Lakshya Education MCQs

Question: If $$x \ne 0,$$ ô  $$y \ne 0$$ ô  and $$z \ne 0$$ ô  and $$\frac{1}{{{x^2}}}$$ ô + $$\frac{1}{{{y^2}}}$$ ô + $$\frac{1}{{{z^2}}}$$ ô = $$\frac{1}{{xy}}$$ ô + $$\frac{1}{{yz}}$$ ô + $$\frac{1}{{zx}}$$ ô then the relation among x, y, z is?
Options:
 A. x + y + y = 0 B. x + y = z C. $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$$ D. x = y = z

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Question 1. If a + b = 1, c + d = 1 and a - b = $$\frac{d}{c}{\text{,}}$$ ô then the value of c2 - d2 = ?
1.    $$\frac{a}{b}$$
2.    $$\frac{b}{a}$$
3.    1
4.    -1
Question 2. If x = 3t, y = $$\frac{1}{2}$$(t + 1), then the value of t for which x = 2y is?
1.    1
2.    $$\frac{1}{2}$$
3.    -1
4.    $$\frac{2}{3}$$
Question 3. If $${x^2} + \frac{1}{5}x + {a^2}$$ ô  is a perfect square, then a is?
1.    $$\frac{1}{{100}}$$
2.    $$\pm \frac{1}{{10}}$$
3.    $$\frac{1}{{10}}$$
4.    $$- \frac{1}{{10}}$$
Question 4. If a2 + b2 + 4c2 = 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a2 + b2 + c2) is?
1.    3
2.    $${\text{3}}\frac{1}{4}$$
3.    2
4.    $${\text{2}}\frac{1}{4}$$
Question 5. If $$\frac{a}{b} = \frac{4}{5}$$ ô  and $$\frac{b}{c} = \frac{{15}}{{16}}{\text{,}}$$ ô  then $$\frac{{18{c^2} - 7{a^2}}}{{45{c^2} + 20{a^2}}}$$ ô  is equal to?
1.    $$\frac{1}{3}$$
2.    $$\frac{2}{5}$$
3.    $$\frac{3}{4}$$
4.    $$\frac{1}{4}$$
Question 6. If $$\frac{{x - {a^2}}}{{b + c}}$$ ô  + $$\frac{{x - {b^2}}}{{c + a}}$$ ô  + $$\frac{{x - {c^2}}}{{a + b}}$$ ô  = 4(a + b + c), then x = ?