CBSE Class 11-science Maths Counting Theorems

• in a survey 25 students it was found that 15 had taken math 12 had taken physics and 11 had taken chemistry 5 had taken math and chemistry 9 had taken math and physics 4 had taken physics and chemistry and 3 had taken all three subjects find the number of students who had physics and chemistry but not mat
• A and B are two sets such that n (A) = 4 and n(B) = 8. Find the minimum value of n(A  B).
• A survey was conducted on 110 people of Delhi. It was found that 65 people watched Hindi movie and 51 watched English movie and where as 24 watched both the movies. Find the number of people who did not watch any movie on that day.
• Let A and B be two finite disjoint sets such that n (A  B) = 400, n(A) = 250. Find n(B).
• Let A and B be two finite sets such that n(A – B) = 30, n (A  B) = 180, n(A  B) = 60, find n(B).
• Out of 600 mobile owners investigated, 500 owned Nokia hand set and 180 owned Tata hand set; 30 owned both Nokia and Tata hand sets. Is this data correct?
• In a group of 85 people, 50 like Hindi movies, 10 like both Hindi and English movies. How many like English movies and not Hindi. How many like English movies?
• In a group, students know at least one of the languages, German or French. 100 students know German and 40 know French and 10 know both German and French. If there are 20 students who know neither of the two languages, how many students are there in the group?
• A class got 48 distinctions in maths, 25 in physics and 30 in chemistry. If these went to a total of 68 students and only 5 students got distinctions in all the three subjects, how many students got distinctions in exactly two of the three subjects?
• If A and B are two sets such that    has 40 elements, A has 30 elements and B has 20 elements, how many elements does the shaded region have?

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