JEE Main 2024 · 6 Apr 2024 Shift 1

Let the relations R₁ and R₂ on the set X = {1, 2, 3, ..., 20} be given by R₁ = {(x, y): 2x − 3y = 2} and R₂ = {(x, y): −5x + 4y = 0}. If M and N be the minimum number of elements required to be added in R₁ and R₂, respectively, in order to make the relations symmetric, then M+N equals

1. A8
2. B10
3. C12
4. D16

The function f(x) = (x² + 2x − 15)/(x² − 4x + 9), x ∈ R is

1. Aboth one-one and onto.
2. Bone-one but not onto.
3. Conto but not one-one.
4. Dneither one-one nor onto.

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

1. A16
2. B24
3. C56
4. D48

Let α, β be the distinct roots of the equation x² − (t² − 5t + 6)x + 1 = 0, t ∈ R and aₙ = αⁿ + βⁿ. Then the minimum value of (a₂₀₂₃ + a₂₀₂₅)/a₂₀₂₄ is

1. A−1/4
2. B1/4
3. C−1/2
4. D1/2

For α, β ∈ R and a natural number n, let Aᵣ = | r, 1, n²/2 + α; 2r, 2, n² − β; 3r − 2, 3, n(3n−1)/2 |. Then 2A₁₀ − A₈ is

1. A0
2. B2n
3. C2α+4β
4. D4α+2β

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. A280
2. B290
3. C300
4. D310

If f(x) = {x³ sin(1/x), x ≠ 0; 0, x = 0}, then

1. Af″(0) = 0
2. Bf″(2/π) = (24 − π²)/(2π)
3. Cf″(0) = 1
4. Df″(2/π) = (12 − π²)/(2π)