1
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

$$\sum\limits_{r=1}^{20}\left(r^{2}+1\right)(r !)$$ is equal to

A
$$22 !-21 !$$
B
$$22 !-2(21 !)$$
C
$$21 !-2(20 !)$$
D
$$21 !-20$$ !
2
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder when $$7^{2022}+3^{2022}$$ is divided by 5 is :

A
0
B
2
C
3
D
4
3
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder when $$(2021)^{2022}+(2022)^{2021}$$ is divided by 7 is

A
0
B
1
C
2
D
6
4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

$$\sum\limits_{\matrix{ {i,j = 0} \cr {i \ne j} \cr } }^n {{}^n{C_i}\,{}^n{C_j}} $$ is equal to

A
$$2^{2 n}-{ }^{2 n} C_{n}$$
B
$${2^{2n - 1}} - {}^{2n - 1}{C_{n - 1}}$$
C
$$2^{2 n}-\frac{1}{2}{ }^{2 n} C_{n}$$
D
$${2^{2n - 1}} + {}^{2n - 1}{C_n}$$
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