1
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0

Let $$f(x) = {x^m}$$, m being a non-negative integer. The value of m so that the equality $$f'(a + b) = f'(a) + f'(b)$$ is valid for all a, b > 0 is

A
0
B
1
C
2
D
3
2
WB JEE 2020
MCQ (More than One Correct Answer)
+2
-0
Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is
A
$$2\left[ {{3 \over {{{(x + 1)}^4}}} - {3 \over {{{(x + 1)}^3}}} + {4 \over {{{(x + 2)}^3}}}} \right]$$
B
$$3\left[ {{2 \over {{{(x + 1)}^3}}} + {4 \over {{{(x + 1)}^2}}} - {5 \over {{{(x + 2)}^3}}}} \right]$$
C
$${6 \over {{{(x + 1)}^3}}} - {4 \over {{{(x + 1)}^2}}} + {3 \over {{{(x + 1)}^3}}}$$
D
$${7 \over {{{(x + 1)}^3}}} - {3 \over {{{(x + 1)}^2}}} + {2 \over {{{(x + 1)}^3}}}$$
3
WB JEE 2019
MCQ (More than One Correct Answer)
+2
-0
Let f and g be differentiable on the interval I and let a, b $$\in$$ I, a < b. Then,
A
If f(a) = 0 = f(b), the equation f'(x) + f(x)g'(x) = 0 is soluble in (a, b)
B
If f(a) = 0 = f(b), the equation f'(x) + f(x)g'(x) = 0 may not be soluble in (a, b)
C
If g(a) = 0 = g(b), the equation g'(x) + kg(x) = 0 is soluble in (a, b), k $$\in$$ R
D
If g(a) = 0 = g(b), the equation g'(x) + kg(x) = 0 may not be soluble in (a, b), k $$\in$$ R
4
WB JEE 2017
MCQ (More than One Correct Answer)
+2
-0
If f(x) = xn, being a non-negative integer, then the values of n for which f'($$\alpha$$ + $$\beta$$) = f'($$\alpha$$) + f'($$\beta$$) for all $$\alpha$$, $$\beta$$ > 0 is
A
1
B
2
C
0
D
5
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