#### Numbers and Sequences Book Back Questions

10th Standard EM

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
6 x 1 = 6
1. 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)

$\le$ r < b

(d)

0 < r $\le$ b

2. 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

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

4. Given F1 = 1, F2 = 3 and Fn = Fn-1+Fn-2 then F5 is

(a)

3

(b)

5

(c)

8

(d)

11

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

(a)

0

(b)

6

(c)

7

(d)

13

6. 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

7. 3 x 2 = 6
8. Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

9. Find the remainders when 70004 and 778 is divided by 7

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

11. 2 x 5 = 10
12. In the given factor tree, find the numbers m and n.

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

14. 1 x 8 = 8
15. A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?