JEE Main 2022 (Online) 30th June Morning Shift | Application of Derivatives Question 71 | Mathematics

If xy⁴ attains maximum value at the point (x, y) on the line passing through the points (50 + $$\alpha$$, 0) and (0, 50 + $$\alpha$$), $$\alpha$$ > 0, then (x, y) also lies on the line :

y = 4x

x = 4y

y = 4x + $$\alpha$$

x = 4y $$-$$ $$\alpha$$

JEE Main 2022 (Online) 30th June Morning Shift

MCQ (Single Correct Answer)

-1

Let $$f(x) = 4{x^3} - 11{x^2} + 8x - 5,\,x \in R$$. Then f :

has a local minina at $$x = {1 \over 2}$$

has a local minima at $$x = {3 \over 4}$$

is increasing in $$\left( {{1 \over 2},{3 \over 4}} \right)$$

is decreasing in $$\left( {{1 \over 2},{4 \over 3}} \right)$$

JEE Main 2022 (Online) 29th June Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let f : R $$\to$$ R be a function defined by f(x) = (x $$-$$ 3)^n₁ (x $$-$$ 5)^n₂, n₁, n₂ $$\in$$ N. Then, which of the following is NOT true?

For n₁ = 3, n₂ = 4, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local maxima.

For n₁ = 4, n₂ = 3, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local minima.

For n₁ = 3, n₂ = 5, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local maxima.

For n₁ = 4, n₂ = 6, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local maxima.

JEE Main 2022 (Online) 29th June Morning Shift

MCQ (Single Correct Answer)

-1

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

$${{22} \over {9 + 4\sqrt 3 }}$$

$${{66} \over {9 + 4\sqrt 3 }}$$

$${{22} \over {4 + 9\sqrt 3 }}$$

$${{66} \over {4 + 9\sqrt 3 }}$$

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