Mathematics Tes...

Consider the following Linear Programming Problem (LPP):

Maximize \(Z=3 x_{1}+2 x_{2}\)

Subject to:

\(x_{1} \leq 4 \)

\(x_{2} \leq 6 \)

\(3 x_{1}+2 x_{2} \leq 18 \)

\(x_{1} \geq 0, x_{2} \geq 0\)

There are 4 flags of different colours and each can be used for signals. Determine how many signals can be sent using one or more flags at a time.

If \(x=a\) and \(x=\beta\) satisfy the equations \(\cos ^{2} x+a \cos x+b=0, \sin ^{2} x+p \sin x+q=0\) both, then the relation among \({a}, {b}, {p}\) and \({q}\) will be:

A box contains \(4\) tennis balls, 6 season balls and \(8\) dues balls. \(3\) balls are randomly drawn from the box. What is the probability that the balls are different?

If lines \(\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}\) and \(\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}\) are mutually perpendicular, then \(k\) is equal to:

In a class of 50, 20 students like mathematics, 15 like science and 5 like both mathematics and science. Find the number of students who do not like any of the 2 subjects.

For \(n \in N\), \(7^{2 n}+16 n-1\) is divisible by:

In a survey of 1,000 consumers, it is found that 720 consumers liked product \(A\) and 450 liked product \(B\). What is the least number that must have liked both the products?

\(\lim _{x \rightarrow \frac{1}{\sqrt{2}}} \frac{\sin \left(\cos ^{-1} x\right)-x}{1-\tan \left(\cos ^{-1} x\right)} \text { is equal to : }\)

Let a unit vector \(\hat{\mathrm{u}}=\mathrm{x} \cdot \hat{\mathrm{i}}+\mathrm{y} \hat{\mathrm{j}}+\mathrm{z} \hat{\mathrm{k}}\) make angles \(\frac{\pi}{2}, \frac{\pi}{3}\) and \(\frac{2 \pi}{3}\) with the vectors \(\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{k}, \frac{1}{\sqrt{2}} \hat{j}+\frac{1}{\sqrt{2}} \hat{k}\) and \(\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{j} \quad\) respectively. If \(\overrightarrow{\mathrm{v}}=\frac{1}{\sqrt{2}} \hat{\mathrm{i}}+\frac{1}{\sqrt{2}} \hat{\mathrm{j}}+\frac{1}{\sqrt{2}} \hat{\mathrm{k}}\), then \(|\hat{\mathrm{u}}-\overrightarrow{\mathrm{v}}|^2\) is equal to: