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The students of a class are offered three languages (Hindi, English and French). 15 students learn all the three languages whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11. How many students learn at least one languages?

In a class , 22 studets offered Mathematics , 18 students offered Chemistry and 24 students offered Physics . All of them have to offer atleast one of these . 11 are in both Mathematics and Chemistry ,13 in Chemistry and Physics and 14 in Mathematics and Physics and 7 have offered all the three subjects Find : (i) how many students are there in the class ? (ii) how many students offered only Mathematics ?

The Students of a class are offered three language (Hindi. English and French). 15 students learn all the three language whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11. How many students learn at least one language?

In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (iii) How many took exactly one of the three subjects.