The equation of a straight line which passes through the point $\left(a{\cos }^3\mathrm{\theta },a{\sin }^3\mathrm{\theta }\right)$ and perpendicular to $x\mathrm{sec\theta }+y\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{\theta }=a$ is

If \(a \pm i b\) and \(b \pm a i\) are the roots of \(x^4-10 x^3+50 x^2-130 x+169=0\), then \(\frac{a}{b}+\frac{b}{a}=\)

The value of \(\left|\begin{array}{cc}\log _5 729 & \log _3 5 \\ \log _5 27 & \log _9 25\end{array}\right|\) \(\times\left|\begin{array}{ll}\log _3 5 & \log _{27} 5 \\ \log _5 9 & \log _5 9\end{array}\right|\) is

\(\cos ^2(x)+\cos ^2\left(x+\frac{\pi}{3}\right)+\cos ^2\left(x-\frac{\pi}{3}\right)=\)

The centre of a circle is \((2,-3)\) and the circumference is \(10 \pi\). Then its equation is

The vectors \(\mathbf{a}\) lies in the plane of vectors \(\mathbf{b}\) and \(\mathbf{c}\), then

The minimum value of \(27 \tan ^2 \theta+3 \cot ^2 \theta\) is

The standard reduction potentials of \(\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Ag}\) are respectively \(-0.76,0.34\) and \(0.8 \mathrm{~V}\). The following cells were constructed :
(1) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}\)
(2) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}\)
(3) \(\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}\)
What is the correct order of \(E_{\text {cell }}^{\circ}\) of these cells?

The number of protons, neutrons and electrons in ${}_6{}^{13}C$ respectively are

The variance of the observations \(2,3,5,7,11\), \(13,17,22\) is

The weight percentage of \(\mathrm{C}\) and \(\mathrm{H}\) in a hydrocarbon is in the ratio of \(4: 1\). What is its empirical formula?

A person of mass \(M=90 \mathrm{~kg}\) standing on a smooth horizontal plane of ice throws a body of mass \(m=10 \mathrm{~kg}\) horizontally on the same surface. If the distance between the person and body after \(10 \mathrm{~s}\) is \(10 \mathrm{~m}\), then the KE of the person (in \(\mathrm{J}\)) is

If \(\alpha\) and \(\beta\) are non-real roots of \(x^3-x^2-x-2=0\), then \(\alpha^{2020}+\beta^{2020}+\alpha^{2020} \cdot \beta^{2020}=\)