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JEE Main 2024 (Online) 4th April Morning ShiftNumericalMedium📈 Topic in 9% papers+4

Ques. 1JEE Main 2024, 4 April (Morning Shift)

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let m and n respectively be the least and the most number of students who studied all the three subjects. Then m+n is equal to .

Answer

Solution

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Let x = number who studied all three

n(M )=220-10=210

210=n(M)+n(P)+n(C)-(40+30+50)+x

n(M)+n(P)+n(C)=330-x

125+85+75 n(M)+n(P)+n(C) 130+95+90

285 330-x 315 15 x 45

Also Physics and Chemistry only =30-x 0 x 30

15 x 30 m=15, n=30 m+n=45

Answer: 45

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Ques. 2JEE Main 2024, 30 January (Morning Shift)

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is .

Ques. 3JEE Main 2024, 29 January (Evening Shift)

Let the set C= \(x, y) x2-2y=2023, x, y N \. Then (x, y) C(x+y) is equal to .

Ques. 4JEE Main 2024, 27 January (Evening Shift)

Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B. Then the distance of the point P(m,n) from the point Q(-2,-3) is :

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