JEE Main 2023 (Online) 1st February Evening Shift | Definite Integrals and Applications of Integrals Question 1 | Mathematics

JEE Main 2023 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

-1

The value of the integral

$$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{x + {\pi \over 4}} \over {2 - \cos 2x}}dx} $$ is :

$${{{\pi ^2}} \over {6\sqrt 3 }}$$

$${{{\pi ^2}} \over 6}$$

$${{{\pi ^2}} \over {3\sqrt 3 }}$$

$${{{\pi ^2}} \over {12\sqrt 3 }}$$

JEE Main 2023 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

-1

The area of the region given by $$\{ (x,y):xy \le 8,1 \le y \le {x^2}\} $$ is :

$$16{\log _e}2 - {{14} \over 3}$$

$$8{\log _e}2 - {{13} \over 3}$$

$$16{\log _e}2 + {7 \over 3}$$

$$8{\log _e}2 + {7 \over 6}$$

JEE Main 2023 (Online) 1st February Morning Shift

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {1 + n}} + {1 \over {2 + n}} + {1 \over {3 + n}}\, + \,...\, + \,{1 \over {2n}}} \right]$$ is equal to

$${\log _e}2$$

$${\log _e}\left( {{2 \over 3}} \right)$$

$${\log _e}\left( {{3 \over 2}} \right)$$

JEE Main 2023 (Online) 31st January Evening Shift

MCQ (Single Correct Answer)

-1

Let $\alpha>0$. If $\int\limits_0^\alpha \frac{x}{\sqrt{x+\alpha}-\sqrt{x}} \mathrm{~d} x=\frac{16+20 \sqrt{2}}{15}$, then $\alpha$ is equal to :

$2 \sqrt{2}$

$\sqrt{2}$

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