Three charges, each equal to +q, are placed at the corners of an equilateral triangle ABC of side 'a' as shown in the figure. P and R are the mid-points of BC and CA. The work done in taking a charge Q from point P to R is:

Match List - I with List - II.

List I	List II
(A) Direction of induced current in a conductor moving in a magnetic field.	(I) Ampere's swimming rule
(B) Direction of the magnetic field due to a current carrying long wire	(II) Fleming's left hand rule
(C) Force experienced by a moving charged particle in the magnetic field	(III) Fleming's right hand rule
(D) Direction of deflection of magnetic needle due to current in the wire	(IV) Right hand rule

Choose the correct answer from the options given below :

An electron moving with velocity of \(5.4 \times 10^6\) m/sec. What is the de-Broglie wavelength associated with them (\(h = 6.63 \times 10^{-34}\) J/s)

The dimension of magnetic induction can be written as

A resistance of \( 15\Omega \) is connected in series with an unknown resistance \( R_1 \). This combination is connected to one gap of a meter bridge, while a resistance \( R_2 \) is connected in the other gap. The balance point is at 50 cm. When \( 15\Omega \) is removed, the balance point shifts by 10 cm. The value of \( R_1 \) is

A metal foil of neglible thickness is introduced between two parallel plates of a capacitor at the centre. The new capacitance of the capacitor would be :

The current-voltage graphs for a given metallic wire at two different temperatures, \( T_1 \) and \( T_2 \) are shown in the figure. The correct relation of temperatures and resistances will be :

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 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. 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 represents the correct pair?

If \(A =\left(\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right)\), be such that \(A ^{-1}=K A\), then the value of \(K\) is :

In the case of co-evolved plant pollinator mutualism where one of the species got extinct, what would be the impact on the other species?

Let [t] denote the greatest integer ≤ t and aZ = {ax : x ∈ Z, a ∈ R} (where Z is set of integer and R is set of real number). The set of points of discontinuity of the function f(x) = [2x] is given by

If in a pond there were 20 lotus plants last year and through reproduction 8 new plants are added, taking the current population to 28, then the birth rate will be -

In the (i) absence of electric field, and in the (ii) presence of electric field, the paths of electrons between successive collisions with the positive ions of the metal, are