1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let f be a twice differentiable function on (1, 6). If f(2) = 8, f’(2) = 5, f’(x) $$\ge$$ 1 and f''(x) $$\ge$$ 4, for all x $$\in$$ (1, 6), then :
A
f(5) $$\le$$ 10
B
f(5) + f'(5) $$\ge$$ 28
C
f(5) + f'(5) $$\le$$ 26
D
f'(5) + f''(5) $$\le$$ 20
2
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10 cm, is :
A
9
B
10
C
18
D
20
3
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
The function, f(x) = (3x – 7)x2/3, x $$\in$$ R, is increasing for all x lying in :
A
$$\left( { - \infty ,0} \right) \cup \left( {{3 \over 7},\infty } \right)$$
B
$$\left( { - \infty ,0} \right) \cup \left( {{{14} \over {15}},\infty } \right)$$
C
$$\left( { - \infty ,{{14} \over {15}}} \right)$$
D
$$\left( { - \infty ,{{14} \over {15}}} \right) \cup \left( {0,\infty } \right)$$
4
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let f : (–1, $$\infty$$) $$\to$$ R be defined by f(0) = 1 and
f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$, x $$\ne$$ 0. Then the function f :
A
decreases in (–1, $$\infty$$)
B
decreases in (–1, 0) and increases in (0, $$\infty$$)
C
increases in (–1, $$\infty$$)
D
increases in (–1, 0) and decreases in (0, $$\infty$$)
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