WB JEE 2019 | Differentiation Question 29 | Mathematics

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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

2

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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