1
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is
A
$$\sqrt 3$$
B
$$2\sqrt 3$$
C
$$\sqrt 6$$
D
$${2 \over 3} {\sqrt 3}$$
2
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
If S1 and S2 are respectively the sets of local minimum and local maximum points of the function,

ƒ(x) = 9x4 + 12x3 – 36x2 + 25, x $$\in$$ R, then :
A
S1 = {–1}; S2 = {0, 2}
B
S1 = {–2}; S2 = {0, 1}
C
S1 = {–2, 0}; S2 = {1}
D
S1 = {–2, 1}; S2 = {0}
3
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
Let ƒ : [0, 2] $$\to$$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $$\in$$ (0, 2). If $$\phi$$(x) = ƒ(x) + ƒ(2 – x), then $$\phi$$ is :
A
decreasing on (0, 2)
B
decreasing on (0, 1) and increasing on (1, 2)
C
increasing on (0, 2)
D
increasing on (0, 1) and decreasing on (1, 2)
4
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
If the function f given by f(x) = x3 – 3(a – 2)x2 + 3ax + 7, for some a$$\in$$R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $${{f\left( x \right) - 14} \over {{{\left( {x - 1} \right)}^2}}} = 0\left( {x \ne 1} \right)$$ is :
A
$$-$$ 7
B
5
C
7
D
6
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