For the following questions answer them individually
What is the value of $$\frac{(1.2)^3 + (0.8)^3 + (0.7)^3 - 2.016}{1.35[(1.2)^2 + (0.8)^2 + (0.7)^2 - 0.96 - 0.84 - 0.56]}$$ ?
What is the unit digit of $$(217)^{413} \times (819)^{547} \times (414)^{624} \times (342)^{812}$$?
What is the value of $$S = \frac{1}{1 \times 3 \times 5} + \frac{1}{1 \times 4} + \frac{1}{3 \times 5 \times 7} +Â \frac{1}{4 \times 7} +Â \frac{1}{5 \times 7 \times 9 } +Â \frac{1}{7 \times 10}+.....$$upto 20 terms, then what is the value of S?
Which of the following is TRUE?
$$I. \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt{5}}$$
$$II. \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt{5}}$$
$$III. \frac{1}{\sqrt{5}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}}$$
$$IV.  \frac{1}{\sqrt{5}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}}$$
N is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when N is divided by 5?
Which of the following is TRUE?
$$I. \sqrt[3]{11} > \sqrt{7} > \sqrt[4]{45}$$
$$II. \sqrt{7} > \sqrt[3]{11} > \sqrt[4]{45}$$
$$III. \sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$$
$$IV. \sqrt[4]{45} > \sqrt{7} > \sqrt[3]{11}$$
A and B are positive integers. If $$A + B + AB = 65$$, then what is the difference between $$A$$ and $$B (A, B \leq 15)?$$
