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 be treated as a wrong answer. Each question in the second section carries 3 marks, whereas each question in the third section carries 5 marks. For any wrong answer or unattempted question in the second and third sections, no marks will be deducted. A student's score is the addition of marks obtained in all the three sections. What is the sixth highest possible score?

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…

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…

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…

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 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:

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

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…

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?