Answer :
Let's break down the questions one by one:
What is the place value of 6 in the greatest 4-digit number formed using the digits 4, 5, 6, and 9 without repetition?
To form the greatest 4-digit number from the digits 4, 5, 6, and 9 without repeating any digits, we would arrange them in descending order: 9, 6, 5, 4. So the greatest number is 9654.
In 9654, the digit 6 is in the hundreds place. Therefore, the place value of 6 is calculated as:
[tex]6 \times 100 = 600[/tex]
Therefore, the correct option is c. 600.
The expanded form of a number is [tex]6 \times 10000 + a \times 1000 + 6 \times 100 + 5 \times 10 + 4[/tex]. What is the greatest possible value of [tex]a[/tex] from the given options, if the number is smaller than 64,000?
The expression given is:
[tex]60000 + a \times 1000 + 600 + 50 + 4
= 60654 + a \times 1000[/tex]To ensure this number is less than 64,000, we need:
[tex]60654 + a \times 1000 < 64000[/tex]
Rearranging gives:
[tex]a \times 1000 < 64000 - 60654[/tex]
[tex]a \times 1000 < 3346[/tex]
Since [tex]a[/tex] is a single-digit number, the greatest possible value is 3, as incrementing to 4 would violate the inequality. Therefore, the correct option is c. 3.
A clock in our house loses a second every half a minute. How many minutes will it lose in a day?
A day contains 24 hours, and each hour has 60 minutes, so:
[tex]24 \times 60 = 1440 \text{ minutes per day}[/tex]
If the clock loses a second every half minute, then in one minute, it loses 2 seconds. Thus, in 1440 minutes, it will lose:
[tex]1440 \times 2 = 2880 \text{ seconds}[/tex]
Convert seconds to minutes (since 60 seconds = 1 minute):
[tex]\frac{2880}{60} = 48 \text{ minutes}[/tex]
Therefore, the clock will lose 48 minutes in a day. Hence, the correct option is b. 48.
A customer purchases a new computer under an exchange scheme by giving his old computer and paying ₹15,200 cash. If the actual price of the new computer is ₹24,800 how much is the old computer worth?
The equation to solve this is:
[tex]\text{Value of old computer} + 15200 = 24800[/tex]
Solving for the value of the old computer:
[tex]\text{Value of old computer} = 24800 - 15200[/tex]
[tex]\text{Value of old computer} = 9600[/tex]
Therefore, the old computer is worth ₹9,600. Hence, the correct option is a. ₹9,600.
The smallest 4-digit number formed by using the digits 3, 0, 5, 7, and 1 without repetition will have:
To form the smallest 4-digit number using the digits 3, 0, 5, 7, and 1 without repetition, ensure the first digit is the smallest non-zero digit. Thus, we choose 1 for the thousands place, then arrange the remaining digits in ascending order: 0, 3, 5, and 7.
The smallest possible number is 1035, so the thousands place will have 1. Hence, the correct option is d. 1 in thousand's place.
