Simplification Questions

• 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)]}?
• What is the value of 3.6×1.62+0.48×3.61.8×0.8+10.8×0.3-2.16 ?
• If 11+11+11+1x = 58 , then what is the value of x?
• If 1+121+141+161+181-131-151-17 = 1+ 1x , then what is the value of x?
• What is the value of 13×7+17×11+111×15+...+1899×903 ?
• What is the unit digit of 15+25+35+...+205 ?
• N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?
• p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?
• If α and β are the roots of the equation x2+ x – 1 = 0 , then what is the equation whose roots are α5 and β5 ?
• If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x+ (– 1)y ?
• If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?
• If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9?
• If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?
• The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?
• What is the value of [(cos 7A + cos 5A)÷(sin 7A – sin 5A)]?
• What is the value of [1 – sin (90 – 2A)] / [1 + sin (90 + 2A)]?
• What is the value of sin 75°+ sin 15° ?
• What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?
• What is the value of [2 sin (45 + θ) sin (45 – θ)]/cos 2θ?