1
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
2
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
$${{9 - \sqrt {17} } \over 2}$$
3
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 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
4
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1 Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2 / sec) at which the wet conical surface area of the vessel increases is

A
5
B
$${{\sqrt {21} } \over 5}$$
C
$${{\sqrt {26} } \over 5}$$
D
$${{\sqrt {26} } \over {10}}$$
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