Simplification Questions

• If (333 + 333 + 333) (233 + 233) = 6x , then what is the value of x?
• Which of the following statement(s) is/are true? I. (65)1/6 > (17)1/4 > (12)1/3 II. (17)1/4 > (65)1/6 > (12)1/3 III. (12)1/3 > (17)1/4 > (65)1/6
• If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2) ?
• If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6 ?
• If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?
• A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c) ?
• If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2 ?
• If [a + (1/a)]2 – 2[a – (1/a)] = 12 , then which of the following is a value of 'a'?
• If x2 – 4x + 1 = 0 , then what is the value of x9 + x7 – 194x5 – 194x3 ?
• If x + y = 3, then what is the value of x3 + y3 + 9xy ?
• A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value of A2 + 2AB + AB2?
• If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?
• If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?
• In the given figure, AB is a diameter of the circle with center O and XY is the tangent at a point C. If ACX = 35 deg, then what is the value (in deg) of CAB?
• What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?
• What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)] ?
• What is the value of tanπ4+A×tan3π4+A ?
• What is the value of sin (630 + A) + cos A?
• What is the value of [(sin 59° cos 31° + cos 59° sin 31° )÷(cos 20° cos 25° – sin 20° sin 25° )]?
• What is the value of cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) – sin (90 – C) cos (A + B)?