Mathematics Tes...

Let \(f(x)=\log x^{3}+2 x^{2}-3 x+100\), then find \(f'(3)\).

Find the area between the curve \(y=\sin x\) and lines \(x=-\frac{\pi}{3}\) to \(x=\frac{\pi}{3}\).

If \(A\) and \(B\) are two non-empty sets having n elements in common, then what is the number of common elements in the sets \(A \times B\) and \(B \times A ?\)

A bag contains \(7\) red and \(4\) blue balls. Two balls are drawn at random with replacement. The probability of getting the balls of different colors is:

Let \(\mathrm{S}_{\mathrm{n}}=1+\mathrm{q}+\mathrm{q}^2+\ldots .+\mathrm{q}^{\mathrm{n}}\) and \(\mathrm{T}_{\mathrm{n}}=1+\left(\frac{\mathrm{q}+1}{2}\right)+\left(\frac{\mathrm{q}+1}{2}\right)^2+\ldots+\left(\frac{\mathrm{q}+1}{2}\right)^{\mathrm{n}}\) where \(\mathrm{q}\) is a real number and \(\mathrm{q} \neq 1\). If \({ }^{101} \mathrm{C}_1+{ }^{101} \mathrm{C}_2 \cdot \mathrm{S}_1+\ldots .+{ }^{101} \mathrm{C}_{101} \cdot \mathrm{S}_{100}=\alpha \mathrm{T}{ }_{100}\), then \(\alpha\) is equal to:

The graph of the inequations \(x \leq 0, y \leq 0\), and \(2 x+y+6 \geq 0\) is:

Find the value of \(\lim _{\mathrm{x} \rightarrow 3} \frac{\mathrm{x}^{4}-81}{\mathrm{x}^{3}-27} \)

Find distance between the parallel lines \(p(x+y)+q=0\) and \(p(x+y)-r=0\)?

Let \(S\) be the set of all values of \(a_1\) for which the mean deviation about the mean of 100 consecutive positive integers \(a_1, a_2, a_3, \ldots, a_{100}\) is 25 . Then \(\mathrm{S}\) is:

For a distribution of student’s height, the quartiles are \(60.125, 61.345, 62.688\). The absolute measure of skewness is: