Simplification Questions

• Which of the following statements is/are true? I. 1112+1734-515-2110 = 43920II. 91078>111127>121219III. 149151>153155>157159
• If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then what is the value of M/N?
• M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?
• Which of the following statement(s) is/are TRUE? I. 12>163>244II. 253>324>486III. 94>153>246
• If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2 ?
• If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?
• If α and β are the roots of equation x2 – 2x + 4 = 0, then what is the equation whose roots are α3/β2 and β3/α2?
• If one root of the equation Ax2 +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?
• If x2 – 12x + 33 = 0 , then what is the value of (x – 4)2 + [1/(x – 4)2] ?
• If a4 + 1 = [a2 /b2 ] (4b2 – b4 – 1) , then what is the value of a4 + b4 ?
• If a + b = 10 and ab- 13 = -ba - 11 , then what is the value of 3ab + 4a2 + 5b2 ?
• If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?
• If x + 3y - 2z4 = 6, x + 232y + 3z = 33 and 17x + y +z + 2z =9, then what is the value of 46x+ 131y ?
• What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]?
• What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?
• What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?
• If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?
• What is the value of 1sin490-θ+1cos290-θ - 1 ?
• What is the value of [tan (90 – A) + cot (90 – A)]2/[2 sec2(90 – 2A)] ?
• What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}?