For a > b > c > 0, the minimum value of the function \(f(x)=|x-a|+|x-b|+|x-c|\) is

The function \(f(x)=\frac{x^3+5x^2-8x}{3}\) is

Let \(\alpha,\beta\) be the roots of \(x^2-x+p=0\) and \(\gamma,\delta\) be the roots of \(x^2-4x+q=0\) where p and q are integers. If \(\alpha,\beta,\gamma,\delta\) are in geometric progression then p + q is

If inverse of the matrix \(\begin{bmatrix}2&-0.5\\-1&x\end{bmatrix}\) is \(\begin{bmatrix}1&1\\2&4\end{bmatrix}\), then the value of x is

If \((1+x-2x^2)^6=A_0+\sum_{r=1}^{12}A_rx^r\), then value of \(A_2+A_4+A_6+\cdots+A_{12}\) is

If \(\sin\theta+\cos\theta=m\), then \(\sin^6\theta+\cos^6\theta\) equals

The number of terms common to both the arithmetic progressions 2, 5, 8, 11, ...., 179 and 3, 5, 7, 9, ....., 101 is

Given that \(\cos x+\cos y=1\), the range of \(\sin x-\sin y\) is

From a pack of 52 cards, we draw one by one, without replacement. If f(n) is the probability that an Ace will appear at the nth turn, then