Question : Which of the following numbers is a divisor of $\left(49^{15}-1\right)$?

Option 1: 46

Option 2: 14

Option 3: 8

Option 4: 50

Question : The value of $15 \div 8-\frac{5}{4}$ of $\left(\frac{8}{3} \times \frac{9}{16}\right)+\left(\frac{9}{8} \times \frac{3}{4}\right)-\left(\frac{5}{32} \div \frac{5}{7}\right)+\frac{3}{8}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : Directions: Which of the following numbers will replace the question mark (?) in the given series?
$\left [ \frac{1}{176} \right ],\left [ \frac{1}{88} \right ],?,\left [ \frac{1}{22} \right ],\left [ \frac{1}{11} \right ]$

Option 1: $\left[\frac{1}{32}\right]$

Option 2: $\left\lceil\frac{1}{44}\right]$

Option 3: $\left\lceil\frac{1}{48}\right]$

Option 4: $\left\lceil\frac{1}{42}\right]$

Question : If $\frac{1}{x^2+a^2}=x^2-a^2$, then the value of $x$ is:

Option 1: $\left(1-a^4\right)^\frac{1}{4}$

Option 2: $a$

Option 3: $\left(a^4-1\right)^\frac{1}{4}$

Option 4: $\left(a^4+1\right)^\frac{1}{4}$

Question : Directions: Which of the following interchanges of numbers would make the given equation correct?
7 × 4 ÷ 14 + 12 + 30 = 50

Option 1: 12, 14

Option 2: 7, 14

Option 3: 4, 7

Option 4: 30, 50

Question : If ${\left(x-\frac{1}{x}\right)=\sqrt{6}}$ and $x > 1$, what is the value of ${\left(x^8-\frac{1}{x^8}\right)}$?

Option 1: $1024 \sqrt{15}$

Option 2: $992 \sqrt{15}$

Option 3: $998 \sqrt{15}$

Option 4: $1012 \sqrt{15}$