Let's go through each of the questions one by one to provide a detailed step-by-step solution:
### (i) Security personnel with code number; 'one minus the negative multiples of 10' will be on duty. The duty list contains code numbers:
The negative multiples of 10 are -10, -20, -30, and so on. By applying the formula 'one minus the negative multiples of 10':
[tex]\[ \text{Code number} = 1 - (-10) = 1 + 10 = 11 \][/tex]
[tex]\[ \text{Code number} = 1 - (-20) = 1 + 20 = 21 \][/tex]
Thus, the code numbers are 11 and 21. The correct option is:
(a) 11,21
### (ii) Five security personnel with code numbers as multiples of 4, when added, give sum '-60' will be on duty:
Checking each option to see which sums to -60:
- (a) [tex]\(20 + 16 + 12 + 8 + 4 = 60\)[/tex]
- (b) [tex]\(-20 + (-16) + (-12) + (-8) + (-4) = -60\)[/tex]
- (c) [tex]\(20 + (-16) + (-12) + (-8) + 4 = -12\)[/tex]
- (d) [tex]\(-20 + (-16) + (-12) + (-8) + 4 = -52\)[/tex]
The correct option with the sum -60 is:
(b) [tex]\(-20, -16, -12, -8, -4\)[/tex]
### (iii) Two security personnel with code numbers such that one code is the fourth multiple of three and one code divided by the other gives -1 as quotient:
The fourth multiple of 3 is [tex]\(4 \times 3 = 12\)[/tex], therefore the numbers must be 12 and -12 since:
[tex]\[ \frac{12}{-12} = -1 \][/tex]
The correct option is:
(c) 12, -12
### (iv) A security personnel with code number [tex]\(= 100 \div 100 \times 10\)[/tex], gave his life for saving the life of the cabinet minister. His code is:
The arithmetic operation:
[tex]\[ 100 \div 100 = 1 \][/tex]
[tex]\[ 1 \times 10 = 10 \][/tex]
So, the code number is 10. The correct option is:
(d) 10
To summarize:
(i) (a) 11,21
(ii) (b) -20, -16, -12, -8, -4
(iii) (c) 12, -12
(iv) (d) 10
