If \(\cos\alpha + \cos\beta = 1\), then the maximum value of \(\sin\alpha - \sin\beta\) is

The equation \(x^2 + y^2 - 2x - 4y + 5 = 0\) represents

Let p be a positive integer such that the unit digit of \(p^3\) is 4. What are the possible unit digits of \((p+3)^3\)?

A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such w…

The probability that a randomly chosen positive divisor of \(10^{2023}\) is an integer multiple of \(10^{2001}\) is

Which of the following straight lines are both tangent to the circle \(x^2 + y^2 - 6x + 4y - 12 = 0\)

From the passage: Directions (Q.41-Q.45): A pharmaceutical company has tested five drugs...

Organism R can be treated with

Let \(a_1, a_2, a_3\) be three distinct real numbers in geometric progression. If the equations \(a_1x^2 + 2a_2x + a_3 = 0\) and \(b_1x^2 + 2b_2x + b_3 = 0\) have a common root, then which of the following is necessarily true?

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is