Correct Answer - Option 1 : 1.2223

**Concept used:**

Follow BODMAS rule to solve this question, as per the order given below:

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

formula (a + b)^{2} = a^{2} + 2ab + b^{2}

**Calculations:**

⇒\(\frac{{3 + \;\frac{1}{{2 + \;\frac{1}{3}}}\; \times 7}}{{0.2}} \div 1.2 + 2\sqrt {99} = \;\sqrt a + \;\sqrt b + 5\)

⇒ \(\frac{{3 + \frac{3}{7}\; \times 7}}{{0.2}} \div 1.2 + 2\sqrt {99} = \;\sqrt a + \;\sqrt b + 5\)

⇒ 20 + \(2\sqrt {99} = \;\sqrt a + \;\sqrt b \)

(99 = 11 × 9 and 11 + 9) so we can write by above formula is:

\(\sqrt {11} + \;\sqrt 9 = \;\sqrt a + \;\sqrt b \)

hence a = 11 and b = 9

**∴ a/b = 11/9 = 1.2223**