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1
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The value of $$\sum\limits_{r = 0}^{22} {{}^{22}{C_r}{}^{23}{C_r}} $$ is

A
$${}^{44}{C_{23}}$$
B
$${}^{45}{C_{23}}$$
C
$${}^{44}{C_{22}}$$
D
$${}^{45}{C_{24}}$$
2
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
$$21 !-20$$ !
3
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
4
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
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