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 : If $m$ and $n$ are two positive real numbers such that $9 m^2+n^2=40$ and $mn = 4$, then the value of $3m + n$ is:

Option 1: 160

Option 2: 64

Option 3: 10

Option 4: 8

Question : Directions: If 1 * 2 = 1, 2 * 3 = –1 and  3 * 4 = –5, then find the value of 7 * 9 = ?

Option 1: –47

Option 2: –29

Option 3: –2

Option 4: –9

Question : $\triangle$LMN is right angled at M. If $\angle$N = 45$^\circ$, what is the length of MN (in cm), if NL = 9$\sqrt2$cm?

Option 1: $9\sqrt2$

Option 2: $\frac{9}{\sqrt2}$

Option 3: $18$

Option 4: $9$

Question : If $\frac{\cos\alpha}{\cos\beta}= m$ and $\frac{\cos\alpha}{\sin\beta}= n$, then the value of $(m^{2}+n^{2})\cos^{2}\beta$ is:

Option 1: n²

Option 2: m²

Option 3: mn

Option 4: 1