Find the value of: (sin⁶15° + sin⁶75° + 6 sin²15° sin²75°) / (sin⁴15° + sin⁴75° + 5 sin²15° sin²75°)

Rajnish bought an item at 25% discount on the printed price. He sold it at 10% discount on the printed price. What is his profit in percentage?

A painter draws 64 equal squares of 1 square inch on a square canvas measuring 64 square inches. She chooses two squares (1 square inch each) randomly and then paints them. What is the probability that two painted squares have a common side?

ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that BC < AD. P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC. If the area of the triangle CPD is 4√3, find the area of the triangle…

Let x and y be two positive integers and p be a prime number. If x(x – p) – y(y + p) = 7p, what will be the minimum value of x – y?

There are three sections in a question paper and each section has 10 questions. First section only has multiple-choice questions, and 2 marks will be awarded for each correct answer. For each wrong answer, 0.5 marks will be deducted. Any unattempted question in this section will…

Five students appeared for an examination. The average mark obtained by these five students is 40. The maximum mark of the examination is 100, and each of the five students scored more than 10 marks. However, none of them scored exactly 40 marks. Based on the information given, w…

Suppose Haruka has a special key ∆ in her calculator called delta key: Rule 1: If the display shows a one-digit number, pressing delta key ∆ replaces the displayed number with twice its value. Rule 2: If the display shows a two-digit number, pressing delta key ∆ replaces the disp…

Consider a(n+1) = 1/(1 + 1/a(n)) for n = 1, 2, ...., 2008, 2009 where a(1) = 1. Find the value of a1a2 + a2a3 + a3a4 + ⋯ + a2008a2009