A system of three charges -q, + Q and -q are placed at three points at equal distances on a straight line in the same order. If the potential energy of the system is found to be zero, find the ratio Q/q.

The energy of a photon of wavelength 1 \( \text{\AA} \) is
(Given: \( h = 6.63 \times 10^{-34} \text{ J s} \))

Identify the correct statement(s) among the following:
(A) If three electrical cells each of emf, E and internal resistance r are connected in series to a resistance R, the current drawn from them is 3E/(R+3r).
(B) If these three cells are connected in parallel combination, across resistance R then the current drawn will be E/(3R+r).
(C) If the two cells are connected in series and then one in parallel which are then connected across resistance R, then the current drawn will be 2E/(2R+2r).
(D) In a mixed grouping of cells, current will be maximum when total external resistance is equal to total equivalent internal resistance.
Choose the correct answer from the options given below :

Which of the following combination should be selected for better tuning of an LCR circuit used for communication ?

Time taken by sunlight to pass through a window of thickness 8 mm and refractive index \( \left( \frac{3}{2} \right) \) is :

In a series LCR circuit, \( C = 80 \, \mu\text{F} \), \( L = 5.0 \, \text{H} \) and \( R = 40 \, \Omega \) are connected to a variable frequency source of 240 V. The angular frequency of the source which drives the circuit at resonance will be:

A straight long wire carrying a current of 30 A is placed in an external uniform magnetic field of \( 4 \times 10^{-4} \, T \) parallel to the current. The magnitude of the resultant magnetic field at a point 2 cm away from the wire is

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_2\), set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\), orbitals will increase by \((3 / 5) \Delta_0\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_0\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_0\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Choose the correct statement from the following:

List-1	List-2
(A) \(y=\sqrt{x^3}\)	(I) \(-1\)
(B) \(y=\sqrt{x}\)	(II) 1
(C) \(y=x^3-47 x\)	(III) 1/4
(D) \(x y=16\)	(IV) 3

Choose the correct answer from the options given below :

Which of the following statements are correct?
(A) In ideal solutions, the enthalpy of mixing of the pure components to form the solution is zero.
(B) The volume of the solution is equal to the sum of the volumes of the two components.
(C) In binary ideal solutions, attractive forces between A-A and B-B are nearly equal to those between A-B.
(D) In negative Raoult's law deviation, attractions between A-B are weaker than those of A-A and B-B attractions.
Choose the correct answer from the options given below:

Arrange the given steps of 'Recombinant DNA Technology' in correct sequence.
A. Transfer of recombinant plasmid into host cell for cloning.
B. Ligation of desired DNA to plasmid.
C. Selection of desired DNA and plasmid.
D. Cutting of desired DNA and plasmid using same restriction enzyme.
Choose the correct answer from the options given below:

A non-polar dielectric material is placed in an external electric field. Choose the correct statement(s) from the following:
(A) There will be no change in the positions of positive and negative charges inside the dielectric.
(B) The positive charges of molecules will shift opposite to the direction of the electric field.
(C) The negative charges of molecules will shift in the direction of the electric field.
(D) The positive charges of the molecules will shift in the direction of the field and negative charges of the molecules will shift opposite to the field.
Choose the correct answer from the options given below:

When data of the variable is collected at distinct time intervals for a specified period of time, it is called