Relations and Functions

JEE Main 2026 (Online) 5th April Evening ShiftNumericalMedium📈 Topic in 9% papers+4

Ques. 1JEE Main 2026, 5 April (Evening Shift)

Let A=\1, 4, 7\ and B=\2, 3, 8\. Then the number of elements, in the relation R=\((a1, b1), (a2, b2)) ((A B) (A B)) : a1+b2 divides a2+b1\ is .

Answer

Solution

Let u=a1+b2 and v=a2+b1; each of (a1, b2) and (a2, b1) runs over the 9 pairs of A B.

Values of a+b: a=1: 3, 4, 9; a=4: 6, 7, 12; a=7: 9, 10, 15 (9 occurs twice)

Count the values v divisible by each u:

u=3: v=3, 6, 9, 9, 12, 15 6

u=4: v=4, 12 2; u=6: v=6, 12 2; u=7: v=7 1

u=9 (two pairs): v=9, 9 2 2=4

u=10: v=10 1; u=12: v=12 1; u=15: v=15 1

n(R)=6+2+2+1+4+1+1+1=18

Answer: 18

Keep practising — Relations and Functions

Ques. 2JEE Main 2026, 2 April (Morning Shift)

If the domain of the function f(x)= (0.6) ( | 2x-5x2-4 | ) is (- , a] \b\ [c, d) (e, ), then the value of a+b+c+d+e is .

Ques. 3JEE Main 2026, 2 April (Evening Shift)

Let A=\2, 3, 4, 5, 6\. Let R be a relation on the set A A given by (x, y)R(z, w) if and only if x divides z and y w. Then the number of elements in R is .

Ques. 4JEE Main 2026, 24 January (Morning Shift)

If the domain of the function f(x) = (10x2 - 17x + 7) (18x2 - 11x + 1 ) is (- , a) (b, c) (d, ) - \e\, then 90(a + b + c + d + e) equals:

Ques. 5JEE Main 2026, 23 January (Evening Shift)

The sum of all the real solutions of the equation (x+3) (6x2 + 28x + 30 ) = 5 - 2 (6x+10) (x2 + 6x + 9 ) is equal to :

Ques. 6JEE Main 2026, 22 January (Morning Shift)

If the domain of the function f(x) = -1 ( 5 - x3 + 2x ) + 1 e(10 - x) is (- , ] [ , ) - \ \, then 6( + + + ) is equal to

Ques. 7JEE Main 2026, 22 January (Evening Shift)

Let f(x) = [x]2 - [x + 3] - 3, x R, where [.] is the greatest integer function. Then

f(x) = 0 for finitely many values of x
f(x) < 0 only for x [-1, 3)
02 f(x) dx = -6
f(x) > 0 only for x [4, )

Ques. 8JEE Main 2026, 22 January (Evening Shift)

Let the domain of the function f(x) = 3 5 (7 - 2 (x2 - 10x + 85 ) ) + -1 ( | 3x - 717 - x | ) be ( , ]. Then + is equal to :

Ques. 9JEE Main 2026, 22 January (Evening Shift)

The number of elements in the relation R = \(x, y) : 4x2 + y2 < 52, x, y Z \ is

Ques. 10JEE Main 2025, 8 April (Evening Shift)

Let the domain of the function f(x) = -1 ( 4x + 53x - 7 ) be [ , ] and the domain of g(x) = 2 (2 - 6 27(2x + 5) ) be ( , ). Then |7( + ) + 4( + )| is equal to .

Ques. 11JEE Main 2025, 7 April (Evening Shift)

If the range of the function f(x) = 5-xx2-3x+2, x 1, 2, is (- , ] [ , ), then 2 + 2 is equal to :

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