In the figure below, two circular curves y and x create 60° and 90° angles with their respective centres. If the length of the bottom curve Y is 10π, find the length of the other curve. (Figure: two arcs X (upper) and Y (lower) with common end points.) [Figure: see page 18 of source PDF]

If a, b and c are 3 consecutive integers between -10 to +10 (both inclusive), how many integer values are possible for the expression? (a³ + b³ + c³ + 3abc) / (a + b + c)² = ?

ABCD is a quadrilateral such that AD = 9 cm, BC = 13 cm and ∠DAB = ∠BCD = 90°. P and Q are two points on AB and CD respectively, such that DQ : BP = 1 : 2 and DQ is an integer. How many values can DQ take, for which the maximum possible area of the quadrilateral PBQD is 150 sq.cm…

Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1 km, he reached a temple when his wife called to say that he can now take the car. Pradeep figu…

From the passage: Region \ Shop Type | North | East | West | South | All India Grocers |...

A consultant observing the data made the following two inferences: Inference I: The number of Grocers per-thousand-population is the highest in North India. Inference II: The number of Cosmetic per-thousand-population is the highest in South India. Which of following options is D…

For two positive integers a and b, if (a + b)^(a+b) is divisible by 500, then the least possible value of a × b is:

A person standing on the ground at point A saw an object at point B on the ground at a distance of 600 meters. The object started flying towards him at an angle of 30° with the ground. The person saw the object for the second time at point C flying at 30° angle with him. At point…

The difference between the area of the circumscribed circle and the area of the inscribed circle of an equilateral triangle is 2156 sq. cm. What is the area of the equilateral triangle? Assume that π = 22/7

From the passage: This graph depicts the last eight years' annual salaries (in Rs. lacs....

In which year were a maximum number of students offered salaries between Rs. 20 to Rs. 30 lacs (both inclusive)? [Figure: see page 20 of source PDF]