In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?

A set of all possible values the function \(f(x)=\frac{x}{|x|}\), where \(x \ne 0\), takes is

From the passage: A showroom is open on all seven days of the week throughout the year....

Number of days Bhabha and Cathy work together in a week is

The value of k for which the following lines x-y-1 = 0 2x+3y-12 = 0 2x-3y+k = 0 are concurrent is

If one of the factors of the number \(3^7\, 2^8\, 17^3\) is randomly chosen, then the probability that the chosen factor will be a perfect square is.

Ayesha is standing atop a vertical tower 200m high and observes a car moving away from the tower on a straight horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be 45°. At 11:02 AM, she observes the angle of depression of…

The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

The curve represented by the equation \(\frac{x^2}{\sin\sqrt{2}-\sin\sqrt{3}}+\frac{y^2}{\cos\sqrt{2}-\cos\sqrt{3}}=1\)

If \(f(x^2 + f(y)) = xf(x) + y\) for all non-negative integers x and y, then the value of \([f(0)]^2 + f(0)\) equals ________.