1
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let the function, ƒ:[-7, 0]$$ \to $$R be continuous on [-7,0] and differentiable on (-7, 0). If ƒ(-7) = - 3 and ƒ'(x) $$ \le $$ 2, for all x $$ \in $$ (-7,0), then for all such functions ƒ, ƒ(-1) + ƒ(0) lies in the interval:
A
$$\left[ { - 6,20} \right]$$
B
$$\left( { - \infty ,\left. {20} \right]} \right.$$
C
$$\left[ { - 3,11} \right]$$
D
$$\left( { - \infty ,\left. {11} \right]} \right.$$
2
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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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