2024120 marks30 questions
10 of its 30 questions are here. The rest have a figure or are still being checked, so for now they're only in the official PDF.
Sit this paper against the clock, marked by its official answers, or get a new paper like it. Sign in first; practising is part of Pro.
Source: JEE (Main) 2024, Paper 1 (B.E./B.Tech), 5 Apr 2024 Shift 2, Maths, published by NTA. The official PDF
If y(θ) = (2 cos θ + cos 2θ)/(cos 3θ + 4 cos 2θ + 5 cos θ + 2), then at θ = π/2, y″ + y′ + y is equal to:
The number of solutions of sin²x + (2 + 2x − x²) sin x − 3(x − 1)² = 0, where −π ≤ x ≤ π, is ________.
If 1 + (√3 − √2)/(2√3) + (5 − 2√6)/18 + (9√3 − 11√2)/(36√3) + (49 − 20√6)/180 + ... upto ∞ = 2 + (√(b/a) + 1) logₑ(a/b), where a and b are integers with gcd(a, b) = 1, then 11a + 18b is equal to ________.
Let a > 0 be a root of the equation 2x² + x − 2 = 0. If limₓ→₁/ₐ 16(1 − cos(2 + x − 2x²))/(1 − ax)² = α + β√17, where α, β ∈ Z, then α + β is equal to ________.
Let the maximum and minimum values of (√(8x − x² − 12) − 4)² + (x − 7)², x ∈ R be M and m, respectively. Then M² − m² is equal to ________.
If f(t) = ∫₀ᵖⁱ 2x dx/(1 − cos²t sin²x), 0 < t < π, then the value of ∫₀ᵖⁱ/² π² dt/f(t) equals ________.
Let y = y(x) be the solution of the differential equation dy/dx + (2x/(1 + x²)²)y = xe^(1/(1 + x²)); y(0) = 0. Then the area enclosed by the curve f(x) = y(x)e^(−1/(1 + x²)) and the line y − x = 4 is ________.
Let a line perpendicular to the line 2x − y = 10 touch the parabola y² = 4(x − 9) at the point P. The distance of the point P from the centre of the circle x² + y² − 14x − 8y + 56 = 0 is ________.
Let the point (−1, α, β) lie on the line of the shortest distance between the lines (x + 2)/(−3) = (y − 2)/4 = (z − 5)/2 and (x + 2)/(−1) = (y + 6)/2 = (z − 1)/0. Then (α − β)² is equal to ________.
The number of real solutions of the equation x|x + 5| + 2|x + 7| − 2 = 0 is ________.