Home
Class 12
MATHS
The number of positive integer solutions...

The number of positive integer solutions of a+b+c=60, where a is a factor of b and c, is

A

184

B

200

C

144

D

270

Text Solution

Verified by Experts

The correct Answer is:
C
`because` a is a factor of b and `cimpliesa` divides 60
`thereforea=1,2,3,4,5,6,10,12,15,30" "[because a ne60]`
and b=ma, c=na, when m, `n ne 1`
`because a+b+c=60`
`impliesa+ma+na=60 impliesm+n=((60)/(a)-1)`
`therefore`Number of solutions`=.^((60)/(a)-1-1)C_(2-1)=((60)/(a)-1)`
Hence, total number of solutions for all values of a
`=58+28+18+13+10+8+4+3+2+0=144`
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of terms in the expansion of (a+b+c)^(n), where n in N is:

Number of non-negative integral solutions of the equation a+b+c=6 is

The number of solutions of equation z^(2) + barz = 0 , where z in C are

a and b are two positive integers such that the least prime factor of b is 3 and the least prime factor of b is 5. Then, the least prime factor of (a + b) is:

Let n denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_n = the number of such n-digit integers ending with digit 1 and c_n = the number of such n-digit integers ending with digit 0. The value of b_6 , is

The number of positive integers satisfying the inequality C(n+1,n-2) - C(n+1,n-1)<=100 is

Euclids Division Lemma states that for any two positive integers a and b, there exists unique integers q and r such that a=bq+r , where r must satisfy.

The number of points having position vector a hat i + b hat j + c hatk , where 1 leq a,b,cleq10 and a,b,c in N , such that 2^a + 3^b+5^c is a multiple of 4 is

Two positive integers p and q can be expressed as p = ab^(2) and q = a^(3)b, a and b being prime numbers. LCM of p and q is :

If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.