Question

# The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

- 93324
- 66666
- 84844
- None of these

Hint:

### We start solving the problem by finding the total possibilities of getting numbers by fixing each digit in unit place. We then find the sum of all the numbers present in the unit place. Similarly, we multiply 10 for the sum of digits in tenth place, 100 for the sum of digits in tenth place and 1000 for the sum of digits in thousandth place. We then add all these sums to get the required answer.

## The correct answer is: 93324

### Detailed Solution

According to the problem, we need to find the sum of all the numbers that can be formed with the digits 2,3,4,5 taken all at a time.

Let us first fix a number in a unit place and find the total number of words possible due on fixing this number.

We need to arrange the remaining three places with three digits. We know that the number of ways of arranging n objects in n places is n! ways.

So, we get 3! = 6 numbers on fixing the unit place with a particular digit.

Now, let us find the sum of all digits.

We use the same digits in ten, hundred and thousand places also. So, the sum of those digits will also be 84 but with the multiplication of its place value.

i.e., We multiply the sum of the digits in tenth place with 10, hundredth place with 100 and so on. We then add these sums.

Thus, the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) : 93324

Alternatively, we can use the formula for the sum of numbers as

We can also solve this problem by writing all the possible numbers and finding the sum of them which will be time taking and make us confused. We should know that the value of the digits is determined by the place where they were present. We should check whether there is zero in the given digits and whether there are any repetitions present in the numbers. Similarly, we can expect problems to find the sum of numbers formed by these digits with repetition allowed.

### Related Questions to study

### Total number of divisors of 480, that are of the form 4n + 2, n 0, is equal to :

In this question, we have been asked to find the total number of divisors of 480 which are of the form 4n + 2, n 0

In order to solve this question, we should know that the number of the divisor of any number

where a, b, c are prime numbers and is given by (m + 1) (n + 1) (p + 1)…..

We know that 480 can be expressed as

Now, we have been asked to find the number of divisors which are of the form 4n + 2 = 2 (2n + 1), which means odd divisors cannot be a part of the solution.

Now, we can say the total number of even divisors are = all divisors – odd divisor = 24 - 4 = 20

Now, we have been given that the divisor should be of 4n + 2, which means they should not be a multiple of 4 but multiple of 2. For that, we will subtract the multiple of 4 which are divisor of 480 from the even divisors.

And, we know that,

Hence, we can say that there are 16 divisors of 480 which are multiple of 4.

Thus, total number of divisors of 480, that are of the form 4n + 2, n 0, is equal to 4.

### Total number of divisors of 480, that are of the form 4n + 2, n 0, is equal to :

In this question, we have been asked to find the total number of divisors of 480 which are of the form 4n + 2, n 0

In order to solve this question, we should know that the number of the divisor of any number

where a, b, c are prime numbers and is given by (m + 1) (n + 1) (p + 1)…..

We know that 480 can be expressed as

Now, we have been asked to find the number of divisors which are of the form 4n + 2 = 2 (2n + 1), which means odd divisors cannot be a part of the solution.

Now, we can say the total number of even divisors are = all divisors – odd divisor = 24 - 4 = 20

Now, we have been given that the divisor should be of 4n + 2, which means they should not be a multiple of 4 but multiple of 2. For that, we will subtract the multiple of 4 which are divisor of 480 from the even divisors.

And, we know that,

Hence, we can say that there are 16 divisors of 480 which are multiple of 4.

Thus, total number of divisors of 480, that are of the form 4n + 2, n 0, is equal to 4.

### If ^{9}P_{5} + 5 ^{9}P_{4} = , then r =

Here we need to find the value of the given variable.

The given expression is :

### If ^{9}P_{5} + 5 ^{9}P_{4} = , then r =

Here we need to find the value of the given variable.

The given expression is :

### Assertion (A) :If , then

Reason (R) :

### Assertion (A) :If , then

Reason (R) :

A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

Or (i)

Potential energy at (ii)

Kinetic energy potential energy

A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

Or (i)

Potential energy at (ii)

Kinetic energy potential energy