1
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.
2
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
$${{66} \over {4 + 9\sqrt 3 }}$$
3
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of real solutions of

$${x^7} + 5{x^3} + 3x + 1 = 0$$ is equal to ____________.

A
0
B
1
C
3
D
5
4
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :

A
2 : 5
B
19 : 45
C
3 : 8
D
19 : 15
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