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Solving Simultaneous Linear Equation Using Cramer's Rule

Number of 4...

Question

Number of $4$ digit numbers of the form $N = a b c d$ which satisfy following three conditions:
(i) $4000 \leq N < 6000$ (ii) $N$ is multiple of $5$ (iii) $3 \leq b < c \leq 6$ is equal to

12

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18

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24

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48

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Solution

The correct option is C $24$
$N = a b c d$
(i) $4000 \leq N < 6000$
$\Rightarrow a = 4 a r 5$
(ii) $3 \leq l n < c \leq 6$
$\Rightarrow b = 3, c = 4, 5, 6$
$b = 4, c = 5, 6$
$b = 5, c = 6$
(iii) $d = 0,$ or $5$
Total $= 2 \times 2 \times (3 + 2 + 1)$
$= 24$

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