WB JEE 2019 | Differentiation Question 24 | Mathematics

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WB JEE 2019

MCQ (Single Correct Answer)

-0.25

Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,

f(x) > 0 for all x > 0

f(x) < 0 for all x > 0

no sign of f(x) can be ascertained

f(x) is a constant function

WB JEE 2019

MCQ (Single Correct Answer)

-0.5

Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then

f(x) has infinitely many zeroes in (1, 2) for all c

f(x) has exactly one zero in (1, 2) if $$-$$1 < c < 0

f(x) has double zeroes in (1, 2) if $$-$$1 < c < 0

whatever be the value of c, f(x) has no zero in (1, 2)

WB JEE 2018

MCQ (Single Correct Answer)

-0.25

Let $${f_1}(x) = {e^x}$$, $${f_2}(x) = {e^{{f_1}(x)}}$$, ......, $${f_{n + 1}}(x) = {e^{{f_n}(x)}}$$ for all n $$ \ge $$ 1. Then for any fixed n, $${d \over {dx}}{f_n}(x)$$ is

$${f_n}(x)$$

$${f_n}(x)$$$${f_{n - 1}}(x)$$

$${{f_n}(x)}$$$${f_{n - 1}}(x)$$...$${f_1}(x)$$

$${f_n}(x)$$...$${f_1}(x)$$$${e^x}$$

WB JEE 2018

MCQ (Single Correct Answer)

-0.5

The equation x log x = 3 $$-$$ x

has no root in (1, 3)

has exactly one root in (1, 3)

x log x $$-$$ (3 $$-$$ x) > 0 in [1, 3]

x log x $$-$$ (3 $$-$$ x) < 0 in [1, 3]

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