Question : If $n= 7+4\sqrt{3}$, the value of $(\sqrt{n}+\frac{1}{\sqrt{n}})$ is:

Option 1: $2\sqrt{3}$

Option 2: $4$

Option 3: $-4$

Option 4: $-2\sqrt{3}$

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 : If $\sqrt{x}=\sqrt{3}-\sqrt{5}$, then the value of $x^2-16x+6$ is:

Option 1: $0$

Option 2: $-2$

Option 3: $2$

Option 4: $4$

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 $\sin  \theta + \operatorname{cosec}  \theta = \sqrt{5}$, the value of $\sin^3 \theta + \operatorname{cosec}^3 \theta = $?

Option 1: $0$

Option 2: $3 \sqrt{5}$

Option 3: $\frac{1}{\sqrt{5}}$

Option 4: $2 \sqrt{5}$