1
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

Let $$5 f(x)+4 f\left(\frac{1}{x}\right)=\frac{1}{x}+3, x > 0$$. Then $$18 \int_\limits{1}^{2} f(x) d x$$ is equal to :

A
$$10 \log _{\mathrm{e}} 2+6$$
B
$$5 \log _{e} 2-3$$
C
$$10 \log _{\mathrm{e}} 2-6$$
D
$$5 \log _{\mathrm{e}} 2+3$$
2
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1

The value of the integral

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

A
$${{{\pi ^2}} \over {6\sqrt 3 }}$$
B
$${{{\pi ^2}} \over 6}$$
C
$${{{\pi ^2}} \over {3\sqrt 3 }}$$
D
$${{{\pi ^2}} \over {12\sqrt 3 }}$$
3
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

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

A
0
B
$${\log _e}2$$
C
$${\log _e}\left( {{2 \over 3}} \right)$$
D
$${\log _e}\left( {{3 \over 2}} \right)$$
4
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-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 :
A
4
B
2
C
$2 \sqrt{2}$
D
$\sqrt{2}$
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12
© ExamGOAL 2024