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## MCQ (Single Correct Answer)

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If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx}$$, $${I_2} = \int\limits_0^1 {{e^{ - {x^... WB JEE 2022 Let$$f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt} $$. Then$$f'\left( {{\pi \over 4}} \right)$$equals... WB JEE 2022 Let$$\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x...
WB JEE 2022
The value of $$\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{\sin x}}} \over {{{(\cos x)}^{\sin x}} + {{(\sin x)}^{\cos... WB JEE 2022 Let f be derivable in [0, 1], then WB JEE 2022 Let$$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx} $$. Then WB JEE 2021 If$$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt} $$, then$$\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}}...
WB JEE 2021
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx}$$. Then
WB JEE 2021
The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx}$$ is
WB JEE 2021
If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}}$$, then the value of x is
WB JEE 2021
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \r... WB JEE 2021$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx} $$is equal to WB JEE 2021 Let f, be a continuous function in [0, 1], then$$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over...
WB JEE 2020
$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to
WB JEE 2020
The value of $$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^... WB JEE 2020$$\mathop {\lim }\limits_{n \to \infty } {3 \over n}\left[ {1 + \sqrt {{n \over {n + 3}}} + \sqrt {{n \over {n + 6}}} ...
WB JEE 2019
The value of the integral $$\int\limits_{ - 1}^1 {\left\{ {{{{x^{2015}}} \over {{e^{|x|}}({x^2} + \cos x)}} + {1 \over {... WB JEE 2019 The value of$$\mathop {\lim }\limits_{x \to 0} {1 \over x}\left[ {\int\limits_y^a {{e^{{{\sin }^2}t}}dt - } \int\limits...
WB JEE 2019
The value of the integration $$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over ... WB JEE 2019 The value of$$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\left\{ {{{\sec }^2}{\pi \over {4n}} + {{\sec }^2}{{2\...
WB JEE 2018
The value of $$I = \int_{\pi /2}^{5\pi /2} {{{{e^{{{\tan }^{ - 1}}(\sin x)}}} \over {{e^{{{\tan }^{ - 1}}(\sin x)}} + {e... WB JEE 2018 Let$$I = \int\limits_{\pi /4}^{\pi /3} {{{\sin x} \over x}} dx$$. Then WB JEE 2018 The value of the integral$$I = \int_{1/2014}^{2014} {{{{{\tan }^{ - 1}}x} \over x}} dx$$is WB JEE 2018 If$$M = \int\limits_0^{\pi /2} {{{\cos x} \over {x + 2}}dx} $$,$$N = \int\limits_0^{\pi /4} {{{\sin x\cos x} \over {{{...
WB JEE 2018
Let $$I = \int_0^{100\pi } {\sqrt {(1 - \cos 2x)} } \,dx$$, then
WB JEE 2017
If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to
WB JEE 2017
$$\int_0^{100} {{e^{x - [x]}}} dx$$ is equal to
WB JEE 2017
The value of the integral $$\int_0^1 {{e^{{x^2}}}} dx$$
WB JEE 2017
The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ..... WB JEE 2017 Let$${I_1} = \int_0^n {[x]} \,dx$$and$${I_2} = \int_0^n {\{ x\} } \,dx$$, where [x] and {x} are integral and fraction... WB JEE 2017 The value of$$\int\limits_0^\pi {{{\sin }^{50}}x{{\cos }^{49}}x\,dx} $$is WB JEE 2011 The value of$$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{{{r^3}} \over {{r^4} + {n^4}}}} $$is... WB JEE 2011$$\int\limits_\pi ^{16\pi } {|\sin x|dx = } $$WB JEE 2011 The value of$$\int\limits_{ - 2}^2 {(x\cos x + \sin x + 1)dx} $$is WB JEE 2011 If$$I = \int\limits_0^1 {{{dx} \over {1 + {x^{\pi /2}}}}} $$, then WB JEE 2010 The value of$$I = \int\limits_{ - \pi /2}^{\pi /2} {|\sin x|dx} $$is WB JEE 2010 If$${I_1} = \int\limits_0^{3\pi } {f({{\cos }^2}x)dx} $$and$${I_2} = \int\limits_0^\pi {f({{\cos }^2}x)dx} $$, then... WB JEE 2010 If$${d \over {dx}}\{ f(x)\} = g(x)$$, then$$\int\limits_a^b {f(x)g(x)dx} $$is equal to WB JEE 2010 The value of the integral$$\int\limits_0^{\pi /2} {{{\sin }^5}xdx} $$is WB JEE 2010$$\int\limits_0^{1000} {{e^{x - [x]}}dx} $$is equal to WB JEE 2009$$\int\limits_{ - 1}^4 {f(x)dx = 4} $$and$$\int\limits_2^4 {\{ 3 - f(x)\} dx = 7} $$, then the value of$$\int\limits_...
WB JEE 2009
If $${I_1} = \int\limits_0^{\pi /4} {{{\sin }^2}xdx}$$ and $${I_2} = \int\limits_0^{\pi /4} {{{\cos }^2}xdx}$$, then...
WB JEE 2009
The value of $$\int\limits_0^\infty {{{dx} \over {({x^2} + 4)({x^2} + 9)}}}$$ is
WB JEE 2009
If $$f(x) = f(a - x)$$, then $$\int\limits_0^a {xf(x)dx}$$ is equal to
WB JEE 2009
The value of the $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + ... + {1 \over... WB JEE 2008 The value of the integral$$\int\limits_{ - a}^a {{{x{e^{{x^2}}}} \over {1 + {x^2}}}dx} $$is WB JEE 2008 The value of$$\int\limits_{ - 3}^3 {(a{x^5} + b{x^3} + cx + k)dx} $$, where a, b, c, k are constants, depends only on... WB JEE 2008 The value of$$\int\limits_0^\pi {|\cos x|dx} $$is WB JEE 2008 The value of the integral$$\int\limits_0^2 {|{x^2} - 1|dx} $$is WB JEE 2008 If$$h(x) = \int\limits_0^x {{{\sin }^4}t\,dt} $$, then$$h(x + \pi )$$equals WB JEE 2008 If$$I = \int\limits_{ - \pi }^\pi {{{{e^{\sin x}}} \over {{e^{\sin x}} + {e^{ - \sin x}}}}dx} $$, then I equals WB JEE 2008$$\int\limits_{ - \pi /2}^{\pi /2} {{{\sin }^9}x{{\cos }^5}x\,dx} $$equals WB JEE 2008 ## MCQ (More than One Correct Answer) More Let$$f(x) = \left\{ {\matrix{ {0,} & {if} & { - 1 \le x \le 0} \cr {1,} & {if} & {x = 0} \cr {2,} & {if} &...
WB JEE 2021
Whichever of the following is/are correct?
WB JEE 2021
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 $$\ge... WB JEE 2019 Let$$I = \int\limits_0^I {{{{x^3}\cos 3x} \over {2 + {x^2}}}dx} $$, then WB JEE 2018 Let f be a non-constant continuous function for all x$$ \ge $$0. Let f satisfy the relation f(x) f(a$$-$$x) = 1 for ... WB JEE 2017 ## Subjective More Prove that$$I = \int\limits_0^{\pi /2} {{{\sqrt {\sec x} } \over {\sqrt {\cos ecx} + \sqrt {\sec x} }}dx = {\pi \over...
WB JEE 2011
Evaluate the following integral $$\int\limits_{ - 1}^2 {|x\sin \pi x|dx}$$
WB JEE 2010
If m, n be integers, then find the value of $$\int\limits_{ - \pi }^\pi {{{(\cos mx - \sin nx)}^2}dx}$$
WB JEE 2009

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