WB JEE 2017 | Definite Integration Question 69 | Mathematics

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ... + {1 \over {2n}}} \right]$$ is

$${{n\pi } \over 4}$$

$${\pi \over 4}$$

$${\pi \over {4n}}$$

$${\pi \over {2n}}$$

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

The value of the integral $$\int_0^1 {{e^{{x^2}}}} dx$$

is less than 1

is greater than 1

is less than or equal to 1

lies in the closed interval [1, e]

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

$$\int_0^{100} {{e^{x - [x]}}} dx$$ is equal to

$${{{e^{100}} - 1} \over {100}}$$

$${{{e^{100}} - 1} \over {e - 1}}$$

$$100(e - 1)$$

$${{e - 1} \over {100}}$$

WB JEE 2017

MCQ (Single Correct Answer)

-0.5

If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to

$${1 \over 2}(1 - {x^2})$$

$$1 - {x^2}$$

$${1 \over 2}(1 + {x^2})$$

$$1 + {x^2}$$

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