For a heavily doped n-type semiconductor, Fermi level lies:

Match List-I with List-I

List-I	List-II
A. Electric field outside a uniformly charged thin spherical shell	(I) zero
B. Electric field inside a uniformly charged thin spherical shell	(II) \(\frac{\lambda}{2 \pi \epsilon_0 r} \vec{n}\)
C. Electric field due to an infinitely long straight uniformly charged wire	(III) \(\frac{\sigma}{2 \epsilon_0} \vec{n}\)
D. Electric field due to a uniformly charged infinite plane sheet	(IV) \(\frac{k q}{r^2} \vec{r}\)

Choose the correct answer from the options given below:

A current of 15 A in the primary coil of a circuit is reduced to zero at a uniform rate in \( 10^{-6} \, \text{s} \). If the coefficient of the Mutual Inductance is 4 H, what is the Induced emf in secondary coil?

A printed page is kept pressed by a glass cube (\(\mu = 1.5\)) of 5 cm edge. By what amount will the printed letters appear to be shifted when viewed from the top?

Match List-I with List-II for the band gap energy for different materials

List-I (Substances)	List-II (Band gap Energy)
(A) Germanium	(I) 1.1 eV
(B) Silicon	(II) 0.7 eV
(C) Insulator	(III) Zero
(D) metal	(IV) 5 eV

Choose the correct answer from the options given below:

Given below are two statements :
Statement (I) : In a ground wave communication system, low frequency signal (< 2 MHz) can be transmitted.
Statement (II) : If frequency is high then it will induce electrical signal on the surface of the earth and so attenuation takes place.
In the light of the above statements, choose the most appropriate answer from the options given below :

The current sensitivity of a moving coil galvanometer can be increased by
A. Decreasing the magnetic field
B. Increasing the number of turns
C. Increasing the area of the coil
D. Inserting a soft iron core in the coil
E. Decreasing the area of the coil
Choose the correct answer from the options given below:

Match List-l with List-II

List-I(Concentration term)	List-II(Formula)
(A) Mass percentage	(I) \(\frac{\text { Volume of solute }}{\text { Volume of solution }} \times 100\)
(B) Volume percentage	(II)\(\frac{\text {Moles of a component}}{\text {Total moles of all the components } \mathrm{}}\)
(C) Mole Fraction	(III) \(\frac{\text { Moles of solute }}{\text { Mass of solvent in } \mathrm{kg}}\)
(D) Molality	(IV) \(\frac{\text { Mass of solute }}{\text { Volume of solution × Density of solution }} \times 100\)

Choose the correct answer from the options given below:

Answer the question on the basis of passage given below :
Aldehydes and ketones represent two essential classes of organic compounds
which are extensively used in the synthesis of a wide variety of other organic molecules.
Due to the inherent polarity of the central carbonyl group, these substances readily undergo nucleophilic addition reactions.
Broadly speaking, these addition reactions can be categorized into two types:
one in which simple addition of the nucleophilic reagent occurs across the \(> C = O\) bond, and the second type where the initial addition is subsequently followed by the elimination of a water molecule.
A variety of ammonia derivatives, including hydroxylamine, hydrazine, phenylhydrazine,
2, 4-dinitroplhenylhdrasine, and semicarbaside, all belong to this second category of reactions.
These specific derivatives are fundamentally used for the identification and definitive characterization of aldehydes and ketones. Significantly, both types of nucleophilic addition reactions are strongly influenced by both steric and electronic factors.
As a general rule, aliphatic aldehydes exhibit higher reactivity compared to aromatic aldehydes.
The aliphatic aldehydes demonstrate the ability to reduce both Fehling's solution and Tollen's reagent, whereas aromatic aldehydes are limited to reducing only Tollen's reagent.
In a similar manner to aldehydes, aromatic ketones are observed to be less reactive than aliphatic ketones towards all nucleophilic addition reactions.
In a separate context, phenols and carborylic acids both exhibit acidic properties in nature.
Both classes of compounds readily dissolve in NaOH solution and cause blue litmus to turn red.
However, carboxylic acids stand out as much stronger acids than phenols and thus can decompose sodium bicarbonate \(\left( NaHCO _3\right)\) with the distinct evolution of \(CO _2\) gas, a reaction which phenols do not undergo.
It is important to note that both electron- donating and electron- withdrawing substituents significantly influence the acid strength of both aliphatic as well as aromatic carborylic acids.
Furthermore, unlike all other common aliphatic acids, formic acid uniquely possesses reducing properties and simultaneously does not display the typical reactions characteristic of the alkyl group.
Which of the following compound most readily undergoes nucleophilic addition reaction?

Answer the question on the basis of passage given below :
All transition elements display typical metallic properties like high melting point, boiling point, tensile strength, high malleability and ductility, luster, etc. Their metallic character increases down the group and elements of \(4 d\) and 5d series exhibit higher metallic characters. They show variable oxidation states and forms a number of coloured compounds due to the presence of unpaired electrons which shows d-d transitions and makes them paramagnetic.
The two strongest oxidising agents among the oxides will be :
A. \(MoO _3\)
B. \(CrO _3\)
C. \(Mn _2 O _7\)
D. \(WO _3\)
E. \(VO _2\)
Choose the correct answer from the options given below:

If the objective function Z = px + qy is maximum at (2,-2) and the maximum value is 8, such that p = 3q, then the values of p and q respectively are:

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds viz. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1) d , ns np\) or ns, np, nd 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.
\(CoCl _3 \cdot 6 NH _3\) gives 3 moles of AgCl on reacting with \(AgNO _3\).
The correct formula for this compound is :

Which one of the following sex determination systems is found in honey bee?