Question : In a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?

Option 1: 4(AD + BE + CF) > 3(AB + BC + AC)

Option 2: 2(AD + BE + CF) > (AB + BC + AC)

Option 3: 3(AD + BE + CF) > 4(AB + BC + AC)

Option 4: AB + BC + AC > AD + BE + CF

Question : If $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers, $x$ equals to:

Option 1: $\frac{2abc}{ab+bc–ac}$

Option 2: $\frac{2abc}{ab+ac–bc}$

Option 3: $\frac{2abc}{ac+bc–ab}$

Option 4: $\frac{2abc}{ab+bc+ac}$

Question : Simplify the following expression:
$\frac{\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2}{b^2-c^2}$

Option 1: $3a^2$

Option 2: $4a^2$

Option 3: $5a^2$

Option 4: $2a^2$

Question : Simplify the expression:
$(c+d)^2-(c-d)^2$

Option 1: $4cd$

Option 2: $\left(c^2+d^2\right)$

Option 3: $2\left(c^2+d^2\right)$

Option 4: $2cd$

Question : The simplified value of the following is:
$\left (\frac{3}{15}a^{5}b^{6}c^{3}\times \frac{5}{9}ab^{5}c^{4} \right )\div \frac{10}{27}a^{2}bc^{3}$.

Option 1: $\frac{9a^{2}bc^{4}}{10}$

Option 2: $\frac{3ab^{4}c^{3}}{10}$

Option 3: $\frac{3a^{4}b^{10}c^{4}}{10}$

Option 4: $\frac{1a^{4}b^{4}c^{10}}{10}$