Graph shows the variation of fringe width \((\mathrm{X})\) versus distance of the screen from the plane of the slits (D) in Young's double slit experiment. (keeping other parameters same, \(\mathrm{d}=\) distance between the slits). The wavelength of light used can be calculated as

Three coils of inductance \(\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H}\) and \(\mathrm{L}_3=6 \mathrm{H}\) are connected such that they are separated from each other. To obtain the effective inductance of 1 henry, out of the following combinations as shown in figure, the correct one is

In Young's double slit experiment using monochromatic light of wavelength ' \(\lambda\) ', the maximum intensity of light at a point on the screen is \(\mathrm{K}\) units. The intensity of light at point where the path difference is \(\frac{\lambda}{3}\)

A simple pendulum performs simple harmonic motion about \(\mathrm{x}=0\) with an amplitude ' \(\mathrm{a}\) ' and time period ' \(T\) '. The speed of the pendulum at \(x=\frac{a}{2}\) is

A carnot engine, whose efficiency is \(40 \%\) takes heat from a source maintained at temperature 600 K . It is desired to have an efficiency \(60 \%\), then the intake temperature for the same exhaust (sink) temperature should be

Time period of a simple pendulum will be doubled if we

Orbital acceleration of electron is

What is vapour pressure of a solution containing \(1 \mathrm{~mol}\) of a nonvolatile solute in \(36 \mathrm{~g}\) of water \(\left(\mathrm{P}_1^0=32 \mathrm{~mm} \mathrm{Hg}\right) ?\)

If the function \(f: R-\{-1,1\} \rightarrow A\) defined by \(f(x)=\frac{x^2}{1-x^2}\) is surjective, then \(A\) is equal to

Which of the following compounds follows octet rule?

A car is moving with speed \(30 \mathrm{~ms}^{-1}\) on a circular path of radius \(500 \mathrm{~m}\). Its speed is increasing at a rate of \(2 \mathrm{~ms}^{-2}\), what is the acceleration of the car?

Let \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) be three non-coplanar vectors and \(\overline{\mathrm{p}}, \overline{\mathrm{q}}, \overline{\mathrm{r}}\) defined by the relations
\(\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}, \overline{\mathrm{q}}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}, \overline{\mathrm{r}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}\)
then the value of the expression \((\bar{a}+\bar{b}) \cdot \bar{p}+(\bar{b}+\bar{c}) \cdot \bar{q}+(\bar{c}+\bar{a}) \cdot \bar{r}\) is equal to

The teacher wants to arrange 5 students on the platform such that the boy \(\mathrm{B}_1\) occupies second position and the girls \(\mathrm{G}_1\) and \(\mathrm{G}_2\) are always adjacent to each other, then the number of such arrangements is