Mathematics Tes...

Calculate the area under the curve \(y=2 \sqrt{x}\) and included between the lines \(x=0, x=4\).

Evaluate:

\(\frac{\cos x-\sin x+1}{\cos x+\sin x-1}\)

Let \(\vec{\alpha}=3 \hat{i}+\hat{j}\) and \(\vec{\beta}=2 \hat{i}-\hat{j}+3 \hat{k}\). If \(\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2\), where \(\vec{\beta}_1\) is parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) is perpendicular to \(\vec{\alpha}\), then \(\vec{\beta}_1 \times \vec{\beta}_2\) is equal to:

How many different words can be formed by using all the letters of the word, ALLAHABAD if both L's do not come together? 

What is the product of the perpendiculars drawn from the points \(\left(\pm \sqrt{a^{2}-b^{2}}, 0\right)\) upon the line \(b x \cos \alpha+\) ay \(\sin \alpha=a b\)?

A basket contains \(6\) blue, \(2\) red, \(4\) green and \(3\) yellow balls. If \(5\) balls are picked up at random, what is the probability that at least one is blue?

The feasible solution for a LPP is shown in Figure. Let \(\mathrm{Z}=3 {x}-4 {y}\) be the Objective function, Maximum of \(\mathrm{Z}\) occurs at:

If \(A=\{2,3\}, B=\{4,5\}, C=\{5,6\}\), then what is the number of elements in \(A \times(B \cap C) ?\)

What is \(\lim _{x \rightarrow 0} \frac{\sin x \log (1-x)}{x^{2}}\) equal to?

\(|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|,\) then which one of the following is correct?