Simplification Questions

• If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0 , then what are the values of k1 and k2?
• If (x – y) = 7, then what is the value of (x – 15)3 – (y – 8)3 ?
• If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x2 – y2) ?
• If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)] ?
• If A = 30°, B = 60° and C = 135°, then what is the value of sin3A + cos3B + tan3C – 3sin A cos B tan C ?
• If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz ?
• If x4 + (1/x4) = 34 , then what is the value of x3 – (1/x3) ?
• If x = 1 – y and x2 = 2 – y2 , then what is the value of xy?
• What is the simplified value of (sec A + cos A)(sec A – cos A)?
• What is the simplified value of cosec Acot A + tan A2 ?
• How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346?
• If the expression px3 – qx2 – 7x – 6 is completely divisible by x2 – x – 6 , then what is the value of p and q respectively?
• If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9) , then what is the ratio between p and q respectively?
• If (x/y)a-4 = (y/x)2a-5 , then what is the relation between x and y?
• If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2 ?
• Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?
• If 2 cos θ = 2 – sin θ, then what is the value of cos θ?
• If x3+ 2x2– 5x + k is divisible by x + 1, then what is the value of k?
• If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2+ 15x + 1) ?
• If x + [1/(4x)] = 5/2, then what is the value of (64x6+ 1)/8x3 ?