The following real numbers have decimal expansions as given below. In each case,


2

155

March 30, 2019

Write down the decimal expansions of those rational numbers in the question 1,


2

85

March 30, 2019

Without actually performing the long division, state whether the following rational numbers


2

557

March 30, 2019

Prove that the following are irrational


2

126

March 30, 2019

Show that 3 + √5 is irrational


2

74

March 30, 2019

Prove that √5 is irrational


2

97

March 30, 2019

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field,


2

351

March 30, 2019

Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers


2

185

March 30, 2019

Check whether 6n can end with the digit 0 for any natural number n


2

943

March 30, 2019

Given that HCF (306, 657) = 9, find LCM (306, 657)


2

695

March 30, 2019

Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21


2

433

March 30, 2019

Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of two numbers,


2

241

March 30, 2019

Express each number as a product of its prime factors: (i) 140


2

1054

March 30, 2019

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8


2

287

March 30, 2019

Use Euclid’s division lemma to show that the square of any positive integer is either of the form


2

318

March 30, 2019

An army contingent of 616 members is to march behind an army band of 32 members in a parade


1

179

March 30, 2019

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer


2

1139

March 30, 2019

Use Euclid’s Division Algorithm to find the HCF of: (i) 135 and 225


2

1162

March 30, 2019

Which of the following statements is NOT true for all real numbers a and b?


1

712

March 20, 2018
