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## Number System: Cyclicity Test-1

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Question 1 |

What will be the unit digit of 13

^{41 }?3 | |

0 | |

1 | |

9 |

Question 1 Explanation:

As we know the last digit depends upon the unit digit of the multiplier numbers so the unit digit of 13

is same as the last digit of 3

On dividing the number 41 with 4 and we will get the remainder as 1 and the last digit will be 3

^{41 }is same as the last digit of 3

^{41}and we know that the cyclicity of 3 is 4On dividing the number 41 with 4 and we will get the remainder as 1 and the last digit will be 3

^{1}= 3Question 2 |

What will be the unit digit when 45

^{45}5 | |

0 | |

1 | |

9 |

Question 2 Explanation:

Here the last digit is depend upon the 5

The cyclicity of 5 is 1 so there is no need to divide the power with 1

because whatever is the power of 5 the last digit will remains 5 so the last

digit of 45

5

5

5

The cyclicity of 5 is 1 so there is no need to divide the power with 1

because whatever is the power of 5 the last digit will remains 5 so the last

digit of 45

^{45}will be 5 .5

^{1}= 55

^{2}= 255

^{3 }= 125Question 3 |

What will be the last digit of 3

^{4 }x 4^{5}x 5^{6}8 | |

0 | |

9 | |

3 |

Question 3 Explanation:

Last digit of 3

Last digit of 4

Last digit of 5

So as we discussed earlier that the last digit depends upon the last digits

So 1 x 4 x 5 = 20 so the last digit is 0; also whenever 5 is multiplied by even

number then last digit will be 0

^{4 }= 1Last digit of 4

^{5}= 4Last digit of 5

^{6 }= 5So as we discussed earlier that the last digit depends upon the last digits

So 1 x 4 x 5 = 20 so the last digit is 0; also whenever 5 is multiplied by even

number then last digit will be 0

Question 4 |

Identify the last digit of (79

^{4 }+ 87^{5})8 | |

0 | |

7 | |

4 |

Question 4 Explanation:

Last digit of 79

Last digit of 87

So the last digit of the whole expression will be 1 +7 = 8

So the last digit will be 8

^{4}is depends upon the the 9^{4}i.e 1Last digit of 87

^{5}is depends upon the the 7^{5}i.e 7So the last digit of the whole expression will be 1 +7 = 8

So the last digit will be 8

Question 5 |

What will be the last digit of 43

^{56}x 5^{67 }x 45^{34}8 | |

5 | |

7 | |

4 |

Question 5 Explanation:

Last digit of 43

divisible by 4 so the last term of 3

Last digit of 5

so that means the last digit of whole of the expression is 1 x 5x 5 = 5 therefore the digit is 5.

^{56 }= 1 because cyclicity of 3 is 4 and 56 is completelydivisible by 4 so the last term of 3

^{4 }is 1.Last digit of 5

^{67}is 5 and last digit of 45^{34}is also 5so that means the last digit of whole of the expression is 1 x 5x 5 = 5 therefore the digit is 5.

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There are 5 questions to complete.

List |

very awesme site it is, very useful for gre

good coverage of concepts..

you can add factorial questions also..!!