Simplification Questions

• If a = 3+23-2, b = 3-23+2 then a2+b2-ab ?
• If the difference between the roots of the equation Ax2 – Bx + C = 0 is 4, then which of the following is TRUE?
• α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots α4 and β4 ?
• If a and b are the roots of the equation Px2 – Qx + R = 0 , then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a) ?
• If x2 – 16x – 59 = 0 , then what is the value of (x – 6)2 + [1/(x – 6)2] ?
• If A and B are the roots of the equation Ax2 – A2x + AB = 0 , then what is the value of A and B respectively?
• If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35 , then what is the value of abc?
• If x3 – 4x2 + 19 = 6(x – 1) , then what is the value of [x2 + (1/x – 4)] ?
• If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?
• PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?
• PAB and PCD are two secants to a circle. If PA = 10 cm, AB = 12 cm and PC = 11 cm, then what is the value (in cm) of PD?
• Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?
• What is the value of {(sin 4x + sin 4y) [(tan 2x – 2y)]}/(sin 4x – sin 4y)?
• What is the value of (32 cos6x – 48 cos4x + 18 cos2x – 1)/[4 sin x cos x sin (60 – x) cos (60 – x) sin (60 + x) cos (60 + x)] ?
• What is the value of [2 cot × (p – A)/2]/[1 + tan2× (2p – A)/2] ?
• If tan θ + sec θ = (x – 2)/(x + 2), then what is the value of cos θ?
• What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?
• What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?
• What is the value of [sin (90 – A) + cos (180 – 2A)]/[cos (90 – 2A) + sin (180 – A)]?
• If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812 , then what is the value of P – Q?