Identify the correct statements among the following.
(A) For two unlike equal charges, there is a neutral point on the middle point on the line joining the two charges.
(B) For two, unlike unequal charges, the neutral point will be outside on the line joining the two charges.
(C) For two positive equal charges, the neutral point will be at the middle point of the line joining the two charges.
(D) For two negative charges placed along a line, there will not be any neutral point.
Choose the correct answer from the options given below:

Which of the following is NOT the property of electric field lines?

A thick long straight wire of radius 'a' is carrying steady current I. The current I is uniformly distributed across the cross-section. The ratio of magnetic fields at a distance a/2 and 3a/2 from the central axis of the wire is

Two cells with internal resistances \( r_1 \) and \( r_2 \) are connected across the load resistance R as shown in the figure. The values of \( r_1, r_2 \) and R are (1/2) \( \Omega \), (1/3) \( \Omega \) and (9/5) \( \Omega \), respectively. The current through R is:

The maximum and minimum amplitudes of a modulated carrier wave are 1000 mV and 200 mV respectively, the modulation index is

An electromagnetic wave moves in vacuum. Its speed is c.
Choose the correct options about the characteristics of electromagnetic waves:
(A) \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \)
(B) Electromagnetic waves are transverse in nature.
(C) Both the electric field and magnetic field vibrate perpendicular to the direction of propagation of waves
(D) Electromagnetic waves are longitudinal in nature.
Choose the correct answer from the options given below:

Two capacitors of capacitances of \( 6 \, \mu F \) and \( 12 \, \mu F \) are connected in series with a 12 V battery. The total energy stored in the combination is

For \(y=x e^x\), which of the following is correct ?

The maximum value of the objective function \(z=2 x+3 y\) of an L.P.P. subjected to the constraints \(x-y \leq 1, x+y \leq 3, x, y \geq 0\), 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 \((n-1) d, n s, n p\) 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.
The spin only magnetic moment of \(\left[ MnBr _4\right]^{2-}\) is 5.9 BM. Predict the geometry of the complex ion?

Match List-I with List-II

List-I (Reaction)	List-II (Type of reaction)
(A) Hydrolysis of Ethyl Chloride	(I) Substitution reaction
(B) 2-Propanol is treated with Conc. Sulphuric acid	(II) Addition reaction
(C) Reaction of HCN with Acetone	(III) Degradation reaction
(D) Treatment of acetamide with NaOH and Br2	(IV) Elimination reaction

Choose the correct answer from the options given below:

If \(\int \frac{2 x-5}{(2 x-3)^3} e^{2 x} d x=\frac{\lambda e^{2 x}}{(2 x-3)^2}+C\), where \(C\) is an arbitrary constant then the value of \(\lambda\) is :

Two point charges \( q_1 = 10 \times 10^{-8} \text{ C} \) and \( q_2 = -2 \times 10^{-8} \text{ C} \) are separated by a distance of 6 cm. The distance from \( q_1 \) where the electric potential is zero, can be