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There are 175 students in a class, out of which 100 students opt Maths, 70 opt Physics and, 23 opt Physics and Chemisty, 28 opt Chemistry and Maths and 18 opt of all three subjects. Now find each of the following : No. of students who opt why only Maths (ii) No. of students who opt only Physics (iii) No. of students who opt only Chemistry (iv) No. of students who opt Physics and Chemisty but not Maths (v) No. of students who opt Maths and Physics but not Chemistry (vi) No. of students who opt only one subject (viii) No. of students who opt atleast one subject (viii) No. of student who do not opt any subject.

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A student has to choose 3 subjects out of Maths, Physics, Chemistry, Biology and Computer Science. Find the total possible number of ways of choosing.

Out of 180 students in a class 7 students failed in all the three subjects viz. Physics, Chemistry, Maths only 144 students pass in only one subject and 21 students pass in only two subjects. How many students passed in atleast two subjects?

Out of 180 students in a class 7 students failed in all the three subjects viz. Physics, Chemistry, Maths only 144 students pass in only one subject and 21 students pass in only two subjects. How many students passed in at most two subjects but atleast in one subject?

Study the following information carefully and answer the questions given below: P, Q, R, S, T, V and W are seven students of a college. Each of them has a favourite subject from Physics, Chemistry, English, Biology, History, Geography and Philosophy, not necessarily in the same order. Each of them also has a favourite Sport from Football, Cricket, Hockey, Volleyball, Badminton, Table Tennis and Basketball, not necessarily in the same order. R likes Philosophy and his favourite sport is Hockey. The one who likes Football likes English. T's favourite sport is not Badminton or Table Tennis. V does not like either History or Biology. The one whose favourite sport is Basketball does not like Physics. W likes Chemistry and his favourite sport is volleyball. S likes Geography. Q's favourite sport is Badminton. V does not like English and his favourite sport is not Basketball. P's favourite sport is Cricket. The one whose favourite sport is Badminton does not like Biology. Which subject does P like?

Study the following information carefully and answer the questions given below: P, Q, R, S, T, V and W are seven students of a college. Each of them has a favourite subject from Physics, Chemistry, English, Biology, History, Geography and Philosophy, not necessarily in the same order. Each of them also has a favourite Sport from Football, Cricket, Hockey, Volleyball, Badminton, Table Tennis and Basketball, not necessarily in the same order. R likes Philosophy and his favourite sport is Hockey. The one who likes Football likes English. T's favourite sport is not Badminton or Table Tennis. V does not like either History or Biology. The one whose favourite sport is Basketball does not like Physics. W likes Chemistry and his favourite sport is volleyball. S likes Geography. Q's favourite sport is Badminton. V does not like English and his favourite sport is not Basketball. P's favourite sport is Cricket. The one whose favourite sport is Badminton does not like Biology. Who likes History?

Study the following information carefully and answer the questions given below: P, Q, R, S, T, V and W are seven students of a college. Each of them has a favourite subject from Physics, Chemistry, English, Biology, History, Geography and Philosophy, not necessarily in the same order. Each of them also has a favourite Sport from Football, Cricket, Hockey, Volleyball, Badminton, Table Tennis and Basketball, not necessarily in the same order. R likes Philosophy and his favourite sport is Hockey. The one who likes Football likes English. T's favourite sport is not Badminton or Table Tennis. V does not like either History or Biology. The one whose favourite sport is Basketball does not like Physics. W likes Chemistry and his favourite sport is volleyball. S likes Geography. Q's favourite sport is Badminton. V does not like English and his favourite sport is not Basketball. P's favourite sport is Cricket. The one whose favourite sport is Badminton does not like Biology. What is Q's favourite sport?

Study the following information carefully and answer the questions given below: P, Q, R, S, T, V and W are seven students of a college. Each of them has a favourite subject from Physics, Chemistry, English, Biology, History, Geography and Philosophy, not necessarily in the same order. Each of them also has a favourite Sport from Football, Cricket, Hockey, Volleyball, Badminton, Table Tennis and Basketball, not necessarily in the same order. R likes Philosophy and his favourite sport is Hockey. The one who likes Football likes English. T's favourite sport is not Badminton or Table Tennis. V does not like either History or Biology. The one whose favourite sport is Basketball does not like Physics. W likes Chemistry and his favourite sport is volleyball. S likes Geography. Q's favourite sport is Badminton. V does not like English and his favourite sport is not Basketball. P's favourite sport is Cricket. The one whose favourite sport is Badminton does not like Biology. Whose favourite sport is Basketball ?