CAT 2024 Question Paper | Quant Slot 1

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 7 :Consider two sets $A=\{2,3,5,7,11,13\}$ and $B=\{1,8,27\}$. Let $f$ be a function from $A$ to $B$ such that for every element $b$ in $B$, there is at least one element $a$ in $A$ such that $f(a)=b$. Then, the total number of such functions $f$ is

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Video Explanation

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Explanatory Answer

Total number of functions $=3^6=729$ functions.
Total number of functions exactly mapped to one $=3$.
Total number of functions exactly mapped to two $=\left(2^6-2\right)^* 3=62 * 3=186$
The number of onto functions $=729-3-186=540$

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The question is "Consider two sets $A=\{2,3,5,7,11,13\}$ and $B=\{1,8,27\}$. Let $f$ be a function from $A$ to $B$ such that for every element $b$ in $B$, there is at least one element $a$ in $A$ such that $f(a)=b$. Then, the total number of such functions $f$ is "

Hence, the answer is '540'

Choice A is the correct answer.

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