1
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
2
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
3
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
$${{9 - \sqrt {17} } \over 2}$$
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1
Out of Syllabus

Let S be the set of all the natural numbers, for which the line $${x \over a} + {y \over b} = 2$$ is a tangent to the curve $${\left( {{x \over a}} \right)^n} + {\left( {{y \over b}} \right)^n} = 2$$ at the point (a, b), ab $$\ne$$ 0. Then :

A
S = $$\phi$$
B
n(S) = 1
C
S = {2k : k $$\in$$ N}
D
S = N
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