Mathematics Tes...

Find the value of \(\underset{{x \rightarrow 1}}{\lim} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3}\)

\(x+i y=\sqrt{\frac{a+i b}{c+i d}}\), then the value of \(x^{2}+y^{2}\) is:

Cards numbered from \(107\) to \(1006\) are put in a bag. A card is drawn from it at random. Find the probability that the number on the card is not divisible both by \(11\) and \(37\)?

If \(\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^2 \theta} d \theta=\operatorname{Alog}_e|B(\theta)|+C\), where \(C\) is a constant of integration, then \(\frac{B(\theta)}{A}\) can be:

What is the area bounded by the curves \(|y|=1-x^{2}\)?

What is the equation of the straight line which joins the intersection of the line \(x-y+4=0\) and \(y-2 x-5\) \(=0\) and the point \((3,2)?\)

What is the value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x)^{2}}{x^{4}}\)?

What is the number of ways that 5 boys and 4 girls can be seated in a row, so that, boys and girls sit alternately?

Which of the following is equal to \(\tan ^{-1}\left(\frac{8 x \sqrt{x}}{1-16 x^{3}}\right)?\)