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JEE Main 2025 (Online) 7th April Evening ShiftMCQEasy📈 Topic in 5% papers+4−1
Ques. 1JEE Main 2025, 7 April (Evening Shift)

Let A = \( , ) R R : | - 1| 4 and | - 5| 6\ and B = \( , ) R R : 16( - 2)2 + 9( - 6)2 144\. Then

  1. A B
  2. B A
  3. neither A B nor B A
  4. A B = \(x, y) : -4 x 4, -1 y 11\

Answer

(2) B A

Solution

Set A: | - 1| 4 -3 5 and | - 5| 6 -1 11.

So A is the rectangle [-3, 5] [-1, 11].

Set B: 16( - 2)2 + 9( - 6)2 144 ( - 2)29 + ( - 6)216 1

This is the region inside the ellipse with centre (2, 6), semi-axes 3 (along ) and 4 (along ).

every point of B has -1 5 and 2 10

[-1, 5] [-3, 5] and [2, 10] [-1, 11], every point of B lies in A.

B A (A is not a subset of B, e.g. (-3, -1) A but B).

Also A B = A = \(x, y) : -3 x 5, -1 y 11\, so option (4) is false.

Answer: (2)

Keep practising — Sets

Ques. 2JEE Main 2025, 4 April (Morning Shift)

Let A = \1, 6, 11, 16, \ and B = \9, 16, 23, 30, \ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A B) is

  1. 3814
  2. 4003
  3. 4027
  4. 3761
Ques. 3JEE Main 2025, 23 January (Evening Shift)

Let A=\(x,y) :|x+y| 3\ and B=\(x,y) :|x|+|y| 3\. If C=\(x,y) :x=0 or y=0\, then (x,y) |x+y| is :

  1. 18
  2. 24
  3. 15
  4. 12
Ques. 4JEE Main 2025, 22 January (Morning Shift)

Let A=\1,2,3, ,10\ and B= \ mn:m,n A, m<n and (m,n)=1 \. Then n(B) is equal to :

  1. 29
  2. 31
  3. 37
  4. 36
Ques. 5JEE Main 2024, 6 April (Morning Shift)

Let A = \n [100, 700] N : n is neither a multiple of 3 nor a multiple of 4\. Then the number of elements in A is

  1. 300
  2. 310
  3. 290
  4. 280
Ques. 6JEE 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 .

Ques. 7JEE 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. 8JEE 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. 9JEE 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 :

  1. 8
  2. 10
  3. 4
  4. 6

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