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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider two sets
$A = {x \in \mathbb{Z} : |x - 3| - 3 \le 1}$
and
$B = {x \in \mathbb{R} - {1,2} : \dfrac{(x-2)(x-4)}{x-1}\log_e(|x-2|) = 0}$
Then the number of onto functions $f : A \to B$ is equal to:
Solution
$|x - 3| - 3 \le 1$
$\Rightarrow |x - 3| \le 4$
$\Rightarrow -1 \le x - 3 \le 4$
$\Rightarrow 2 \le x \le 7$
$A = {-1,0,1,5,6,7}$
For $B$
$\dfrac{(x-2)(x-4)}{x-1}\log_e(|x-2|) = 0$
$\Rightarrow x = 2, 4$ or $|x-2| = 1 \Rightarrow x = 3$
$B = {3,4}$
Number of onto functions
$= 2^6 - 2 = 62$
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