In which of the following cases, the value of impact parameter (for alpha particle scattering experiment by Geiger-Marsden) will be minimum ?

The electric field \( E \) associated with a progressive electromagnetic wave is given by \( E = E_0 \sin(kx - \omega t) \). If \( B_0 \) is the amplitude of the magnetic field associated with the wave, then

Match list-I with list-II

List-I	List-II
(A) Rays used in satellite communication	(I) X rays
(B) Rays produced in nuclear reaction	(II) Gamma rays
(C) Radiation used for studying crystal structure	(III) Ultraviolet rays
(D) Radiation absorbed by ozone layer	(IV) microwave

Choose the correct answer from the options given below:

Which of the following spectral series is found in the visible region of the hydrogen spectrum ?

Two conducting spheres of radii 5 cm and 10 cm are given a charge of 15 \(\mu\)C each. If the two spheres are now joined by a conducting wire, the charge on the smaller sphere will be :

A parallel plate capacitor of capacitance 2 \( \mu F \) has energy \( 10 \times 10^{-5} \, J \). The potential difference and the charge on the capacitor are:

An electron is projected into a magnetic field of flux density \( 10 \text{ Wb/m}^2 \) with a velocity of \( 3 \times 10^7 \text{ m/s} \) at an angle of \( 30^{\circ} \) to the field. The magnetic force on the electron is:

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
Among the following, water-soluble vitamin is

Read the passage carefully and answer the Questions:
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1\) )d, ns, np or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Which among the following are diamagnetic complexes?
\(\left[Ni(CN)_4\right]^{2-},\left[Co\left(C_2 O_4\right)_3\right]^{3-},\left[Fe(CN)_6\right]^{4-},\left[CoF_6\right]^{3-},\left[Mn(CN)_6\right]^{3-}\)

Vertical distribution of different species occupying different levels is called as

If \(\vec{a}, \vec{b}, \vec{c}\) are vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=1,|\vec{b}|=2,|\vec{c}|=5\), then the expression \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) equals

A telescope has an objective lens of 0.1 m diameter and is situated at a distance of 500 m from two objects. What will be the minimum distance between these two objects which can be resolved by the telescope? The mean wavelength of light is 600 nm.

A wire has a resistance of \( 3.0 \Omega \) at \( 30^{\circ}C \) and a resistance of \( 4.5 \Omega \) at \( 100^{\circ}C \). The temperature coefficient of resistance of the wire is