1
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $$\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$$ is :

A
$$\frac{2^{51}}{50 !}$$
B
$$\frac{2^{51}}{51 !}$$
C
$$\frac{2^{50}}{50 !}$$
D
$$\frac{2^{50}}{51 !}$$
2
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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

A
0
B
$${\log _e}2$$
C
$${\log _e}\left( {{2 \over 3}} \right)$$
D
$${\log _e}\left( {{3 \over 2}} \right)$$
3
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$S$$ be the set of all solutions of the equation $$\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^{2}}\right)=\pi, x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$$. Then $$\sum_\limits{x \in S} 2 \sin ^{-1}\left(x^{2}-1\right)$$ is equal to :

A
$$\pi-2 \sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$$
B
$$\pi-\sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$$
C
$$\frac{-2 \pi}{3}$$
D
None
4
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The sum of 10 terms of the series

$${1 \over {1 + {1^2} + {1^4}}} + {2 \over {1 + {2^2} + {2^4}}} + {3 \over {1 + {3^2} + {3^4}}}\, + \,....$$ is

A
$${{58} \over {111}}$$
B
$${{56} \over {111}}$$
C
$${{55} \over {111}}$$
D
$${{59} \over {111}}$$
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12