Multiple choice questions

Multiple choice questions

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.

(1) 1 < r < b

(2) 0 < r < b

(3) 0 ≤ r < b

(4) 0 < r â‰¤ b

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

(1) 0, 1, 8

(2) 1, 4, 8

(3) 0, 1, 3

(4) 1, 3, 5

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

(1) 4

(2) 2

(3) 1

(4) 3

4. The sum of the exponents of the prime factors in the prime factorization of 1729 is

(1) 1

(2) 2

(3) 3

(4) 4

5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(1) 2025

(2) 5220

(3) 5025

(4) 2520

6. 74k â‰¡ _____ (mod 100)

(1) 1

(2) 2

(3) 3

(4) 4

Solution

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

(1) 3

(2) 5

(3) 8

(4) 11

Solution

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.

(1) 4551

(2) 10091

(3) 7881

(4) 13531

Solution

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

(1) 0

(2) 6

(3) 7

(4) 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

(1) 16 m

(2) 62m

(3) 31m

(4) 31/2 m

Solution

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 ?

(1) 6

(2) 7

(3) 8

(4) 9

12. If A = 265 and B = 2 64  + 2 63 + 2 62 + … + 20 which of the following is true?

(1) B is 264 more than A

(2) A and B are equal

(3) B is larger than A by 1

(4) A is larger than B by 1

13. The next term of the sequence  is

(1) 1/24

(2) 1/27

(3) 2/3

(4) 1/81

14. If the sequence t1 , t 2,t3,... are in A.P. then the sequence t 6 , t12 , t18,... is

(1) a Geometric Progression

(2) an Arithmetic Progression

(3) neither an Arithmetic Progression nor a Geometric Progression

(4) a constant sequence

15. The value of (13 + 2 3 + 3 3 +  + 15 3 ) − (1 + 2 + 3 +  + 15) is

(1) 14400

(2) 14200

(3) 14280

(4) 14520

Answers: