## Number System

Question 1 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

12:12 PM | |

12:10 PM | |

None of these | |

12:11 PM |

LCM of 48 and 50 secs.

48 = 2*2*2*2*3;

50 = 2*5*5;

LCM = 2*2*2*2*3*5*5 = 1200 secs

= 20 min.

They will beep together at 12:20.

Question 2 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

52 | |

46 | |

42 | |

40 |

2nd no. = x (let)

3rd no. = x+2

4th no. = x+x+2 = 2x+2

5th no. = x+2 + 2x+2 = 3x+4

Sixth no.,

3x+4 + 2x+2 = 26

5x = 20

x = 4

7th no. = 26 + 3x+4 = 26 + 3*4+4 = 42.

Question 3 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

^{th}as long as the rest of the string, then the difference between the larger piece and the shorter piece is :

53 m | |

85 m | |

76 m | |

58 m |

Now,

x + (9x/4) = 221 m

x = 68 meter

and, (9x/4) = 153 m

Difference between two parts = 153 - 68 = 85m.

Question 4 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

18 | |

11 | |

28 | |

26 |

Note: 1 is not a prime number.

**Definition :** A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

Question 5 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

^{6n}- 6

^{6n}, where n is an integer >0, is divisible by

All of these | |

127 | |

13 | |

559 |

7^{6n}-6^{6n} = 7^{6} -6^{6}

= (7^{3})^{2}-(6^{3})^{2}

= (7^{3}-6^{3})( 7^{3}+6^{3})

= (343-216)*(343+216)

= 127*559.

= 127 * 13 *43.

Clearly, it is divisible by 127, 13 as well as 559.

Question 6 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

^{2720}is

1 | |

3 | |

7 | |

9 |

(30)^{2720}, we can write it as[(30)^{4}]^{680}

Or,[(10*3)^{4}]^{680}

The right most non-zero digit depends on the unit digit of [(3)^{4}]^{680}.

Unit digit of [(3)^{4}]^{680},

Or, (81)^{680}

The unit digit of 81 is 1 so any power of 81 will always give its unit digit as 1.

Thus, required unit digit is 1.

Question 7 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

814 | |

840 | |

820 | |

841 |

Length of the room = 15 m 17 cm = 15 *100 +17 = 1517 cm.

Breadth of the room = 9 m 2 cm = 902 cm.

The HCF of the 1517 and 902 will be size of square tiles.

HCF 1517 and 902 = 41 cm.

Area of the room = length * breadth = 1517 * 902 cm^{2}.

Area of tiles = 41 *41 cm^{2}1

So, no. of tiles required = (1517 *902) /(41*41) = 814 tiles.

Question 8 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

28, 52, 53 | |

30, 55, 56 | |

Cannot determined | |

29, 52, 53 |

Since, the magazine has 84 pages it means that there are 21 sheets of paper, which are folded in the middle. The pattern of pages will be this way,

Left | Right |

1, 2 | 83,84 |

3, 4 | 81, 82 |

- - - - | - - - - |

29, 30 |

Question 9 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

6 | |

5 | |

9 | |

8 |

So, (3+8+1+A) = must be divisible by 9;

Thus, smallest natural number be 6.

Or, (3+8+1+6) = 18, this is divisible by 9.

Question 10 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें) |

(45,495)(30,330) | |

(57,627)(285,399) | |

(37,575)(270,390) | |

(45,575)(280,890) |

Hence, numbers are multiples of 57.

Let, the numbers be 57x and 57y, where x and y are prime to each other.

According to the sum,

57x+57y = 684;

Or, x+y = 12;

Hence, required possible pair of values of x and y which are prime to each other are (1, 11) and (5, 7).

Thus, required pairs of numbers are;

{57*1 = 57 and 57*11 = 627}

{57*5 = 285 and 57*7 = 399 }