1
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
y = 4x
B
x = 4y
C
y = 4x + $$\alpha$$
D
x = 4y $$-$$ $$\alpha$$
2
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
has a local minina at $$x = {1 \over 2}$$
B
has a local minima at $$x = {3 \over 4}$$
C
is increasing in $$\left( {{1 \over 2},{3 \over 4}} \right)$$
D
is decreasing in $$\left( {{1 \over 2},{4 \over 3}} \right)$$
3
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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?

A
For n1 = 3, n2 = 4, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local maxima.
B
For n1 = 4, n2 = 3, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local minima.
C
For n1 = 3, n2 = 5, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local maxima.
D
For n1 = 4, n2 = 6, there exists $$\alpha$$ $$\in$$ (3, 5) where f attains local maxima.
4
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
$${{22} \over {9 + 4\sqrt 3 }}$$
B
$${{66} \over {9 + 4\sqrt 3 }}$$
C
$${{22} \over {4 + 9\sqrt 3 }}$$
D
$${{66} \over {4 + 9\sqrt 3 }}$$
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