Let f : R² → R be a real-valued function defined as f(0, y) = y + 1 and f(x + 1, y) = f(x, f(x, y)) + x. What is the value of f(2, 2)?

In a multiple-choice examination, there are 20 questions. Each correct answer is worth 4 marks, while 2 marks are to be deducted for every wrong answer. Further, 1 mark is to be deducted for every unattempted question. One student receives a total of 46 marks in the examination.…

Let a₁ < a₂ < .... < aₙ be the list of all prime numbers less than 25. Define Xᵢ = bᵢ/aᵢ, where bᵢ is the sum of all aₖ where k ranges from 1 to n, k ≠ i. Let B be the set of all integer-valued Xᵢ. What is the Smallest element of B?

Three categories of candidates appear for an admission test: diligent (10%), lazy (30%) and confused (60%). A diligent candidate is 10 times more likely to clear the admission test compared to a lazy candidate. If 40% of the candidates clearing the admission test are confused, wh…

Consider two circles, each having radius of 5cm (centimeters), touching each other at a point P. A direct tangent QR is drawn touching one circle at a point Q and the other circle at a point R. Inside the region PQR inscribed by the two circles and the tangent, a square ABCD is i…

125 is multiplied by either 10 or 15. The resultant number is again multiplied by either 10 or 15. This process continues. Which of the following CANNOT be a resultant number at any point in time?

Rajan is a fruit seller. On any day, he sells only one kind of fruit. On the first day, he buys 9 kg of blueberries. On the second day, he buys 22 kg of kiwis. On the third day, he buys 50 kg of peaches. The per kg purchase price of each fruit is an integer. Further, on each of t…

The swimming pool in an exclusive club is a circular strip. A water flow is artificially maintained in the strip, along a clockwise direction, at a constant speed of 3km/h (kilometers/hour). One morning, Ayub and Rana start swimming at the same time from two diametrically opposit…

How many solutions (x, y, z) of the equation x + y² + z³ = 50 exist, where x, y and z are positive integers?