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Q:

$If x^{3} + y^{3} + z^{3} = 3 (1 + xyz), P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P^{3} + Q^{3} + R^{3} - 3 PQR ?$

A) 9	B) 8
C) 12	D) 6

Answer & Explanation Answer: C) 12

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Q:

x, y and z are real numbers. If $x^{3} + y^{3} + z^{3} = 13, x + y + z = 1$ and xyz = 1, then what is the value of xy + yz + zx?

A) -1	B) 1
C) 3	D) -3

Answer & Explanation Answer: D) -3

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Q:

$If a^{3} + 3 a^{2} + 9 a = 1, then what is the value of a^{3} + (3 / a) ?$

A) 31	B) 26
C) 28	D) 24

Answer & Explanation Answer: C) 28

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Q:

If P = 7 + 4√3 and PQ = 1, then what is the value of $1 / P^{2} + 1 / Q^{2}$ ?

A) 196	B) 194
C) 206	D) 182

Answer & Explanation Answer: B) 194

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Q:

If x + y + z = 0, then what is the value of $(3 y^{2} + x^{2} + z^{2}) / (2 y^{2} - xz) ?$

A) 2	B) 1
C) 3/2	D) 5/3

Answer & Explanation Answer: A) 2

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Q:

What is the value of $\sqrt{4600 + \sqrt{540 + \sqrt{1280 + \sqrt{250 + \sqrt{36}}}}}$ ?

A) 69	B) 68
C) 70	D) 72

Answer & Explanation Answer: B) 68

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Q:

What is the value of $14^{3} + 16^{3} + 18^{3} + . . . + 30^{3} ?$

A) 134576	B) 120212
C) 115624	D) 111672

Answer & Explanation Answer: D) 111672

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Q:

What is the value of $S = \frac{1}{1 x 3 x 5} + \frac{1}{1 x 4} + \frac{1}{3 x 5 x 7} + \frac{1}{4 x 7} + \frac{1}{5 x 7 x 9} + \frac{1}{7 x 10} + . . .$ upto 20 terms. Then what is the value of S?

A) 6179/15275	B) 6070/14973
C) 7191/15174	D) 5183/16423

Answer & Explanation Answer: B) 6070/14973

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