1
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
$${{4 - \sqrt 7 } \over 3}$$
2
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.
3
JEE Main 2020 (Online) 7th January Morning Slot
+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
$$\left( { - \infty ,\left. {11} \right]} \right.$$
4
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
$$\left( {3,3\sqrt 3 } \right)$$
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