Question : If $M = 0.1 + (0.1)^2 + (0.01)^2$ and $N = 0.3 + (0.03)^2 + (0.003)^2$, then what is the value of $(M+ N)$?

Option 1: 0.411009

Option 2: 0.413131

Option 3: 0.313131

Option 4: 0.131313

Question : If $m+n=1$, then the value of $m^{3}+n^{3}+3mn$ is equal to:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $m-n=2$ and $mn=15,(m,n>0)$ , then the value of $(m^2-n^2)(m^3-n^3)$ is:

Option 1: 1856

Option 2: 1658

Option 3: 1586

Option 4: 1568

Question : The value of $\frac{0.7× 0.7× 0.7+0.3 × 0.3 × 0.3}{0.7 × 0.7-0.7× 0.3+0.3 × 0.3}$ is_____.

Option 1: 2

Option 2: 1

Option 3: 3

Option 4: – 1

Question : If $\tan A = n\tan B$ and $\sin A=m \sin B$, then the value of $\cos^{2}A$ is:

Option 1: $\frac{m^{2}-1}{n^{2}+1}$

Option 2: $\frac{m^{2}+1}{n^{2}-1}$

Option 3: $\frac{m^{2}+1}{n^{2}+1}$

Option 4: $\frac{m^{2}-1}{n^{2}-1}$

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