1
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}} $$ is equal to :

A
$$\mathrm{{}^{51}{C_4} - {}^{45}{C_4}}$$
B
$$\mathrm{{}^{51}{C_3} - {}^{45}{C_3}}$$
C
$$\mathrm{{}^{52}{C_3} - {}^{45}{C_3}}$$
D
$$\mathrm{{}^{52}{C_4} - {}^{45}{C_4}}$$
2
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :

A
48
B
120
C
168
D
220
3
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is :

A
125
B
150
C
225
D
120
4
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 receives at least 2 and at most 6 candies, is equal to :

A
205
B
615
C
510
D
430
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