For the following questions answer them individually
If the unit digit of $$(433 \times 456 \times 43N)$$ is $$(N + 2)$$, then what is the value of $$N$$?
Which of the following statement(s) is/are TRUE?
I. $$\left(\frac{0.03}{0.2}\right) + \left(\frac{0.003}{0.02}\right) + \left(\frac{0.0003}{0.002}\right) + \left(\frac{0.00003}{0.0002}\right) = 0.6$$
II. $$(0.01) + (0.01)^2 + (0.001)^2 = 0.010101$$
What is the value of $$\frac{1}{(0.1)^2} + \frac{1}{(0.01)^2} + \frac{1}{(0.5)^2} + \frac{1}{(0.05)^2}?$$
Which of the following statement(s) is/are TRUE?
I. $$\left(1 + \frac{1}{2}\right)\left(1 + \frac{1}{3}\right)\left(1 + \frac{1}{4}\right).......\left(1 + \frac{1}{998}\right)>497$$
II. $$14\frac{3}{4} + 5\frac{1}{4} - 2\frac{1}{2}>11\frac{1}{8}+12\frac{3}{8}-7\frac{1}{4}$$
Which of the following statement(s) is/are TRUE?
I. $$\frac{3}{110}<\frac{9}{308}<\frac{7}{225}$$
II. $$99\frac{1}{7}+99\frac{2}{7}+99\frac{3}{7}......99\frac{6}{7} = 297$$
If $$f(x) = \frac{1}{x}-\frac{1}{x+1}$$,then what is the value of $$f(1) + f(2) + f(3) + ......f(10)?$$
If $$N = 4^{11} + 4^{12} + 4^{13} + 4^{14}$$, then how many positive factors of $$N$$ are there?
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