If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?

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

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

If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

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?

ABC is a right angled triangle. ∠BAC = 90 deg and ∠ACB = 60 deg. What is the ratio of the circum radius of the triangle to the side AB?

In the figure, B and C are the centres of the two circles. ADE is the common tangent to the two circles. If the ratio of the radius of both the circles is 3:5 and AC= 40, then what is the value of DE?