1
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the thickness of ice decreases, is :
A
$${1 \over {18\pi }}$$
B
$${1 \over {36\pi }}$$
C
$${1 \over {54\pi }}$$
D
$${5 \over {6\pi }}$$
2
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If m is the minimum value of k for which the function f(x) = x$$\sqrt {kx - {x^2}}$$ is increasing in the interval [0,3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to :
A
$$\left( {5,3\sqrt 6 } \right)$$
B
$$\left( {4,3\sqrt 3 } \right)$$
C
$$\left( {4,3\sqrt 2 } \right)$$
D
$$\left( {3,3\sqrt 3 } \right)$$
3
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec, then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is :
A
$${{25} \over 3}$$
B
25
C
25$$\sqrt 3$$
D
$${{25} \over {\sqrt 3 }}$$
4
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
$${1 \over {18\pi }}$$
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