The deBroglie wavelength of electron when accelerates through potential \(V\) is given by \(\lambda=\frac{h}{\sqrt{x} \sqrt{V}}\) then x is equal to :
where \(m =\) mass of electron
\(k =\) kinetic energy of electron
\(p =\) momentum
e = charge

A transistor is operated in common emitter configuration at \(V_c = 3V\) such that a change in the base current from \(50 \mu A\) to \(250 \mu A\) produces a change in the collector current from 5 mA to 20 mA. The current gain is :

Which of the following statements are correct?
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
(B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.
Choose the correct answer from the options given below:

The speed of an electromagnetic wave in a medium of dielectric constant 2.25 and relative permeability 4 is:

For a given convex lens, if the object distance is:
(A) \(u = -\infty\)
(B) \(u = -2f\)
(C) \(u = -f\)
(D) \(u = -f/3\)
The distance of the image is arranged in decreasing order:
Choose the correct answer from the options given below:

Match List-I with List-II:

List-I (Physical Quantity)	List-II (Unit)
(A) Magnetic flux	(I) \( T m A^{-1} \)
(B) Magnetic permeability	(II) \( A m^2 \)
(C) Magnetisation	(III) \( T m^2 \)
(D) Magnetic moment	(IV) \( A m^{-1} \)

\( 10^{18} \) electrons pass from point A to point B in 0.1 s in a conductor. The value of the current is

The differential equation representing the curve \(y=e^{2 x}(a+b x)\), where \(a, b\) are arbitrary constants is

Match List-I with List-II

List-I	List-II
(A) Angle between \(\hat{ \imath }-\hat{ \jmath }\) and \(\hat{ \jmath }+\hat{ k }\)	(I) 0
(B) Angle between \(2 \hat{j}-\hat{k}\) and \(\hat{j}+2 \hat{k}\)	(II) \(\frac{2 \pi}{3}\)
(C) Angle between \(\hat{i}+2 \hat{j}\) and \(5 \hat{i}+10 \hat{j}\)	(III) \(\frac{\pi}{6}\)
(D) Angle between \(\sqrt{3} \hat{i}+\hat{j}\) and \(\hat{i}\)	(IV) \(\frac{\pi}{2}\)

Choose the correct answer from the options given below:

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 of the following is not true about the limitations of VBT

Which one is a water-soluble protein?

The corner points of the bounded feasible region for an LPP are (0,4), (4, 4), (6, 6), (0, 12).
If the objective function is \(Z=p x+q y, p>0, q>0\) then the condition on p and q so that the maximum of Z occurs at (6, 6) and (0, 12) is

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
Which carboxylic acid will not undergo HVZ reaction?