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For the following questions answer them individually
If $$x = \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$$, then $$x +\frac{1}{x}$$ =
If $$2^{\alpha}$$ divides 7680, then the largest value of $$\alpha$$ is
The remainder obtained when $$4^{1000}$$ is divided by 7 is
The GCD of two numbers is 23 and their sum is 184. The numbers are
What is the greatest possible length of a scale (in cm) that can be used to measure exactly three cloths of lengths 3m, 5.1 m and 12.9m?
The average of 5 consecutive even integers is 38. What is the product of first and the fifth numbers?
$$\frac{1}{1+\frac{1}{1+\frac{1}{2}}}$$
The gratest among $$\frac{1}{2}, \frac{2}{3}, \frac{3}{5}, \frac{3}{4}$$ is
The desending order of the numbers $$\frac{7}{8}, \frac{5}{6}, \frac{3}{4} and \frac{8}{9}$$ is
The gross income of a person is Rs.22 lakhs. A part of the income is exempted from the tax. The rest of the income is taxed at 30%. If his income after deduction of tax is 19 lakhs, what is the income (in lakhs) exempted from tax?
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