Three charges \(+4 q, Q\) and \(q\) are placed along \(x\)-axis at points, \(x=0, I / 2\) and I respectively. The value of Q to make the net force on \(q\) to be zero :

Which of the following statements are true?
(A) The potential energy for a system of two negative point charges is negative
(B) Electrostatic force is a conservative force
(C) Negative potential energy between two charges implies that the force between them is repulsive
(D) Electrostatic potential energy is a scalar quantity
Choose the correct answer from the options given below:

Which of the following phenomenon is responsible for the reddish appearance of sun during sunset or sunrise ?

When a ray of light is incident on the face AB of prism normally, after refraction it is found to graze the side AC as shown in the figure, the refractive index of the prism is

Choose the correct option from the following:
(A) The internal resistance of a cell depends on its distance between electrodes and on the area of the electrodes.
(B) The emf of a cell is measured when it is used in series in an electrical circuit carrying current I.
(C) If a cell of emf E and of internal resistance r is providing current/through a resistance R then the potential difference across the cell is V = I(R + r).
(D) The emf of a cell is 1 V, if 1 J of work is done by the cell to drive 1 C of charge in the whole circuit.
Choose the correct answer from the options given below:

The primary coil of an ideal step up transformer has 200 turns and transformation ratio is 50. The input voltage is 220 V, the voltage across secondary coil will be:

A thin convex lens of refractive index 1.5 has focal length f1. When immersed in a liquid of refractive index 5/3, its focal length is found to be f2. The relationship between f1 and f2 is:

Among vertebrates, the maximum number of species belong to

Which one of the following plants is the source of cannabinoids commonly used in drug abuse?

Arrange the following compounds in the increasing order of their boiling points:
A. \(\text{CH}_3\text{CH}_2\text{CH}_2\text{COOH}\)
B. \(\text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{OH}\)
C. \(\text{CH}_3\text{CH}_2\text{OCH}_2\text{CH}_3\)
D. \(\text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_3\)
E. \(\text{CH}_3\text{CH}_2\text{CH}_2\text{CHO}\)
Choose the correct answer from the options given below:"

A point charge – 5 µC is at a distance 5 cm directly above the centre of a square of side 10 cm.
The magnitude of electric flux through this square is:

Read the passage given below and answer the question.
The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7 . The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence \(( Cu , Zn )\). Thus early in the series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti (III) or Ti (II). At the other end, the only oxidation state of zinc is \(+ 2\) (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum of the s - and d-electrons upto manganese ( \(Ti ^{I V} O _2, V^V O _2^{+}, Cr ^{V I} O _4^{2-}\), \(Mn ^{\text {VII }} O _4\) ) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe ^{I I, I I I}, Co ^{I I, I I I}, Ni ^{I I}, Cu ^{I, I I}, Zn ^{I I}\).
The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g. \(V ^{I I}, V^{I I I}, V^{I V}, V^V\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit of two.
An interesting feature in the variability of oxidation states of the d-block elements is noticed among the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of dblock. For example, in group 6, \(Mo ( VI )\) and \(W ( VI )\) are found to be more stable than \(Cr ( VI )\). The \(Cr ( VI )\) in the form of dichromate in acidic medium is a strong oxidising agent, whereas \(MoO _3\) and \(WO _3\) are not.
Low oxidation states are found when a complex compound has ligands capable of \(\pi\)-acceptor character in addition to the \(\sigma\)-bonding. For example, in \(Ni ( CO )_4\) and \(Fe ( CO )_5\), the oxidation state of nickel and iron is zero.
Most acidic species among the following is :

The half life of a radioactive substance is 30 s. Calculate the time taken for the sample to decay to \( \frac{3}{4} \) th its initial value.