Mathematics Tes...

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine \(A\) and 3 hours on machine \(B\) to produce a package of nuts. It takes 3 hours on machine \(A\) and 1 hour on machine \(B\) to produce a package of bolts. He earns a profit of Rs. \(17.50\) per package on nuts and Rs 7 per package of bolts. How many packages of each should be produced each day so as to maximize his profits if he operate his machines for at the most 12 hours a day?

The value of \(\left|\begin{array}{ccc}\sec ^{2} x & \tan ^{2} x & 1 \\ 2 & 1 & 1 \\ 10 & 8 & 2\end{array}\right|\):

The probability of success of three students \(X, Y\) and \(Z\) in the one examination are \(\frac{1}{5}, \frac{1}{4}\) and \(\frac{1}{3}\) respectively. Find the probability of success of at least two.

Let \(a_1, a_2, a_3, \ldots, a_n\) be \(n\) positive consecutive terms of an arithmetic progression. If \(d>0\) is its common difference, then :

\(\lim _{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\ldots \ldots .+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right) \text { is }\)

The domain of the function \(\cos ^{-1}\left(\frac{2 \sin ^{-1}\left(\frac{1}{4 x^2-1}\right)}{\pi}\right)\) is :

What is the value of \(\lim _{x \rightarrow 0} \frac{\sqrt{4+x}-2}{3 x}\)?

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is \(\mu\). The standard deviation for this distribution is given by ______.