JEE Main 2020 (Online) 9th January Morning Slot | Application of Derivatives Question 69 | Mathematics

JEE Main 2020 (Online) 9th January Morning Slot

MCQ (Single Correct Answer)

-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 :

$${1 \over {18\pi }}$$

$${1 \over {36\pi }}$$

$${1 \over {54\pi }}$$

$${5 \over {6\pi }}$$

JEE Main 2019 (Online) 12th April Morning Slot

MCQ (Single Correct Answer)

-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 :

$$\left( {5,3\sqrt 6 } \right)$$

$$\left( {4,3\sqrt 3 } \right)$$

$$\left( {4,3\sqrt 2 } \right)$$

$$\left( {3,3\sqrt 3 } \right)$$

JEE Main 2019 (Online) 12th April Morning Slot

MCQ (Single Correct Answer)

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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 :

$${{25} \over 3}$$

25$$\sqrt 3 $$

$${{25} \over {\sqrt 3 }}$$

JEE Main 2019 (Online) 10th April Evening Slot

MCQ (Single Correct Answer)

-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 :

$${5 \over {6\pi }}$$

$${1 \over {9\pi }}$$

$${1 \over {36\pi }}$$

$${1 \over {18\pi }}$$

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