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1
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100 k, then k is equal to _____________.
2
JEE Main 2021 (Online) 22th July Evening Shift
Numerical
+4
-1
If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _____________.
3
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is ____________.
If $$\sum\limits_{r = 1}^{10} {r!({r^3} + 6{r^2} + 2r + 5) = \alpha (11!)}$$, then the value of $$\alpha$$ is equal to ___________.