee and milk and if 8% people liked all three drinks then
(1) The number of people liked at least two drinks
(a) 44 (b) 352 (c) 800 (d) 192
(ii) The number of people liked at most two drinks
(a) 92 (b) 736 (c) 352 (d) 800
(iii) The number of people liked exactly two drinks
(a) 11 (b) 88 (c) 128 (d) 232
(iv) The number of people liked only milk
(a) 11 (b) 88 (b) 140 (d) 232
(v) The number of people liked tea or coffee but not milk
(a) 120 (b) 33 (c) 264 (d) 200
Answer: 1) d 2) b 3) c 4) b 5) a
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