Answer :
1. Place Value of 6
To find the place value of 6 in the greatest 4-digit number formed using the digits 4, 5, 6, and 9 without repetition, we arrange the digits in descending order: 9654. Here, the place value of 6 is in the hundreds place. Thus, the place value of 6 is $600$.
Answer: c. 600
2. Greatest Possible Value of 'a'
The expanded form of the number is given as $6 \times 10000 + a \times 1000 + 6 \times 100 + 5 \times 10 + 4$. We need the number to be smaller than 64,000. Start by estimating:
- If [tex]a = 7[/tex]: 60,000 + 7,000 = 67,000 (Too large)
- If [tex]a = 4[/tex]: 64,000 exactly, which is not smaller, hence, incorrect.
- If [tex]a = 3[/tex]: 63,000, which fits as smaller.
Therefore, using the trial method, [tex]a=3[/tex] yields a number less than 64,000.
Answer: c. 3
3. Time Lost by the Clock
The clock loses 1 second every 30 seconds. To find how many seconds it loses in a day (24 hours or 86,400 seconds), calculate:
[tex]\frac{86400}{30} = 2880 \text{ seconds}\, \text{lost per day}.[/tex]
Convert this time to minutes:
[tex]\frac{2880}{60} = 48 \text{ minutes}.[/tex]
Answer: b. 48
4. Worth of the Old Computer
The actual price of the new computer is ₹24,800. The customer paid ₹15,200 in cash.
Calculating the old computer's value:
[tex]24,800 - 15,200 = ₹9,600.[/tex]
Answer: a. ₹9,600
5. Smallest 4-digit Number
To form the smallest 4-digit number using digits 3, 0, 5, 7, and 1 without repetition (must start with non-zero), place the smallest digit first. Starting with 1, place the next smallest: 1,035. The zero cannot be in the thousand's place.
Answer: d. 1 in thousand's place
II. Specific Tasks
Write the number 93,345,637 in systems:
- Indian System: 9,33,45,637
- International System: 93,345,637
Greatest 6-digit number without repetition from 8, 7, 0, 1, 9, 3:
- Arrange in descending order: 987,310
Difference in place values of 4 in 32246245:
- First 4 (thousand's place): 4000
- Second 4 (units): 4
- Difference: [tex]4000 - 4 = 3996[/tex]
Ascending Order:
- 9,84,671; 37,63,214; 37,90,423; 1,83,40,217; 1,84,31,056
Descending Order:
- 1,84,31,056; 1,83,40,217; 37,90,423; 37,63,214; 9,84,671