The number densities of electrons and holes in pure silicon at 273 K are equal and their values are \( 1.5 \times 10^{16} \text{ m}^{-3} \). On doping, the hole density increases to \( 4.5 \times 10^{27} \text{ m}^{-3} \). The electron density in the doped silicon will be :

The magnetic field in a plane electromagnetic wave is given by \( B = 3 \times 10^{-7} \sin(1.5z + 5 \times 10^{8}t) \text{ T} \), where \( z \) is in meter and \( t \) is in second. The wavelength of the wave is: (Take \( \pi = 3 \))

Two large plane parallel sheets with equal but opposite surface charge densities +\(\sigma\) and -\(\sigma\). A point charge q placed at points \(P_1, P_2,\) and \(P_3\) experiences forces \(F_1, F_2,\) and \(F_3\) respectively. Then :

Equal currents are flowing in four infinitely long wires. The distance between each other is the same and directions of currents are as shown in the figure. The net force on wire 2 is

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The peak value of the electric field associated with an electromagnetic wave traveling through vacuum is \( 8.1 \, \text{N}\cdot\text{C}^{-1} \). The peak value of the associated magnetic field will be:

A system consists of two protons and one electron. They are separated by a distance of 1 \(\text{\AA}\) from each other. If the potential energy at infinity is taken to be zero, the potential energy of the system is

When an \( \alpha \)-particle of mass M moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on M as

Which one of the given structures is not the secondary lymphoid organ?

Arrange the following electrodes in increasing order of strength as an oxidizing agent.
(A) \(Ni ^{2+}+2 e^{-} \rightarrow Ni (s) \quad E^0=-0.25 V\)
(B) \(Cu ^{2+}+2 e^{-} \rightarrow Cu (s) \quad E^0=0.34 V\)
(C) \(Br _2+2 e^{-} \rightarrow 2 Br ^{-} \quad E^0=1.09 V\)
(D) \(O _2(g)+2 H ^{+}+2 e^{-} \rightarrow H _2 O _2 \quad E^0=0.68 V\)
Choose the correct answer from the options given below :

Read the passage carefully and answer the Questions:
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups. Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.
The compound having the highest boiling point is:

If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), where \(|x|<1,|y|<1\) and \(x \neq y\), then

The mutual inductance of a pair of solenoids depends on

Which of the following is not the property of \( \beta \) ray?