Home
Class 12
MATHS
Statement-1: If N the number of positive...

Statement-1: If N the number of positive integral solutions of `x_(1)x_(2)x_(3)x_(4)=770`, then N is divisible by 4 distinct prime numbers.
Statement-2: Prime numbers are 2,3,5,7,11,13, . .

A

`256`

B

`729`

C

`900`

D

`770`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `770=2xx5xx7xx11`
We can assign `2` to `x_(1)`, or `x_(2)` or `x_(3)` or `x_(4)`.
Thus `2` can be assigned in `4` ways similarly each of `5,7,11` can be assigned in `4` ways
No. of solutions `=4xx4xx4xx4=256`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Matching Column Type|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE ENGLISH|Exercise Sovled Examples|22 Videos

Similar Questions

Explore conceptually related problems

If N is the number of positive integral solutions of x_1x_2x_3x_4 = 770 , then N =

If n is the number of positive integral solutions of x_1 x_2 x_3 x_4 = 210 . Then

If N is the number of positive integral solutions of the equation x_(1)x_(2)x_(3)x_(4)=770 , then the value of N is

The number of positive integral solutions of the equation x_(1)x_(2)x_(3)=60 is:

The total number of non-negative integral solutions of x_(1)+x_(2)+x_(3)+x_(4)=100 , is

The number of non-negative integral solutions of x_1+x_2+x_3+4x_4=20 is

The number of integral solutions of (x+1)/(x^2+2)>1/4 is

If n is the number of positive integral solution of x_(1), x_(2)x_(3)x_(4) = 210 , then which of the following is incorrect ?

Find the number of equal positive integral solutions of equation x_1+x_2+x_3=10.

The number of integral solutions of (x+2)/(x^2+1)>1/2 is