Simplification Questions

• A fraction is greater than its reciprocal by (72)/(77). What is the fraction?
• What is the value of (1/√2) Cot 45° + (1/√3) Cosec 60°?
• Δ ABC is right angled at B. If m∠A = 60°, then what is the value of sec C.sin A?
• If [2(4x/5 - 3/4)]/3 - 5/3 = -1/6, then the value of x is?
• If a3 + b3 = 35 and ab = 6, then what is the value of a + b?
• Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
• ax + 5y = 8 has slope of -4/3. What is the value of a?
• What is the value of Cot 45° - (1/√3)Cosec 60°?
• If Cot θ = 21/20, then what is the value of Cosec θ?
• What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?
• If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0 , then what is the value of x + y + z – 5?
• If 2x/3 - [5(4x/5 - 4/3)]/2 = 1/3, then what is the value of x?
• If a3 + b3 = 28 and a + b = 4, then what is the value of ab?
• 6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?
• What is the reflection of the point (-1 , 5) in the line x = 1?
• What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
• What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?
• Δ ABC is right angled at B. If m∠A = 60°, then what is the value of 2 Sec C x 1/2 Sin A?
• If Tan θ = 7/24, then what is the value of Cosec θ?
• Simplify : -21973 × -1253 ÷ 275123