JEE Main 2024 · 29 Jan 2024 Shift 1

If f(x) = {2 + 2x, −1 ≤ x < 0; 1 − x/3, 0 ≤ x ≤ 3}; g(x) = {−x, −3 ≤ x ≤ 0; x, 0 < x ≤ 1}, then range of (f∘g)(x) is

1. A[0, 3)
2. B[0, 1]
3. C[0, 1)
4. D(0, 1]

Let R be a relation on ℤ×ℤ defined by (a, b) R (c, d) if and only if ad − bc is divisible by 5. Then R is

1. AReflexive and transitive but not symmetric
2. BReflexive and symmetric but not transitive
3. CReflexive, symmetric and transitive
4. DReflexive but neither symmetric nor transitive

If z = 1/2 − 2i is such that |z + 1| = αz + β(1 + i), i = √−1 and α, β ∈ ℝ, then α + β is equal to

1. A−1
2. B2
3. C3
4. D−4

Let A be a square matrix such that AAᵀ = I. Then 1/2 A [(A + Aᵀ)² + (A − Aᵀ)²] is equal to

1. AA² + Aᵀ
2. BA³ + Aᵀ
3. CA² + I
4. DA³ + I

Let A = [[1, 0, 0], [0, α, β], [0, β, α]] and |2A|³ = 2²¹ where α, β ∈ ℤ. Then a value of α is

1. A3
2. B5
3. C9
4. D17

In an A.P., the sixth term a₆ = 2. If the product a₁a₄a₅ is the greatest, then the common difference of the A.P. is equal to

1. A5/8
2. B8/5
3. C2/3
4. D3/2

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

1. A4
2. B5
3. C6
4. D7

Suppose f(x) = ((2ˣ + 2⁻ˣ) tan x √(tan⁻¹(x² − x + 1)))/(7x² + 3x + 1)³. Then the value of f′(0) is equal to

1. A0
2. B√π
3. Cπ
4. Dπ/2