2023120 marks30 questions
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Source: JEE (Main) 2023, Paper 1 (B.E./B.Tech), 12 Apr 2023 Shift 1, Maths, published by NTA. The official PDF
Let D be the domain of the function f(x) = sin⁻¹(log₃ₓ((6 + 2 log₃ x)/(−5x))). If the range of the function g : D → R defined by g(x) = x − [x], ([x] is the greatest integer function), is (α, β), then α² + 5/β is equal to
Let α, β be the roots of the quadratic equation x² + √6x + 3 = 0. Then (α²³ + β²³ + α¹⁴ + β¹⁴)/(α¹⁵ + β¹⁵ + α¹⁰ + β¹⁰) is equal to
Let A = [[1, 1/51], [0, 1]]. If B = [[1, 2], [−1, −1]] A [[−1, −2], [1, 1]], then the sum of all the elements of the matrix ∑ₙ₌₁⁵⁰ Bⁿ is equal to
The number of five digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits 0, 1, 3, 5, 7 and 9 without repetition, is equal to
The sum, of the coefficients of the first 50 terms in the binomial expansion of (1 − x)¹⁰⁰, is equal to
If 1/(n + 1) ⁿCₙ + 1/n ⁿCₙ₋₁ + ... + 1/2 ⁿC₁ + ⁿC₀ = 1023/10 then n is equal to
Let C be the circle in the complex plane with centre z₀ = 1/2(1 + 3i) and radius r = 1. Let z₁ = 1 + i and the complex number z₂ be outside the circle C such that |z₁ − z₀||z₂ − z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|² is equal to
Let ⟨aₙ⟩ be a sequence such that a₁ + a₂ + ... + aₙ = (n² + 3n)/((n + 1)(n + 2)). If 28∑ₖ₌₁¹⁰ 1/aₖ = p₁p₂p₃...pₘ, where p₁, p₂,...., pₘ are the first m prime numbers, then m is equal to