For the following questions answer them individually
Which of the following statement(s) is/are TRUE?
I. $$\sqrt{121}+\sqrt{12321}+\sqrt{1234321} = 1233$$
II. $$\sqrt{0.64}+\sqrt{64}+\sqrt{36}+\sqrt{0.36}>15$$
What is the value of $$(2+\sqrt{2})+\left(\frac{1}{2+\sqrt{2}}\right)+\left(\frac{1}{2-\sqrt{2}}\right)+(2-\sqrt{2})$$?
The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares?
What is the value of $$1006^2 - 1007 \times 1005 + 1008 \times 1004 - 1009 \times 1003$$?
If $$a^2 + b^2 = 4b + 6a - 13$$, then what is the value of $$a + b$$
$$x$$ and $$y$$ are positive integers. If $$x^4 + y^4 + x^2y^2 = 481$$ and $$xy = 12$$, then what is the value of $$x^2 - xy + y^2$$?
If $$A = 1 + 2^p$$ and $$B = 1 + 2^{-p}$$,then what is the value of $$B$$?
If $$a$$ and $$b$$ are roots of the equation $$ax^2 + bx + c = 0$$, then which equation will have roots $$(ab + a + b)$$ and $$(ab - a - b)$$?
If $$\sqrt{(1 - p^2)(1 - q^2)} = \frac{\sqrt{3}}{2}$$, then what is the value of $$\sqrt{2p^2 + 2q^2 + 2pq} + \sqrt{2p^2 + 2q^2 - 2pq}$$?
If $$(a + b)^2 - 2(a + b) = 80$$ and $$ab = 16$$, then what is the value of $$3a - 19b$$?
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