Question

42. If a ac 65024, where a, b and care natural numbers, then what will be the value of (a + 1) (b + 2) (c + 3)?
(A) 108 (B) 105 (C) 125 (D) 120 (E) None of these ​

Answer 1

Answer:

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If a, b, c are three natural numbers in AP and a+b+c=21 then the possible number of values of the ordered triplet (a,b,c) is

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Solution

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Correct option is

C

13

We know that

b=

2

a+c

since they are in A.P

Hence 2b=a+c

2(a+b+c)=42

2a+2c+2b=42

2a+2c+a+c=42

3(a+c)=42

a+c=14

Therefore b=7

Now a,b,cϵN, we get

a=1,c=13,

a=2,c=12

:

:

:

a=13,c=1

Hence we will have 13 ordered pairs of (a,b,c) as a=(1,2,...13)

c=(13,12,11...1) and b=7