NIMCET 2027 Permutations And Combinations Previous Year Questions (PYQs) – Page 3 of 5
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Showing 48 questions
If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is
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Solution
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is
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Solution
So Ans is [(6C5)5!](4!) = 6!4! = 17280
A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?
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The number of words that can be formed by using the letters of the word MATHEMATICS that start as
well as end with T is
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How many natural numbers smaller than $2 \times 10^8$ can be formed using the digits 1 and 2 only?
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The number of different license plates that can be formed in the format 3 English letters (A….Z)
followed by 4 digits (0, 1, …9) with repetitions allowed in letters and digits is equal to
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A password consists of two alphabets from English followed by three numbers chosen from 0 to 3.
If repetitions are allowed, the number of different passwords is
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If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is minimum
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The number of 3-digit integers that are multiple of 6 which can be formed by using the
digits 1,2,3,4,5,6 without repetition is
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Solution
To be a multiple of $6$:
• last digit must be even → ${2,4,6}$
• sum of digits must be divisible by $3$.
For each even last digit, exactly 8 valid choices of the first two digits satisfy divisibility by $3$ (checked by mod – 3 pairing).
So total numbers:
3×8=24
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