# Topic: Chapter 2: Numbers and Sequences (Test 1)

Topic: Chapter 2: Numbers and Sequences
Q.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. 0 ≤ r < b
D. 0 < rb
Explaination / Solution:
No Explaination.

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Q.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. 1, 3, 5
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Q.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
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Q.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
Explaination / Solution: Workspace
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Q.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
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Q.6
74k ≡ _____ (mod 100)
A. 1
B. 2
C. 3
D. 4
Explaination / Solution: Workspace
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Q.7
Given F1 = 1 , F2 = 3 and Fn = Fn−1 + Fn−2 then F5 is
A. 3
B. 5
C. 8
D. 11
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Q.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
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Q.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
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Q.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. 62m
C. 31m
D. 31/2 m 