1
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
Let $$f(x) = \left\{ {\matrix{ {0,} & {if} & { - 1 \le x \le 0} \cr {1,} & {if} & {x = 0} \cr {2,} & {if} & {0 < x \le 1} \cr } } \right.$$ and let $$F(x) = \int\limits_{ - 1}^x {f(t)dt}$$, $$-$$1 $$\le$$ x $$\le$$ 1, then
A
F is continuous function in [$$-$$1, 1]
B
F is discontinuous function in [$$-$$1, 1]
C
F'(x) exists at x = 0
D
F'(x) does not exist at x = 0
2
WB JEE 2019
MCQ (More than One Correct Answer)
+2
-0
Let $${I_n} = \int\limits_0^1 {{x^n}} {\tan ^{ - 1}}xdx$$. If $${a_n}{I_{n + 2}} + {b_n}{I_n} = {c_n}$$ for all n $$\ge$$ 1, then
A
a1, a2, a3 are in GP
B
b1, b2, b3 are in AP
C
c1, c2, c3 are in HP
D
a1, a2, a3 are in AP
3
WB JEE 2018
MCQ (More than One Correct Answer)
+2
-0
Let $$I = \int\limits_0^I {{{{x^3}\cos 3x} \over {2 + {x^2}}}dx}$$, then
A
$$- {1 \over 2} < I < {1 \over 2}$$
B
$$- {1 \over 3} < I < {1 \over 3}$$
C
$$- 1 < I < 1$$
D
$$- {3 \over 2} < I < {3 \over 2}$$
4
WB JEE 2017
MCQ (More than One Correct Answer)
+2
-0
Let f be a non-constant continuous function for all x $$\ge$$ 0. Let f satisfy the relation f(x) f(a $$-$$ x) = 1 for some a $$\in$$ R+. Then, $$I = \int_0^a {{{dx} \over {1 + f(x)}}}$$ is equal to
A
a
B
$${a \over 4}$$
C
$${a \over 2}$$
D
f(a)
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