Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.

4

(a)

Use Euclid's division algorithm to the HCF of the following three numbers.
(i) 441, 567 and 693
(ii) 1620, 1725 and 255

4

(a)

If the LCM of 26 and 91 is 182. find their HCF.

4

(a)

If the HCF of 150 and 100 is 50, find the LCM of 150 and 100.

4

(a)

Without actually performing the long division, state whether \(\frac{543}{225}\) has a terminating decimal expansion or non-terminating recurring decimal expansion.

4

(a)

The decimal expansion of the rational number \(\frac { 43 }{ { 2 }^{ 4 }\times { 5 }^{ 3 } } \) will terminate after how many places of decimal?

4

(a)

Prove that \(\sqrt { 5 } \) is irrational number.

4

(a)

Prove that \(3+2\sqrt { 5 } \) is irrational.

4

(a)

In the next Republic Day parade, the commander of an army contingent consisting of 624 members wants to march his contingent behind an army band of 32 members such that the two groups march in the same number of columns.
(i) What is the maximum number of columns in which the two groups can march?
(ii) What value is depicted from this action?

4

(a)

See the following factor tree for factorisation of 156. Find the value of a.

4

(a)