If \(f(x)=e^{|x|}, g(x)=\log x\), then \((g\) of \()(x)=\)

If the Cartesian equation of a line is \(6 x-2=3 y+1=2 z-2\), then the vector equation of the line is

If \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}\) are three non coplanar vectors and \(\overrightarrow{\mathbf{p}}, \overrightarrow{\mathbf{q}}, \overrightarrow{\mathbf{r}}\) are defined by the relations
\(\overrightarrow{\mathbf{p}}=\frac{\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}, \quad \overrightarrow{\mathbf{q}}=\frac{\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}\) and \(\overrightarrow{\mathbf{r}}=\frac{\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}\)
then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{p}}+\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{q}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{r}}\) is equal to

If \(\mathrm{P}(3,2,6), \mathrm{Q}(1,4,5)\) and \(\mathrm{R}(3,5,3)\) are the vertices of \(\Delta \mathrm{PQR}\), then \(\mathrm{m} \angle \mathrm{PQR}\) is

\(\int_{-5}^{5} \log \left(\frac{7-x}{7+x}\right) d x=\)

The approximate value of \(x^3-2 x^2+3 x+2\) at \(x=2.01\) is

If the line \(\overrightarrow{\mathrm{OR}}\) makes angles \(\theta_{1}, \theta_{2}, \theta_{3}\) with the planes XOY, YOZ, ZOX respectively, then \(\cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+\cos ^{2} \theta_{3}\) is equal to

The number of metamers possible for \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\) is

Which of the following statements is correct regarding isobars?

A coin is placed on the horizontal plate. Plate performs S.H.M. vertically with
angular frequency ' \(\omega^{\prime}\). The amplitude (A) of oscillations is gradually increased.
The coin will lose contact with plate for the first time when amplitude is
\((\mathrm{g}=\) acceleration due to gravity \()\)

Identify the hybridisation and geometry of \(\mathrm{SF}_4\) molecule respectively.

If \(f(x)=2 x^{2}+b x+c, f(0)=3\) and \(f(2)=1\), then \((f o f)(1)=\)

Calculate the volume occupied by a particle in bcc unit cell if the volume of unit cell is \(8.2 \times 10^{-23} \mathrm{~cm}^3\)