1
WB JEE 2019
+1
-0.25
Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,
A
f(x) > 0 for all x > 0
B
f(x) < 0 for all x > 0
C
no sign of f(x) can be ascertained
D
f(x) is a constant function
2
WB JEE 2019
+2
-0.5
Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then
A
f(x) has infinitely many zeroes in (1, 2) for all c
B
f(x) has exactly one zero in (1, 2) if $$-$$1 < c < 0
C
f(x) has double zeroes in (1, 2) if $$-$$1 < c < 0
D
whatever be the value of c, f(x) has no zero in (1, 2)
3
WB JEE 2018
+1
-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
A
$${f_n}(x)$$
B
$${f_n}(x)$$$${f_{n - 1}}(x)$$
C
$${{f_n}(x)}$$$${f_{n - 1}}(x)$$...$${f_1}(x)$$
D
$${f_n}(x)$$...$${f_1}(x)$$$${e^x}$$
4
WB JEE 2018
+2
-0.5
The equation x log x = 3 $$-$$ x
A
has no root in (1, 3)
B
has exactly one root in (1, 3)
C
x log x $$-$$ (3 $$-$$ x) > 0 in [1, 3]
D
x log x $$-$$ (3 $$-$$ x) < 0 in [1, 3]
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