1
JEE Main 2022 (Online) 29th July Morning Shift
Numerical
+4
-1

The number of matrices of order $$3 \times 3$$, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is __________.

2
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $$\mathrm{b}+3 \mathrm{~g}$$ is equal to ____________.

3
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1

Let $$S$$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $$\{A, B, C, D, E\}$$ or a number from $$\{1,2,3,4,5\}$$ with the repetition of characters allowed. If the number of passwords in $$S$$ whose at least one character is a number from $$\{1,2,3,4,5\}$$ is $$\alpha \times 5^{6}$$, then $$\alpha$$ is equal to ___________.

4
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits $$1,2,3,4,5$$ and 6 without repetition of digits. Then the total number of such numbers is ____________.