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Maths-

General

Easy

Question

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

10¹⁰ – 9¹⁰ – 1
9¹⁰
10¹⁰ – 8¹⁰
None of these.

The correct answer is: 10¹⁰ – 9¹⁰ – 1

$T o t a l space n u m b e r s space b e t w e e n space 1 space a n d space 10 to the power of 10 space a r e space 10 to the power of 10 minus 2. space open parentheses 2 space i s space s u b t r a c t e d space a s space i t space i n c l u d e s space 1 space a n d space 10 to the power of 10 close parentheses T o t a l space n u m b e r space o f space 10 space d i g i t space n u m b e r space a r e space 9 to the power of 10 B u t comma space t h i s space i n c l u d e s space t h e space n u m b e r space 0000000000 space a s space w e l l. H e n c e comma space t o t a l space n u m b e r space o f space 10 space d i g i t s space n u m b e r space w i t h o u t space 1 space d i g i t space b e t w e e n space 1 space a n d space 10 to the power of 10 equals 9 to the power of 10 minus 1 T h e r e f o r e comma space t h e space t o t a l space n u m b e r s space b e t w e e n space 1 space a n d space 10 to the power of 10 equals 10 to the power of 10 minus 2 minus open parentheses 9 to the power of 10 minus 1 close parentheses equals 10 to the power of 10 minus 9 to the power of 10 minus 1$

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