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

Let $$f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$$, $$x \in [ - 1,1]$$. If [a, b] is the range of the function f, then 4a $$-$$ b is equal to :

A
11
B
11 $$-$$ $$\pi$$
C
11 + $$\pi$$
D
15 $$-$$ $$\pi$$
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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