Question : Simplify the given expression.
$\frac{a^2-b^2-2 b c-c^2}{a^2+b^2+2 a b-c^2}$

Option 1: $\frac{a+b+c}{a-b-c}$

Option 2: $\frac{a-b-c}{a+b-c}$

Option 3: $\frac{a+b-c}{a-b-c}$

Option 4: $\frac{a-b+c}{a+b-c}$

Question : Simplify:
$5 \frac{1}{3}-\left\{4 \frac{1}{3}+\left(3 \frac{1}{3} \div \overline{2 \frac{1}{3}-\frac{1}{3}}\right)\right\}$

Option 1: $\frac{2}{3}$

Option 2: $\frac{1}{3}$

Option 3: $-\frac{1}{3}$

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

Question : What is the value of the given expression?
$\frac{1}{12}+\frac{1}{16}+\frac{1}{8}$

Option 1: $\frac{13}{48}$

Option 2: $\frac{10}{72}$

Option 3: $\frac{3}{48}$

Option 4: $\frac{13}{18}$

Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.

Option 1: $3$

Option 2: $4$

Option 3: $1$

Option 4: $\frac{1}{2}$

Question : Simplify the given expression.
$(1 - 2x)^2 - (1 + 2x)^2$

Option 1: $8x$

Option 2: $-8x$

Option 3: $-(2 + 8x^2)$

Option 4: $2 + 8x^2$

Question : The value of $\frac{a^2-(b-c)^2}{(a+c)^2-b^2}+\frac{b^2-(a-c)^2}{(a+b)^2-c^2}+\frac{c^2-(a-b)^2}{(b+c)^2-a^2}$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 3