Consider the real-valued function f(x) = log(3x − 7) / √(2x² − 7x + 6). Find the domain of f(x).

The Madhura Fruits Company is packing four types of fruits into boxes. There are 126 oranges, 162 apples, 198 guavas and 306 pears. The fruits must be packed in such a way that a given box must have only one type of fruit and must contain the same number of fruit units as any oth…

I have five 10-rupee notes, three 20-rupee notes, and two 50-rupee notes in my wallet. If three notes were taken out randomly and simultaneously, what is the probability that at least 90 rupees were taken out?

Fatima found that the profit earned by the Bala dosa stall today is a three-digit number. She also noticed that the middle digit is half of the leftmost digit, while the rightmost digit is three times the middle digit. She then randomly interchanged the digits and obtained a diff…

Kim’s wristwatch always shows the correct time, including ‘am’ and ‘pm’. Jim’s watch is identical to Kim’s watch in all aspects except its pace, which is slower than the pace of Kim’s watch. At 12 noon on January 1st, Jim sets his watch to the correct time, but an hour later, it…

If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that y > x and z < x, then which of the following values can (a1 − a2)/(b1 − b2) possibly take?

Wilma, Xavier, Yaska and Zakir are four young friends, who have a passion for integers. One day, each of them selects one integer and writes it on a wall. The writing on the wall shows that Xavier and Zakir picked positive integers, Yaska picked a negative one, while Wilma’s inte…

From the passage: [Candlestick chart of a stock's prices over Day 1 to Day 10 (price axi...

On which day is the ratio of the maximum price to the opening price, the highest across the ten days? [Figure: see page 11 of source PDF]

Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are coprimes, that is, their greatest common divisor is 1. She also finds…