Choose the correct answer in questions 17 to 19:
If a, b, c are in A.P., then the determinant `[{:(x+2,x+3,x+2a),(x+3,x+4,x+3b),(x+4,x+5,x+2c):}]` is :
(a) 0
(b) 1
( c) x
(d) 2x

Answer

(a)

Explanation

a, b, c are in arithmetic progression.
`therefore" "2b=a+c`
`"Now, "[{:(x+2,x+3,x+2a),(x+3,x+4,x+3b),(x+4,x+5,x+2c):}]=[{:(0,0,2a+ac-4b),(x+3,x+4,x+3b),(x+4,x+5,x+2c):}]" "(R_(1)toR_(1)+R_(3)-2R_(2))`
`[{:(0,0,0),(x+3,x+4,x+3b),(x+4,x+5,x+2c):}]" "because (2b=a+b)`
=0