JEE Main2007MathematicsDeterminantsActual
If D= | array ccc 1 & 1 & 1 1 & 1+x & 1 1 & 1 & 1+y array | for x 0, y 0 then D is
Options
- Adivisible by neither x nor y
- Bdivisible by both x and y
- Cdivisible by x but not y
- Ddivisible by y but not x
Correct answer
B. divisible by both x and y
Step-by-step solution
D= | array ccc 1 & 1 & 1 1 & 1+x & 1 1 & 1 & 1+y array | C ₂ C ₂- C ₁ & C ₃ C ₃- C ₁ | array lll 1 & 0 & 0 1 & x & 0 1 & 0 & y array |=x y . Hence D is divisible by both x and y .