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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $T_n$ denote the number of triangles which can be formed by using the vertices of a regular polygon
of $n$ sides. If
$T_{n+1} - T_{n} = 21$
then $n$ equals
Solution
$T_{n+1} - T_n = 21$$\binom{n+1}{3} - \binom{n}{3} = 21$
$\frac{(n+1)n(n-1)}{6} - \frac{n(n-1)(n-2)}{6} = 21$
$\frac{n(n-1)}{6}\left[(n+1)-(n-2)\right] = 21$
$\frac{n(n-1)}{6}\times 3 = 21$
$\frac{n(n-1)}{2} = 21$
$n(n-1) = 42$
$n^2 - n - 42 = 0$
$(n-7)(n+6) = 0$
$n = 7$
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