JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Permutations and Combinations

More JEE Main questions on Permutations and Combinations

1. The number of strictly increasing functions f from the set $\{1,2,3,4,5,6\}$ to the set $(1,2,3,\dots ,9)$ such that $\mathrm{f}(\mathrm{i})\ne \mathrm{i}$ for $1\le \mathrm{i}\le 6$, is equal to :
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2. Let $\mathrm{S}=\{(\mathrm{m},\mathrm{n}):\mathrm{m},\mathrm{n}\in \{1,2,3,\dots ..,50\}\}$. If the number of elements ( $\mathrm{m},\mathrm{n}$ ) in S such that $6^{\mathrm{m}}+9^{\mathrm{n}}$ is a multiple of 5 is p and the number of elements …
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3. The largest $\mathrm{n}\in \mathrm{N}$, for which $7^{\mathrm{n}}$ divides 101!, is:
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4. Let ABC be a triangle. Consider four points ${\mathrm{p}}_1,{\mathrm{p}}_2$, ${\mathrm{p}}_3,{\mathrm{p}}_4$ on the side AB , five points ${\mathrm{p}}_5,{\mathrm{p}}_6,{\mathrm{p}}_7,{\mathrm{p}}_8,{\mathrm{p}}_9$ on the side BC and four points …
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5. Let S be the set of the first 11 natural numbers. Then the number of elements in $A=\{B\subseteq S:n(B)\ge 2$ and the product of all elements of B is even $\}$ is
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6. The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.
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