JEE Advanced 2020 Paper 1 Offline | Definite Integrals and Applications of Integrals Question 20 | Mathematics

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JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Which of the following inequalities is/are TRUE?

$$\int_0^1 {x\cos xdx\, \ge \,{3 \over 8}} $$

$$\int_0^1 {x\sin xdx\, \ge \,{3 \over {10}}} $$

$$\int_0^1 {{x^2}\cos xdx\, \ge \,{1 \over 2}} $$

$$\int_0^1 {{x^2}\sin xdx\, \ge \,{2 \over 9}} $$

JEE Advanced 2018 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let f : [0, $$\infty $$) $$ \to $$ R be a continuous function such that

$$f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt} $$ for all x $$ \in $$ [0, $$\infty $$). Then, which of the following statement(s) is (are) TRUE?

The curve y = f(x) passes through the point (1, 2)

The curve y = f(x) passes through the point (2, $$-$$1)

The area of the region $$\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \} $$ is $${{\pi - 2} \over 4}$$

The area of the region $$\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \} $$ is $${{\pi - 1} \over 4}$$

JEE Advanced 2017 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

If $$I = \sum\nolimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx} $$, then

$$I > {\log _e}99$$

$$I < {\log _e}99$$

$$I < {{49} \over {50}}$$

$$I > {{49} \over {50}}$$

JEE Advanced 2017 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

If the line x = $$\alpha $$ divides the area of region R = {(x, y) $$ \in $$R² : x³ $$ \le $$ y $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ 1} into two equal parts, then

2$$\alpha $$⁴ $$-$$ 4$$\alpha $$² + 1 =0

$$\alpha $$⁴ + 4$$\alpha $$² $$-$$ 1 =0

$${1 \over 2} < \alpha < 1$$

0 < $$\alpha $$ $$ \le $$ $${1 \over 2}$$

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