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 displayed number with the sum of the two digits. Suppose Haruka enters the value 1 and then presses delta key ∆ repeatedly. After pressing the ∆ key for 68 times, what will be the displayed number?

Amit has forgotten his 4-digit locker key. He remembers that all the digits are positive integers and are different from each other. Moreover, the fourth digit is the smallest and the maximum value of the first digit is 3. Also, he recalls that if he divides the second digit by t…

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…

ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB² − AE² + 6CD is:

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…

Jose borrowed some money from his friend at simple interest rate of 10% and invested the entire amount in stocks. At the end of the first year, he repaid 1/5th of the principal amount. At the end of the second year, he repaid half of the remaining principal amount. At the end of…

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?

ABC is a triangle and the coordinates of A, B and C are (a, b − 2c), (a, b + 4c) and (−2a, 3c) respectively where a, b and c are positive numbers. The area of the triangle ABC is:

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