Mathematics Tes...

The mean of n terms is \(\bar{x}\). If first term is increased by 1, second term by 2, and so on, then new mean is

Four persons are asked the same question by an interviewer. If each has, independently, a probability 1/6 of answering correctly, then the probability that at least one of them answers correctly is

The integral \(\int \frac{2 x-3}{\left(x^{2}+x+1\right)^{2}} d x\)is equal to

The tangent to the circle x² + y² = a² at the point, where x = 2, makes an angle with the axis of x whose tangent is −2.The area, lying in the first quadrant, bounded by the x-axis, the circle and the line y = 2x is

The points of contact of the tangents drawn from the origin to the curve y = sin x lie on the curve

Let \(3 \mathrm{f}(\mathrm{x})+\) bf \(\left(\frac{1}{\mathrm{x}}\right)=\mathrm{x},(\mathrm{b} \neq\pm 3)\) for all \(\mathrm{x} \in \mathrm{R}-\{0\} .\) If \(\mathrm{x}=2\) is a root of the equation \(\mathrm{f}(\mathrm{x})=0\) then

The coefficient of xⁿ in the expansion of \(\frac{1}{(1-x)(3-x)}\)is:

If sin y = x sin (a + y), then dy/dx is