CAT Exam Model Paper 5 with solutions for free online practice

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Question : 4 of 60

Marks: +1, -0

If ‘a’ is one of the roots of x

^{5}

- 1 = 0 and a ≠ 1, then what is the value of

a ^ { 15 } + a ^ { 16 } + a ^ { 17 } + ......a ^ { 50 } ?

1
5a
35
None of these

Solution:

a ^ { 15 } + a ^ { 56 } + a ^ { 17 } +..... + a ^ { 50 }

{ \Sum } = { a } ^ { 15 } { 1 + { a } + { a } ^ { 2 } + .... + { a } ^ { 35 } }

= a ^ { 15 } \{ { a ^ { 36 } - 1 } /{ a - 1 } \}

where a ≠ 1
Since a is the root of equation x

^5

- 1 = 0.

a ^ { 5 } - 1 = 0 ⇒ a ^ { 5 } = 1

So, Sum

=a ^ { 15 } { { ( a ^ { 5 } ) ^ { 7 } ×a - 1 } /{ a - 1 } } = 1

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