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#### Numbers and Sequences One Mark

10th Standard EM

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 15
15 x 1 = 15
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. The sum of the exponents of the prime factors in the prime factorization of 1729 is

(a)

1

(b)

2

(c)

3

(d)

4

5. 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

6. 74k $\equiv$ ________ (mod 100)

(a)

1

(b)

2

(c)

3

(d)

4

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

(a)

3

(b)

5

(c)

8

(d)

11

8. The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

(a)

4551

(b)

10091

(c)

7881

(d)

13531

9. 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

10. An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

(a)

16 m

(b)

62 m

(c)

31 m

(d)

$\frac { 31 }{ 2 }$

11. 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

12. If A = 265 and B = 264+263+262+...+20 Which of the following is true?

(a)

B is 264 more than A

(b)

A and B are equal

(c)

B is larger than A by 1

(d)

A is larger than B by 1

13. 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)

$\frac { 1 }{ 81 }$

14. 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

15. The value of (13+23+33+...153) - (1+2+3+...+15)is

(a)

14400

(b)

14200

(c)

14280

(d)

14520