Mathematics Tes...

In a group of \(100\) higher secondary students, \(50\) students have cleared the NDA exam, \(40\) students have cleared JEE exam and 30 students have cleared both the exams. How many such students are there who have neither qualified NDA nor JEE exam.

What is \(\int \frac{d x}{2^{x}-1}\) equal to?

For any vector \(\alpha\), what is the value of \((\alpha . \hat{i}) \hat{i}+(\alpha . \hat{j}) \hat{j}+(\alpha. \hat{k}) \hat{k}\)

In how many ways can a team of \(3\) boys and \(3\) girls be selected from \(5\) boys and \(4\) girls?

If \(\beta\) is perpendicular to both \(\vec{\alpha}\) and \(\vec{\gamma}\) where \(\vec{\alpha}=\hat{k}\) and \(\vec{\gamma}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \mathrm{k},\) then what is \(\beta\) equal to?

Which one of the following differential equations has a periodic solution? (where μ > 0)

Find the real numbers \(x\) and \(y\) if \((x-i y)(3+5 i)\) is the conjugate of \(-6-24 i\).

Find the value of \(\frac{d y}{d x}=e^{x-y}+x^{2} e^{-y}\).