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

Two points on a ground are 1 m apart. If a cow moves in the field in such a way that it's distance from the two points is always in ratio 3: 2 then

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

The area enclosed by the curve \(2|x|+3|y|=6\) 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

On a circular path of radius 6 m a boy starts from a point A on the circumference and walks along a chord AB of length 3 m. He then walks along another chord BC of length 2 m to reach point C. The point B lies on the minor arc AC. The distance between point C and A is

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

Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1 : n. Then the ratio of the area of PQRS to the area of ABCD is

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