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JEE 2020 Mathematics : Application of Derivatives-02

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Question 1

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x² such that the rectangle lies inside the parabola, is

Question 2

The maximum value of 3 cosθ + 5 sin

for any real value of θ is

Question 3

The maximum value of the function f(x) = 3x³ – 18x² + 27x – 40 on the set S = {x ∈R : x² + 30 ≤ 11x} is :

Question 4

Let a, b, c be positive real numbers and

for all

. Then,

Question 5

The maximum volume (in cu.m.) of the right circular cone having slant height 3 m is :

Question 6

If f(x) = xex^{(1 – x)}, x ∈ R, then f(x) is

Question 7

Let f : (-∞, ∞) → (-∞, ∞) be defined by f(x) = x³ + 1

Statement 1 : The function f has a local extremum at x = 0

Statement 2 : The function f is continuous and differentiable (-∞, ∞) and f’(0) = 0

Question 8

The function

is strictly increasing in the interval

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Dec 6JEE & BITSAT