JEE Advanced Limits and Derivatives — previous year questions
17 questions from 2025, 2024, 2022, 2020, 2019, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2007.
- Let x₀ be the real number such that e^(x₀) + x₀ = 0. For a given real number α, define g(x) = (3xeˣ + 3x - α…
- Let k ∈ R. If lim_(x → 0⁺) (sin(sin kx) + cos x + x)^(2/x) = e⁶, then the value of k is
- Let S be the set of all (α, β) ∈ R × R such that lim_(x → ∞) (sin(x²)(logₑ x)^α…
- If β = lim_(x → 0) (e^(x³) - (1 - x³)^(1/3) + ((1 - x²)^(1/2) - 1)sin x)/(x sin² x), then the value of 6β is…
- Let α be a positive real number. Let f: R → R and g: (α, ∞) → R be the functions defined by f(x) = sin((π…
- The value of the limit lim_(x → π/2) (4 √2 (sin 3x + sin x))/((2 sin 2x sin(3x/2) + cos(5x/2)) - (√2 + √2 cos…
- Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit…
- Let f: R → R be a function. We say that f has PROPERTY 1: If lim_(h → 0) (f(h) - f(0))/√(|h|) exists and is…
- Let f(x) = (1-x(1+|1-x|))/(|1-x|)cos(1/(1-x)) for x ≠ 1. Then
- Let α, β ∈ R be such that lim_(x → 0)(x²sin(β x))/(α x-sin x)=1 then 6(α+β) equals.
- Let m and n be two positive integers greater than 1. If lim_(α → 0) ( (e^(cos(αⁿ)) - e)/αᵐ ) = -( e/2 ) then…
- The largest value of non-negative integer a for which lim_(x→1) { (-a x+sin(x-1)+a)/(x+sin(x-1)-1)…
- For a ∈ R (the set of all real numbers), a ≠ -1, lim_(n → ∞) ((1ᵃ + 2ᵃ + … + nᵃ))/((n+1)ᵃ⁻¹[(na+1) + (na+2) +…
- Let α(a) and β(a) be the roots of the equation (³√(1+a)-1)x²+(√(1+a)-1)x+(⁶√(1+a)-1)=0 where a>-1. Then…
- If lim_(x → ∞) ( (x² + x + 1)/(x + 1) - ax - b ) = 4, then
- If lim_(x→ 0)[1+xln(1+b²)]^(1/x)=2bsin²θ, b>0 and θ∈(-π,π], then the value of θ is
- lim_(x → π/4) (∫₂^(sec² x) f(t) dt)/(x² - π²/16) equals