SSC CGL Tier-2 20-February-2018 Maths

Which of the following statement(s) is/are TRUE?
$$I. 33^3 > 3^{33}$$
$$II. 333 > (3^3)^3$$

If $$P = 2^2 + 6^2 + 10^2 + 14^2 + … 94^2$$ and $$Q = 1^2 + 5^2 + 9^2 + … 81^2$$, then what is the value of $$P - Q$$?

If $$A = \left(\frac{1}{0.4}\right) + \left(\frac{1}{0.04}\right) + \left(\frac{1}{0.004}\right) + …$$ upto 8 terms, then what is the value of $$A$$?

If $$M = 0.1 + (0.1)^2 + (0.01)^2$$ and $$N = 0.3 + (0.03)^2 + (0.003)^2$$, then what is the value of $$M + N$$?

If $$P = \frac{96}{95 \times 97}, Q = \frac{97}{96 \times 98}$$ and $$R = \frac{1}{97}$$, then which of the following is TRUE?

Which of the following statement(s) is/are TRUE?

I. $$11\frac{1}{2} + 17 \frac{3}{4} - 5\frac{1}{5} - 2\frac{1}{10} = \frac{439}{20}$$

II. $$\frac{9}{1078} > \frac{11}{1127}>\frac{12}{1219}$$

III. $$\frac{149}{151} > \frac{153}{155}>\frac{157}{159}$$

Which of the following statement(s) is/are TRUE?

I. $$\frac{2}{3\sqrt{3}} < \frac{3}{2\sqrt{5}} < \frac{5}{4\sqrt{3}}$$

II. $$\frac{3}{2\sqrt{5}} < \frac{2}{3\sqrt{3}} < \frac{7}{4\sqrt{5}}$$

Which of the following statement(s) is/are TRUE?
I. The total number of positive factors of 72 is 12.
II. The sum of first 20 odd numbers is 400.
III. Largest two digit prime number is 97.

If $$M = \left(\frac{3}{7}\right) \div \left(\frac{6}{5}\right) \times \left(\frac{2}{3}\right) + \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right)$$ and $$N = \left(\frac{2}{5}\right) \times \left(\frac{5}{6}\right) \div \left(\frac{1}{3}\right) + \left(\frac{3}{5}\right) \times \left(\frac{2}{3}\right) \div \left(\frac{3}{5}\right)$$, then what is the value of $$\frac{M}{N}$$?

M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?