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#### Numbers and Sequences Model Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
1. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(a)

2025

(b)

5220

(c)

5025

(d)

2520

2. 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

3. The next term of the sequence $\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 }$, ..... is

(a)

$\frac { 1 }{ 24 }$

(b)

$\frac { 1 }{ 27 }$

(c)

$\frac { 2 }{ 3 }$

(d)

$\frac { 1 }{ 81 }$

4. If the sequence t1,t2,t3...are in A.P. then the sequence t6,t12,t18,....is

(a)

a Geometric Progression

(b)

an Arithmetic Progression

(c)

neither an Arithmetic Progression nor a Geometric Progression

(d)

a constant sequence

5. 5 x 2 = 10
6. Find the HCF of 396, 504, 636.

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

8. Determine the value of d such that 15 $\equiv$ 3 (mod d).

9. Use Euclid's algorithm to find the HCF of 4052 and 12756.

10. Prove that $\sqrt { 3 }$ is irrational

11. 4 x 5 = 20
12. Can the number 6n, n being a natural number end with the digit 5? Give reason for your answer.

13. Is 7 x 5 x 3 x 2 + 3 a composite number? Justify your answer

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

15. In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

16. 2 x 8 = 16
17. Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.

18. How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?