1
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Out of Syllabus
If c is a point at which Rolle's theorem holds for the function,
f(x) = $${\log _e}\left( {{{{x^2} + \alpha } \over {7x}}} \right)$$ in the interval [3, 4], where a $$\in$$ R, then ƒ''(c) is equal to
A
$${1 \over {12}}$$
B
$${{\sqrt 3 } \over 7}$$
C
$$-{1 \over {12}}$$
D
$$-{1 \over {24}}$$
2
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Let ƒ(x) = xcos–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is true?
A
ƒ' is decreasing in $$\left( { - {\pi \over 2},0} \right)$$ and increasing in $$\left( {0,{\pi \over 2}} \right)$$
B
ƒ '(0) = $${ - {\pi \over 2}}$$
C
ƒ is not differentiable at x = 0
D
ƒ' is increasing in $$\left( { - {\pi \over 2},0} \right)$$ and decreasing in $$\left( {0,{\pi \over 2}} \right)$$
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Out of Syllabus
The value of c in the Lagrange's mean value theorem for the function
ƒ(x) = x3 - 4x2 + 8x + 11, when x $$\in$$ [0, 1] is:
A
$${2 \over 3}$$
B
$${{\sqrt 7 - 2} \over 3}$$
C
$${{4 - \sqrt 5 } \over 3}$$
D
$${{4 - \sqrt 7 } \over 3}$$
4
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points.

If $$\mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4$$, then which one of the following is not true?
A
ƒ(1) - 4ƒ(-1) = 4.
B
x = 1 is a point of minima and x = -1 is a point of maxima of ƒ.
C
x = 1 is a point of maxima and x = -1 is a point of minimum of ƒ.
D
ƒ is an odd function.
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