1.

Which of the following statements given below are correct?A: Unit digit of 13123 is 7.B: (31224 – 19224) is completely divisible by 12.C: HCF of 72, 48 and 64 is 4. 1. Only A2. Only A and B3. Only B and C4. All A, B and C

Answer» Correct Answer - Option 2 : Only A and B

CALCULATION:

A:

Below given is the chart of cyclicity of the number:

Numbers

Cyclicity

1, 5, 6

1

4, 9

2

2, 3, 7, 8

4


13123 can be written as: (134)30 × 133

Unit digit of (134)30 is 1 while unit digit of 133 is 7.

Hence, required unit digit = 7

B:

We know that:

(an – bn) is divisible by (a + b) if n is even

So, (31224 – 19224) is completely divisible by (31 – 19) which is 12.

C:

72 = 2 × 2 × 2 × 3 × 3 = 23 × 32

48 = 2 × 2 × 2 × 2 × 3 = 24 × 31

64 = 2 × 2 × 2 × 2 × 2 × 2 = 26

Hence, HCF = 23 = 8

Hence, only A and B are TRUE. 


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