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 ≤ *r* < *b*

**D. ** 0 < *r* ≤ *b*

**Answer : ****Option C**

**Explaination / Solution: **

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No Explaination.

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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. ** 1, 3, 5

**Answer : ****Option A**

**Explaination / Solution: **

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

**A. ** 4

**B. ** 2

**C. ** 1

**D. ** 3

**Answer : ****Option B**

**Explaination / Solution: **

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

**A. ** 1

**B. ** 2

**C. ** 3

**D. ** 4

**Answer : ****Option C**

**Explaination / Solution: **

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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

**Answer : ****Option D**

**Explaination / Solution: **

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7^{4k} ≡
_____ (mod 100)

**A. ** 1

**B. ** 2

**C. ** 3

**D. ** 4

**Answer : ****Option A**

**Explaination / Solution: **

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Given *F*_{1}
= 1 , *F*_{2 }= 3 and *F*_{n} = *F*_{n}_{−1}
+ *F*_{n}_{−2 }then *F*_{5} is

**A. ** 3

**B. ** 5

**C. ** 8

**D. ** 11

**Answer : ****Option D**

**Explaination / Solution: **

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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

**Answer : ****Option C**

**Explaination / Solution: **

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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

**Answer : ****Option A**

**Explaination / Solution: **

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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. ** 62m

**C. ** 31m

**D. ** 31/2 m

**Answer : ****Option C**

**Explaination / Solution: **

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