Question : If $x+y+z = 9$, then the value of $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ is:

Option 1: 6

Option 2: 9

Option 3: 0

Option 4: 1

Question : If A : B = 2 : 3 and B : C = 3 : 7, then (A + B) : (B + C) : (C + A) is:

Option 1: 4 : 8 : 9

Option 2: 5 : 8 : 9

Option 3: 5 : 10 : 9

Option 4: 4 : 10 : 9

Question : Find the value of the given expression:
$10 \div 5 × 1+3 - [8 - \{5 - (7 - 7 - 9)\}]$

Option 1: 11

Option 2: 10

Option 3: 9

Option 4: 8

Question : If $a^3=117+b^3$ and $a=3+b$, then the value of $(a+b)$ is:

Option 1: $\pm 7$

Option 2: $\pm 49$

Option 3: $\pm 13$

Option 4: $0$

Question : If $3\sqrt{\frac{1-a}{a}}+9=19-3\sqrt{\frac{a}{1-a}};$ then, what is the value of $a?$

Option 1: $\frac{3}{10}$ and $\frac{7}{10}$

Option 2: $\frac{1}{10}$ and $\frac{9}{10}$

Option 3: $\frac{2}{5}$ and $\frac{3}{5}$

Option 4: $\frac{1}{5}$ and $\frac{4}{5}$