KVPY 2020-21 SB SX Exam Previous Papers

Question : 17 of 120

Marks: +1, -0

In a regular 15-sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is either a shortest diagonal nor a longest diagonal is

${2}/{3}$
${5}/{6}$
${8}/{9}$
${9}/{10}$

Validate

Solution:

Total diagonals

={ }^{15} {C}_{2}-15=90

Shortest diagonal

=

Diagonal connecting

({A}_{1} {A}_{3}, {A}_{2} {A}_{4}, \.....)

= 15

longest diagonal = Diagonal connecting

({A}_{1} {A}_{8}, {A}_{1} {A}_{9}, \.....)

= 15

Required probability

= {90-15-15}/{90}

={60}/{90}={2}/{3}

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