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

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

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.

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

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 ________.