If \(\cos ^{-1}\left(\frac{12}{13}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1} P\), then the value of \(P\) is

The value of \(\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ}\) is equal to

\((1+\Lambda)^{n} f(a)\) is equal to

If $x=\sqrt{a^{{\sin }^{-1}t}},y=\sqrt{a^{{\cos }^{-1}t}},$ then $\frac{dy}{dx}=$ ………

If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are non-coplanar vectors and \(\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \overline{\mathrm{q}}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \overline{\mathrm{r}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \quad\) then \(2 \overline{\mathrm{a}} \cdot \overline{\mathrm{p}}+\overline{\mathrm{b}} \cdot \overline{\mathrm{q}}+\overline{\mathrm{c}} \cdot \overline{\mathrm{r}}=\)

The distance of the point \((1,2)\) from the line \(x+y=0\) measured parallel to the line \(3 x-y=2\) is

The value of the integral \(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \frac{\pi-x}{\pi+x}\right) \cos x d x\) is equal to

If entropy of a solid is greater than zero, at \(\mathrm{T}=0\), it is called

In series LCR circuit, 'R' represents resistance of electric bulb. If the frequency of a.c. supply is doubled, the value of inductance ' L ' and capacitance ' C ' should be

The particular solution of the differential equation \(y(1+\log x) \frac{d x}{d y}-x \log x=0\) when

The value of \(\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ}=\)

The angle between the lines \(\overline{\mathrm{r}}=(2 \hat{\imath}+\hat{\jmath}-3 \hat{k})+\lambda(\hat{\imath}-\hat{\jmath}+\hat{k})\) and \(\frac{x-1}{1}=\frac{y+2}{3}=\frac{\mathrm{z}-3}{2}\)
is

Which among the following reactions does NOT form alkyl halides?