JEE Main | 2014Math miscellaneousHard

Question

If (10)9 + 2(11)1 (10)8 + 3(11)2 (10)7+ ... + 10(11)9 = k(10)9, then k is equal to

Options

A.100
B.110
C.
D.

Solution

109 + 2.(11)(10)8 + 3(11)2(10)7 +... + 10(11)9 = k(10)9
x = 109 + 2.(11)(10)8 + 3(11)2(10)7+ ... + 10(11)9
x = 11.108 + 2.(11)2.(10)7 +... + 9(11)9 + 1110

x = 109 + 11(10)8 + 112 × (10)7 +... +119 - 1110
⇒     - = 109 - 1110
⇒     - = (1110 - 1010 ) - 1110 = - 1010
⇒     x = 1011 = k.109
⇒     k = 100

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