Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?
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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 x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1 )] + [1/(2 + x2 )] + [1/(2 + x3 )]?
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?
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 a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?
If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?
If x + y + z = 0, then what is the value of (3y2 + x2 + z2 )/(2y2 – xz)?
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