Question

Q14 :} Prove that is irrational if p and q are prime numbers.

Q15 :} Find the largest number which divides 245 and 1205 leaving the remainder

5 in each case.

Q16 :} Find the largest number which divides 303, 455 and 757 leaving the

remainder 3, 5 and 7 respectively.

Q17 :} Prove that is irrational.

Q18 :} Prove that is irrational.

Q19 :} Find the HCF and the LCM of the following by prime factorization.

a) 360 , 756

b) 2x

4

y

3

z , 32x

3

y

4

p

2

Q20 :} Find the HCF by Euclid's Division Algorithm.

a) 256 , 352

b) 450 , 500 , 625

Q21 :} Explain why 7x11x13+13 is a composite number.

Q22 :} Show that any positive odd number is of the form 6q + 1, 6q + 3 or 6q + 5,

where q is an integer.

Q23 :} Show that the square of any positive integer is of the form 3m or 3m + 1,

where m is an integer.

Q24 :} Use Euclid's division lemma to show that the cube of any positive integer is

of the form 9m, 9m + 1, 9m + 8, where m is an integer.

Q25 :} There are 3 consecutive traffic lights which turn "green" after every 36, 42

and 72 seconds. They all were at "green" at 9:00 AM. At what time will they all

turn "green" simultaneously? ​

Answer 1

Answer:

bc,jfskgdkgdkydktdkgdkgziydkgkgzkgxmgj

Step-by-step explanation:

msjidmfkxllxmmkxkfjcklslsjkkzkkxllx