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Q:

Triangle ABC is similar to triangle PQR and AB : PQ = 2 : 3. AD is the median to the side BC in triangle ABC and PS is the median to the side QR in triangle PQR. What is the value of (BD/QS)2?

A) 3/5 B) 4/9
C) 2/3 D) 4/7
 
Answer & Explanation Answer: B) 4/9

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Q:

If α and β are the roots of equation x2   x + 1 = 0, then which equation will have roots α3 and β3?

A) x2 + 2x + 1 = 0 B) x2 – 2x – 1 = 0
C) x2 + 3x – 1 = 0 D) x2 – 3x + 1 = 0
 
Answer & Explanation Answer: A) x2 + 2x + 1 = 0

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Q:

If x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1  )] + [1/(2 + x2 )] + [1/(2 + x3 )]?

A) 1 B) 1/2
C) 2 D) 1/3
 
Answer & Explanation Answer: B) 1/2

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Q:

If x3 + y3 + z3 = 3(1 + xyz), P = y + z  x, Q = z + x  y and R = x + y  z, then what is the value of P3 + Q3 + R3  3PQR?

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 x3 + y3 + z3 = 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 a3 + 3a2 + 9a = 1, then what is the value of a3 + (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/P2 + 1/Q2?

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 (3y2 + x2 + z2 )/(2y2  xz)?

A) 2 B) 1
C) 3/2 D) 5/3
 
Answer & Explanation Answer: A) 2

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