If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?
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If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?
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?
If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?
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?
If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?
A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?
N is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when N is divided by 5?
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