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### Advanced Maths By Rakesh Yadav

The last Digit of the number is called Unit Digit 1 2 3 4 unit digit In This no. 4 is a unit digit.

The unit digit of the Resultant value depends upon The unit digit of all participating numbers.

Ex.1: 23 + 34 + 46 + 78 = 181, unit digit of 181.

Sol. \ unit digit = 1 It is clear that the unit digit of the Resultant value 181 depends upon the unit digits 3,

4, 6, 8

3 + 4 + 6 + 8 = 21

So, units digit = 1

Ex.2: What is the unit digit of? 31 × 37 × 36 × 46 × 89

sol. 31 × 37 × 36 × 46 × 89 Unit digit = 1, 7, 6, 6, 9 multiply the unit digits = 1 × 7 × 6 × 6 × 9

1 × 7 = 7

7 × 6 = 42

2 × 6 = 12

2 × 9 = 18

unit digit = 8

Ex.3: What is the unit digit of? 31 × 33 × 37 × 39 × 43 Sol. 31 × 33 × 37 × 39 × 43 multiply the unit digits

= 1 × 3 × 7 × 9 × 3 unit digit = 7

Ex.4: What is the unit digit of ? 91 × 93 × 95 × 96 × 97 × 98

Sol. multiply the unit digit 1 × 3 × 5 × 6 × 7 × 8 = 0

Ex.5: Find the unit digit of 135 × 136 × 170

Sol. The unit digits = 5, 6, 0 multiply the units digit = 5 × 6 × 0

= unit digit = 0

If 78*3945 is divisible by 11 where * is a digit, then * is equal to :

(a) 1 (b) 0 (c) 3 (d)5

When a number is divided by 357 the remainder is 39. If same number is divided by 17, the remainder will be :

(a) 0 (b) 3 (c) 5 (d)11

A number when divided by 6 leaves the remainder of 3. When the square of the same number is divided by 6, the remainder is :

(a) 0 (b) 1 (c) 2 (d)3

When a number is divided by 893, the remainder is 193. What will be the remainder when it is divided by 47?

(a) 3 (b) 5 (c) 25 (d)33

A number divided by 13 leaves a remainder of 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65?

(a) 28 (b) 16 (c) 18 (d)40

Which of the following number is NOT divisible by 18?

(a)54036 (b)50436

(c)34056 (d)65043

If n is an integer, then (n3n) is always divisible by :

(a) 4 (b) 5 (c) 6 (d)7

A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc. Any number of this form is always

exactly divisible by:

(a)7 only (b)11 only

(c)13 only (d) Smallest 3

digit prime number

If two numbers are each divided by the same divisor, the remainders are respectively 3 and 4. If the sum of the two

numbers are divided by the same divisor, the remainder is The divisor is :

(a) 9 (b) 7 (c) 5 (d)3

A number when divided by 5 leaves the remainder 3. What is the remainder when the square of the same number is

divided by 5?

(a) 1 (b) 2 (c) 3 (d)4

Author | – |

Language | English |

No. of Pages | 653 |

PDF Size | 20 MB |

Category | Mathematics |

Source/Credits | drive.google.com |

Rakesh Yadav Advance Math Book PDF Free Download