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?

What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 1:4 and area of ΔADE is 6 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

Slope of the line AB is 4/3. Co-ordinates of points A and B are (x , -5) and (2 , -3) respectively. What is the value of x?

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 reflection of the point (-1 , 5) in the line x = 1?

What is the sum of the first 11 terms of an arithmetic progression if the first term is -31 and last term is 29?

6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?