The separation between the plates of a parallel plate capacitor of capacitance 2 pF is 0.5 mm . The area of the plates of the capacitor is (Given: \(\varepsilon_0=8.85 \times 10^{-12} C ^2 N^{-1} m^{-2}\) )

Two point charges \(+3 \mu C\) and \(-8 \mu C\) attracts each other with a force of 40 N , when separated by finite distance d . If a charge of \(+5 \mu C\) is added to each of them, then the force between them will become:

A current element \(\Delta \vec{l}=\Delta x \hat{i}\) (where \(\Delta x=1 cm\) ) is placed at the origin and carries a current 10 A . The magnetic field on y -axis at a distance of 0.5 m is :

A magnet of magnetic moment \( 50 \hat{i} \text{ A m}^2 \) is placed along the X-axis in a magnetic field \( \vec{B} = (0.5 \hat{i} + 3.0 \hat{j}) \text{ T} \). The torque acting on it is

Match List-I with List-II

List-I	List-II
(A) Resistive Circuit	(I) No power dissipation
(B) Purely inductive or capacitive circuit	(II) Maximum power dissipated because \( X_L = X_C \)
(C) LCR series circuit	(III) Power dissipated only in resistor
(D) Power dissipated at resonance in LCR circuit	(IV) Maximum power dissipation

Choose the correct answer from the options given below :

A conducting circular loop is placed in a uniform magnetic field of \( B = 0.5 \text{ T} \), with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at the rate of \( \frac{dr}{dt} = 4 \text{ mm/s} \). When the radius of the loop is \( r = 4 \text{ cm} \), the induced emf in the loop is

The number of electrons in one coulomb of electric charge is :

Which of the following steps are included to make a healthy society?
(A) Aware the people to uncontrolled population growth
(B) Aware the people to social evil like sex abuse
(C) Aware the people to sex related crime
(D) The Peoples lead to increase the mortality rate of mother and infant
Choose the correct answer from the options given below:

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.
Identify the stable pair of ions :

India has more than 1000 varieties of mango. This is an example of:

Which of the following statements are true?
(A) Rheostat can be used both as a variable resistance and a potential divider.
(B) An electrical circuit is functional only if all the components of the circuit are connected in proper order, assuming that all circuit components/ devices are in working condition and key is closed.
(C) An open circuit means a break in some part of a circuit which could be deliberate such as a key in open position or a fault such as broken wire or burnt out component(s) or loose connection.
(D) Rheostat as a potential divider gives variable resistance.
Choose the correct answer from the options given below:

The equation of the normal to the curve \(y=\sin x\) at \((0,0)\) is :

Pick the correct structure for carbolic acid among the following compounds: