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For the following questions answer them individually
If $$I_n = \left\{x \epsilon R: -\frac{1}{n} < x < \frac{1}{n}\right\}$$ for n = 1, 2, 3, --- ---- ---- then $$I_7 \cap I_{13} = $$
Let L be the set of all straight lines in a plane and R = {$$(l_1, l_2) \epsilon L \times L \mid l_1$$ is perpendicular to $$l_2$$}. Then on the L the relation R is
Let N be theset of all natural numbers and $$f : N \rightarrow N$$ be defined by f(n) = r, where r is the remainder when n is divided by 17 for any $$n \epsilon N$$. Then $$\left\{n \epsilon N: f(n) = 3 \right\} =$$
If the lines ax + 2y + 1 = 0, bx + 3y + 1 = O and cx + 4y + 1 = 0 are concurrent then a, b and c are in
If the line through the points (7. -2) and (4, -5) cuts the coordinate axes at A and B then the length AB is
$$\tan 40^\circ =x \Rightarrow \frac{\tan 250^\circ + \tan 150^\circ}{1 - \tan 250^\circ\tan 150^\circ} =$$
If $$270^\circ < \theta < 360^\circ$$ and $$\cot \theta = -\sqrt{3}$$ then $$\cos \theta =$$
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