Mathematics Tes...

A merchant plans to sell two types of personal computers, a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant would stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000 .

Let \(f(x)=\frac{1}{\sqrt{10-x^{2}}} \). What is the value of \(\lim _{x \rightarrow 1} \frac{{f}({x})-{f}(1)}{{x}-1}\)?

\(\mathrm{ABC}\) is a triangle, right angled at \(\mathrm{A}\). The resultant of the forces acting along \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}\) with magnitudes \(\frac{1}{\mathrm{AB}}\) and \(\frac{1}{\mathrm{AC}}\) respectively is the force along \(\overline{\mathrm{AD}}\), where \(\mathrm{D}\) is the foot of the perpendicular from \(\mathrm{A}\) onto \(\mathrm{BC}\). The magnitude of the resultant is:

Let \(\overrightarrow{\mathrm{a}}=\alpha \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\beta \mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\) be two vectors, such that \(\vec{a} \times \vec{b}=-\hat{i}+9 \hat{i}+12 \hat{k}\). Then the projection of \(\vec{b}-2 \vec{a}\) on \(\vec{b}+\vec{a}\) is equal to:

\(\mathrm{P(n)=2 \times 7^{n}+3 \times 5^{n}}-5\) is divisible by:

If the expected value of a random variable \(X\) is 2 and its variance is 1, then what will be the variance of \(3 X+4\)?

What is the equation to the plane through (1, 2, 3) parallel to 3x + 4y - 5z = 0?

Which of the following equals \(1+\cot ^{2} \theta ?\)

Let \(A=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\) and \(B=\left[\begin{array}{ccc}9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & -14^2 \\ -15^2 & 16^2 & 17^2\end{array}\right]\), then the value of A'BA is: