Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

(a)

1 < r < b

(b)

0 < r < b

(c)

0 \(\le\) r < b

(d)

0 < r \(\le\) b

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

(a)

0, 1, 8

(b)

1, 4, 8

(c)

0, 1, 3

(d)

0, 1, 3

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

(a)

4

(b)

2

(c)

1

(d)

3

Given F₁ = 1, F₂ = 3 and F_n = F_n-1 + F_n-2 then F₅ is

(a)

3

(b)

5

(c)

8

(d)

11

If 6 times of 6^th term of an A.P. is equal to 7 times the 7^th term, then the 13^th term of the A.P. is

(a)

0

(b)

6

(c)

7

(d)

13

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

(a)

6

(b)

7

(c)

8

(d)

9

Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

Find the remainders when 70004 and 778 is divided by 7

Find the number of integer solutions of 3x \(\equiv \) 1 (mod 15).

In the given factorisation, find the numbers m and n.

Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?