JEE Advanced Application of Derivatives — previous year questions
33 questions from 2026, 2025, 2024, 2022, 2021, 2020, 2019, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007.
- Let P be the point on the parabola y = x² such that the slope of the tangent to the parabola at the point P…
- Let R denote the set of all real numbers. Define the function f: R → R by f(x) = 2 - 2x² - x²sin1/x if x ≠ 0,…
- Let R denote the set of all real numbers. Let f: R → R be defined by f(x)= (6x+sin x)/(2x+sin x) if x ≠ 0,…
- Let the function f : R → R be defined by f(x) = (sin x)/(e^(π x)) ( (x²⁰²³ + 2024x + 2025)/(x² - x + 3) ) +…
- Let α=∑ₖ₌₁^∞ sin ^(2 k)(π/6). Let g:[0,1] → R be the function defined by g(x)=2^(α x)+2^(α(1-x)). Then, which…
- Let f : R → R be defined by f(x) = (x² - 3x - 6)/(x² + 2x + 4) Then which of the following statements is…
- Consider all rectangles lying in the region {(x, y) ∈ R × R : 0 ≤ x ≤ π/2 and 0 ≤ y ≤ 2sin(2x)} and having…
- Let the function f:(0, π) → R be defined by f(θ) = (sin θ + cos θ)² + (sin θ - cos θ)⁴. Suppose the function…
- Let f(x)=(sin π x)/x², x>0 Let x₁<x₂<x₃<…<xₙ<… be all the points of local maximum of f and y₁<y₂<y₃<…<yₙ<… be…
- Define the collections {E₁, E₂, E₃, …} of ellipses and {R₁, R₂, R₃, …} of rectangles as follows : E₁ : x²/9 +…
- If f : R → R is a differentiable function such that f'(x) > 2f(x) for all x ∈ R, and f(0) = 1, then
- If f : R → R is a twice differentiable function such that f''(x)>0 for all x ∈ R, and f(1/2)=1/2, f(1)=1, then
- If f(x) = cos(2x) cos(2x) sin(2x) -cos x cos x -sin x sin x sin x cos x , then
- The least value of a ∈ R for which 4ax²+1/x ≥ 1, for all x > 0, is
- Let f: R → (0, ∞) and g: R → R be twice differentiable functions such that f'' and g'' are continuous…
- Let f, g: [-1, 2] → R be continuous functions which are twice differentiable on the interval (-1, 2). Let the…
- A cylindrical container is to be made from certain solid material with the following constraints: It has a…
- The slope of the tangent to the curve (y - x⁵)² = x(1 + x²)² at the point (1, 3) is
- A vertical line passing through the point (h, 0) intersects the ellipse x^2/4 + y^2/3 = 1 at the points P and…
- A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into…
- Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x =…
- let f: IR → IR be defined as f(x) = |x| + |x² - 1|. The total number of points at which f attains either a…
- If f(x)=∫₀ˣ e^(t²)(t-2)(t-3) dt for all x ∈ (0,∞), then
- Let P(6, 3) be a point on the hyperbola x²/a² - y²/b² = 1. If the normal at the point P intersects the x-axis…
- Let f be a function defined on R (the set of all real numbers) such that f '(x) = 2010…
- Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the…
- For the function, f(x) = xcos1/x, x ≥ 1,
- Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and lim_(x → 0)(1 + p(x)/x²) = 2. Then the…
- The maximum value of the function f(x) = 2x³ - 15x² + 36x - 48 on the set A = {x mid x² + 20 ≤ 9x} is
- Let the function g:(-∞, ∞) → (-π/2, π/2) be given by g(u) = 2tan⁻¹(eᵘ) - π/2. Then, g is
- Consider the two curves C₁ : y² = 4x, C₂ : x² + y² - 6x + 1 = 0. Then,
- The total number of local maxima and local minima of the function f(x)= (2+x)³, -3<x≤ -1 x^(2/3), -1<x<2 is
- The tangent to the curve y = eˣ drawn at the point (c, eᶜ) intersects the line joining the points (c - 1,…