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In this article you will get the NCERT Solutions for CBSE Class 10 Mathematics chapter, Real Numbers. You will get detailed and accurate solutions to all the NCERT questions. Download all NCERT solutions in PDF format
Some of the questions and their solutions from NCERT Solutions for Class 10 Maths: Real Numbers, are as follows:
Q.┬аShow that any positive odd integer is of the form 6q┬а+ 1, or 6q┬а+ 3, or 6q┬а+ 5, where┬аq┬аis some integer.
Sol.
By EuclidтАЩs algorithm,
┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а a┬а= 6q┬а+┬аr, and┬аr┬а= 0, 1, 2, 3, 4, 5
Hence,┬аa┬а= 6q┬аor 6q┬а+ 1 or 6q┬а+ 2 or 6q +┬а3 or 6q┬а+ 4 or 6q┬а+ 5
`Clearly, 6q┬а+ 1, 6q┬а+ 3, 6q┬а+ 5 are of the form 2k┬а+ 1, where┬аk┬аis an integer.
Therefore, 6q┬а+ 1, 6q┬а+ 3, 6q┬а+ 5 are not exactly divisible by 2.
Hence, these numbers are odd numbers.
Q.┬аAn army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Sol.
EuclidтАЩs algorithm
┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а 616 = 32 ├Ч 19 + 8
┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а 32 = 8 ├Ч 4 + 0
The HCF (616, 32) is 8.
Therefore, they can march in 8 columns each.