(a) Given that p is a non negative integer, which of these gives positive integers that are multiple of 5
(1) 10 p and 10 p +2 (2) 10p and 10p +3 (3) 10p and 10p +4 (4) 10 p and 10p +5
(b) Which of the following is an irrational number
(1) 12/18 (2) V3 / 3V5 (3) V5/v20 (4) V63/ V7
c)
(c) Rahul has 40 cm long red and 84 cm long blue ribbon He cuts each ribbon into pieces such that all
pieces are of equal length. What is the length of each piece
(1) 4 cm as it is the LCM(40,84) (2) 4 cm as it is the HCF (40,84) (3) 8 cm as it is the LCM (40,84)
(4) 8 cm as it is the HCF (40,84)
Answers
a) Given that p is a non negative integer, which of these gives positive integers that are multiple of 5 :-
(1) 10 p and 10 p +2 (2) 10p and 10p +3 (3) 10p and 10p +4 (4) 10 p and 10p +5
Answer :-
given that,
→ P = non negative integer .
so, multiple of 5,
→ 5P
→ 5* 2P = 10P
→ 5 * 3P = 15P = (10P + 5P) = (10P + 5)
therefore, Option (4) is correct answer .
(b) Which of the following is an irrational number
(1) 12/18 (2) √3 / 3√5 (3) √5/√20 (4) √63/ √7
Answer :-
1) 12/18 = 2/3 = p/q and q ≠ 0 , so a rational number .
2) √3 / 3√5 = √3 / (√3 * √3 * √5) = 1/(√3 * √5) = 1/√15 = an irrational number .
3) √5 / √20 = √5 / (√5 * √4) = √5 / 2√5 = 1/2 = a rational number .
4) √63 / √7 = √7 * √9 / √7 = 3 = a rational number .
(c) Rahul has 40 cm long red and 84 cm long blue ribbon He cuts each ribbon into pieces such that all pieces are of equal length. What is the length of each piece
(1) 4 cm as it is the LCM(40,84)
(2) 4 cm as it is the HCF (40,84)
(3) 8 cm as it is the LCM (40,84)
(4) 8 cm as it is the HCF (40,84)
Answer :-
Length of each piece will be HCF of 40cm and 84cm .
so,
→ 40 = 2 * 2 * 2 * 5
→ 84 = 2 * 2 * 3 * 7
HCF = 2 * 2 = 4 .
therefore, option (2) is correct answer .
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Answer:
10p and 10p+5 is the correct answer