When the electron orbiting in hydrogen atom goes from one orbit to another orbit (principal quantum number \(=n\) ), the de-Broglie wavelength \((\lambda)\) associated with it is related to n as

A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is ( \(R=\) radius of earth)

A toroid has a non-ferromagnetic wire of inner radius ' \(\mathrm{r}_{1}{ }^{\prime}\) and outer radius ' \(\mathrm{r}_{2}\) ', around which 'N' turns of wire are wound. If the current in the wire is ' \(\mathrm{I}^{\prime}\), then the
magnetic field inside the toroid is \(\left(\mu_{0}=\right.\) permeability of free space \()\)

For a particle performing linear S.H.M., its average speed over one oscillation is
( \(A=\) amplitude of S.H.M., \(n=\) frequency of oscillation)

At room temperature, a p-type semiconductor has

A metal conductor of length \(1 \mathrm{~m}\) rotates vertically about one of its ends at an angular velocity of \(5 \mathrm{rad} / \mathrm{s}\). if horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \mathrm{~T}\), then the e.m.f. developed between the two ends of the conductor is

In the production of beats by two waves of same amplitude and nearly same frequency, the maximum intensity to each of the constituent waves is

If \(A=\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]\), then \(A^{-1}\) is

If the leaf 'X' grows from \(50 \mathrm{~cm}^2\) to \(100 \mathrm{~cm}^2\) in a day and another leaf 'Y' grows from \(50 \mathrm{~cm}^2\) to \(55 \mathrm{~cm}^2\) in a day, then RGR of leaf X and Y respectively will be ____________ % and ____________ %.

The integral \(\int \frac{2 x^3-1}{x^4+x} \mathrm{~d} x\) is equal to

Which among the following compounds is a primary alcohol?

If \(\bar{x}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \bar{y}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) and \(\overline{\mathrm{z}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) where \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are non-coplanar vectors, then value of \(\bar{x} \cdot(\overline{\mathrm{a}}+\overline{\mathrm{b}})+\bar{y} \cdot(\overline{\mathrm{~b}}+\overline{\mathrm{c}})+\overline{\mathrm{z}} \cdot(\overline{\mathrm{c}}+\overline{\mathrm{a}})\) is

Identify the INCORRECT statement from the following with reference to lac operon.