1
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3 /min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :
A
$${5 \over {6\pi }}$$
B
$${1 \over {9\pi }}$$
C
$${1 \over {36\pi }}$$
D
$${1 \over {18\pi }}$$
2
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
If the tangent to the curve $$y = {x \over {{x^2} - 3}}$$ , $$x \in \rho ,\left( {x \ne \pm \sqrt 3 } \right)$$, at a point ($$\alpha$$, $$\beta$$) $$\ne$$ (0, 0) on it is parallel to the line 2x + 6y – 11 = 0, then :
A
| 6$$\alpha$$ + 2$$\beta$$ | = 9
B
| 2$$\alpha$$ + 6$$\beta$$ | = 11
C
| 2$$\alpha$$ + 6$$\beta$$ | = 19
D
| 6$$\alpha$$ + 2$$\beta$$ | = 19
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $${\tan ^{ - 1}}\left( {{1 \over 2}} \right)$$. Water is poured into it at a constant rate of 5 cubic meter per minute. The the rate (in m/min.), at which the level of water is rising at the instant when the depth of water in the tank is 10m; is :-
A
$${1 \over {15\pi }}$$
B
$${1 \over {5\pi }}$$
C
$${1 \over {10\pi }}$$
D
$${2 \over \pi }$$
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
If ƒ(x) is a non-zero polynomial of degree four, having local extreme points at x = –1, 0, 1; then the set
S = {x $$\in$$ R : ƒ(x) = ƒ(0)}
Contains exactly :
A
four rational numbers.
B
four irrational numbers.
C
two irrational and one rational number.
D
two irrational and two rational numbes.
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