`a`
`b`
`c`
`0`
` 1 + x + y + z`
`2 xyz`
`x^2y^2z^2`
`2x^2y^2z^2`
`x/y ` is one of the cube roots of unity
`x` is one of the cube roots of unity
`y` is one of the cube roots of unity
`x/y ` is one of the cube roots of `-1`
-1
24
35
50
62
63
65
68
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
`lamda = 5 ` and `mu != 9`
`lamda = 5 ` and ` mu = 9`
`lamda = 9` and ` mu =5 `
`lamda = 9` and `mu != 5`
`lamda = 5 ` and `mu != 9`
`lamda != 5 ` and ` mu = 7` only
`lamda != 5`` and ` mu ` has any real value
`lamda ` has any real value and `mu != 9`
`p^(3)`
`3p^(3)`
`6p^(3)`
` -6p^(3)`
` - 1/6` or `0`
` - 1` or `0`
` - 1/6` or `1`
` - 1` or `1`
`1` and `2`
`2` and `3`
`1` and `3`
`1, 2` and `3`
`k != 1` and `k != - 2`
`k != 1` and `k != 2`
`k != -1` and `k != - 2`
`k != -1` and `k != 2`
Only `1`
Only `2`
Both `1` and `2`
Neither `1` nor `2`
Only I
Only II
Both I and II
Neither I nor II
`x + y`
`x - y`
`xy`
`1 +x+ y `
`0`
`(a- b)(b- c)(c- a)`
`(a+ b + c)^2`
`(a+ b + c)^3`
`2`
`3`
`4`
`5`
Only `(1, 0)`
Only `(7, 2)`
Either `( 1, 0)` or `(7, 2)`
Neither `(1, 0)` nor `(7, 2)`
non - negative
non - positive
negative
positive
`3`
`2`
`1`
`0`
`abc`
`a+ b + c`
`-(a + b + c)`
`-abc`
Becomes zero
Remains the same
Changes its sign
ls doubled
`a/b` is one of the cube roots of unity
`a/b` is one of the cube roots of `-1`
`a` is one of the cube roots of unity
`b` is one of the cube roots of unity
`2`
`4`
`6`
`-6`
`0`
`abc`
`ab + bc + ca`
`abc(a + b +c)`
`- 9`
`-7`
`7`
`0`
`1, 2`
`-1 ,2`
`1,-2`
`-1, -2`
is a perfect cube
is a perfect square
has linear factor
is zero
`D' = D^2`
`D' = D^3`
`D' = 2D^2`
`D' = 3D^3`
`0`
`x^2 + y^2 + z^2`
`x^2 + y^2 + z^2 + 1`
None of these
`4abc`
`4a^2bc`
`4a^2b^2c^2`
`- 4a^2b^2c^2`
`0`
`1`
`-1`
Can be any real value
`4`
`5`
`6`
`8`
`0`
`3`
`6`
`15`
`alpha`
`beta`
`gamma`
`alpha,beta` and `gamma`
`a^3 + b^3 + c^3`
`3bc`
`a^3 + b^3 + c^3 - 3abc`
`0`
p is one of the cube roots of unity
q is one of the cube roots of unity
p/q is one of the cube roots of unity
None of the above
`-abc`
`abc`
`0`
`1`
`x + 2`
`x^2 + 2`
`2`
`-2`
`-12`
`9`
`13`
`14`
`10`
`20`
`40`
`60`
`2`
`1`
`- 1`
`0`
`12`
`-12`
`7`
`-7`