Question : (mx + n) is a factor of:

Option 1: m²x² + 2nx + n²

Option 2: m²x² + 2mnx + n²

Option 3: m²x² + 2mx + n²

Option 4: m²x² + 2mn + n²

Question : When x^m is multiplied by xⁿ product is 1. The relation between m and n is:

Option 1: mn = 1

Option 2: m = n

Option 3: m + n = 1

Option 4: m = – n

Question : If $m x^m-n x^n=0$, then what is the value of $\frac{1}{x^m+x^n}+\frac{1}{x^m-x^n}$ terms of $x^n$ is: Where $x,m,n$ are $>0$

Option 1: $\frac{2 m n}{x^n(n^2+m^2)}$

Option 2: $\frac{2 m n }{x^n(m^2-n^2)}$

Option 3: $\frac{2 m n}{x^n\left(m^2+n^2\right)}$

Option 4: $\frac{2 m n }{x^n(n^2-m^2)}$

Question : What is the simplified form of the expression (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 - x)?

Option 1: 1 – x⁴⁰

Option 2: 1 – x³²

Option 3: 1 – x¹⁶

Option 4: 1 – x⁴²

Question : If the HCF of xy³, x² y, and x³ y⁴ is xy, then their LCM is________.

Option 1: x³ y⁴

Option 2: x³ y³

Option 3: x⁴ y³

Option 4: x⁴ y⁴

Question : The LCM of (x² − 8x + 15) and (x² − 5x + 6) is:

Option 1: (x − 2) (x − 3) (x − 5)

Option 2: (x − 6)² (x + 1) (x − 3)

Option 3: (x − 6) (x + 1) (x − 3)

Option 4: (x + 6) (x + 1) (x − 3)