Question : If $a=\sqrt{6}+\sqrt{5},b=\sqrt{6}-\sqrt{5}$, then $2a^{2}-5\; ab+2b^{2} =?$

Option 1: 38

Option 2: 39

Option 3: 40

Option 4: 41

Question : If $a^{2}+b^{2}+c^{2}=ab+bc+ca,$ then the value of $\frac{a+c}{b}$ is:

Option 1: 3

Option 2: 2

Option 3: 0

Option 4: 1

Question : If $a+b+c=1, ab+bc+ca=-1$ and $abc=-1$, then the value of $a^{3}+b^{3}+c^{3}$ is:

Option 1: 1

Option 2: – 1

Option 3: 2

Option 4: – 2

Question : In $\triangle ABC, \angle B=90^{\circ}$ and AB : BC = 1 : 2. The value of $\cos A+\tan C$ is:

Option 1: $\frac{5+\sqrt{5}}{2 \sqrt{5}}$

Option 2: $\frac{1+\sqrt{5}}{2 \sqrt{5}}$

Option 3: $\frac{2 \sqrt{5}}{2+\sqrt{5}}$

Option 4: $\frac{2+\sqrt{5}}{2 \sqrt{5}}$

Question : If A : B = 3 : 4 and B : C = 6 : 5, then A : ( A + C) is equal to:

Option 1: 9 : 10

Option 2: 10 : 9

Option 3: 9 : 19

Option 4: 19 : 9