JEE Main 2023 · 8 Apr 2023 Shift 2

Let A = {1, 2, 3, 4, 5, 6, 7}. Then the relation R = {(x, y) ∈ A × A : x + y = 7} is

1. Areflexive but neither symmetric nor transitive
2. Bsymmetric but neither reflexive nor transitive
3. Ctransitive but neither symmetric nor reflexive
4. Dan equivalence relation

Let A = {θ ∈ (0, 2π) : (1 + 2i sin θ)/(1 − i sin θ) is purely imaginary}. Then the sum of the elements in A is

1. A2π
2. B3π
3. C4π
4. Dπ

Let S be the set of all values of θ ∈ [−π, π] for which the system of linear equations x + y + √3 z = 0, −x + (tan θ)y + √7 z = 0, x + y + (tan θ)z = 0 has non-trivial solution. Then (120/π) ∑_{θ∈S} θ is equal to

1. A10
2. B20
3. C30
4. D40

If A = [[1, 5], [λ, 10]], A⁻¹ = αA + βI and α + β = −2, then 4α² + β² + λ² is equal to :

1. A10
2. B12
3. C14
4. D19

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k, then k is equal to

1. A945
2. B1890
3. C2835
4. D5670

25¹⁹⁰ − 19¹⁹⁰ − 8¹⁹⁰ + 2¹⁹⁰ is divisible by

1. Aboth 14 and 34
2. B14 but not by 34
3. C34 but not by 14
4. Dneither 14 nor 34

The absolute difference of the coefficients of x¹⁰ and x⁷ in the expansion of (2x² + 1/(2x))¹¹ is equal to

1. A11³ − 11
2. B12³ − 12
3. C10³ − 10
4. D13³ − 13

Let aₙ be the nᵗʰ term of the series 5 + 8 + 14 + 23 + 35 + 50 + ... and Sₙ = ∑ₖ₌₁ⁿ aₖ. Then S₃₀ − a₄₀ is equal to

1. A11260
2. B11280
3. C11290
4. D11310