NCERT MATHS Class 10 Ex- 1.1 Q No. 2 : Show that any positive add integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.


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Real Numbers CHAPTER : 1

Symbol of real numbers (ℝ) In mathematics, the real number is the value presented to any amount corresponding to the simple line. Actual numbers include all rational numbers such as -5 and fractional numbers such as 4/3 and all irrational numbers such as √2 (1.41421356 …, square root of 2, an unregulated algebraic number). By incorporating the ample numbers in the actual numbers, they can be presented from the eternal points that can be attributed on a line in the form of a real number line.

Class 10 Exercise 1.1 Question No. 2 : Show that any positive add integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Class 10 Exercise 1.1 Question No. 2 Solutions

Let a be any positive integer and b = 6.

Then, by  Euclid’s algorithm, a = 6q + r for some integer q ≥ 0, and r = 0, 1, 2, 3, 5 because 0 ≤ r 6.

Therefore, a = 6q or 6q  + 1 or 6q + 2 or 6q + 2 or 6q + 3 or 6q + 4 6q + 5

 Also, 6q + 1 = 2 × 3q + 1 = 2k1 + 1, where k1 is a positive integ

6q + 5 = (6q +2) +1 =2 (3q + 1 ) + 1 = 2k2 + 1, where k2 is an integer

6q + 5 = (6q + 4) +1 =2 (3q + 2 ) +1 = 2k3 + 1, where k is an integer clearly,

6q + 1, 6q +3, 6q+5 are of the form 2k3 +1, where k is an integer.

Therefore, 6q + 1, 6q + 3, 6q + 5 are mpt exactly divisible by 2.

Hence, these expressions of numbers are odd numbers.

And therefore, any odd integer can be expressed in  the form 6q + 1, or 6q + 5

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NCERT MATHS Class 10 Ex- 1.1 Q No. 3 : An army contingent of 616 members is to march behind an army……….

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