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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
Find how many two$-$digit numbers are divisible by $6.$
  • ✓
    $15$
  • B
    $16$
  • C
    $14$
  • D
    $17$
✓

Answer

Correct option: A.
$15$
The two$-$digit numbers that are divisible by $6$ are $12,18,24, \ldots, 96$.
It forms an $A.P.$ with $a=12, d=6$
Since, $n^{\text {th }}$ term of an $A.P.$ is $a_n=a+(n-1) d$
$\therefore 12+(n-1) \times 6=96$
$\Rightarrow 2+(n-1)=16$
$\Rightarrow n=14+1=15$
Thus, there are $15$ two$-$digit numbers that are divisible by $6.$

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