Mathematics Tes...

If \(y=\cos ^{2} x^{2}\), find \(\frac{d y}{d x}\):

The roots of equation \(x^{2}-m x+4=0\) are imaginary and \(m^{2}-4 m+3<0\) where \(m \in W\) (whole number), then find the possible value of \(m\).

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?

If \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|^{2}+|\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}|^{2}=144\) and \(|\overrightarrow{\mathrm{a}}|=4\), then what is \(|\overrightarrow{\mathrm{b}}|\) equal to?

A weight of \(500 \mathrm{~N}\) is supported by two metallic ropes as shown in the figure. The values of tensions \(T_{1}\) and \(T_{2}\) are respectively:

Condition of static equilibrium of a planar force system is written as:

The equation x² - y² = 0 represents:

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 .