1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-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 :

A
$${{22} \over {9 + 4\sqrt 3 }}$$
B
$${{66} \over {9 + 4\sqrt 3 }}$$
C
$${{22} \over {4 + 9\sqrt 3 }}$$
D
$${{66} \over {4 + 9\sqrt 3 }}$$
2
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

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
3
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

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
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

The sum of the absolute minimum and the absolute maximum values of the

function f(x) = |3x $$-$$ x2 + 2| $$-$$ x in the interval [$$-$$1, 2] is :

A
$${{\sqrt {17} + 3} \over 2}$$
B
$${{\sqrt {17} + 5} \over 2}$$
C
5
D
$${{9 - \sqrt {17} } \over 2}$$
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