For a set of $5$ true or false questions,no student has written all the correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is
- A$30$
- B$31$
- C$32$
- D$16$
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If $x={ }^{16} C_5+{ }^{12} C_4, y=\sum_{r=1}^3{ }^{(20-r)} C_4, z=\sum_{k=1}^4{ }^{(16-k)} C_3$,then $x+y+z=$
DifficultTS EAMCET 2021
View SolutionThe number of numbers between $2000$ and $5000$ that can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits not allowed) and are multiples of $3$ is:
In an examination,the maximum marks for each of three subjects is $n$ and that for the fourth subject is $2n$. The number of ways in which a candidate can get $3n$ marks is
The number of $4$-letter permutations formed using the English alphabet such that the number of distinct vowels is equal to the number of distinct consonants,when repetition is allowed,is
Statement-$1$: The number of $4$-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by $4$ is $200$.
Statement-$2$: $A$ number is divisible by $4$ if its unit digit is divisible by $4$.
Statement-$2$: $A$ number is divisible by $4$ if its unit digit is divisible by $4$.
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