If \(f(x)=3 x^2+10 x-5\), then by using differentials the appropriate value of \(f(2.03)\) is

The transfer of integral number of ___________ is one of the evidence of quantization of electric charge.

Let \(\theta\) be the angle between two vectors \(\vec{a}\) and \(\vec{b}\). Then match List-I with List-II

List-I	List-II
(A) \(\sin \theta\)	(I) \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}\)
(B) \(\cos \theta\)	(II) \(|\vec{a} \times \vec{b}|\)
(C) Area of the parallelogram with adjacent sides represented by \(\vec{a}\) and \(\vec{b}\)	(III) \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|}\)
(D) Projection of \(\vec{a}\) on \(\vec{b}\)	(IV) \(\frac{|\vec{a} \times \vec{b}|}{|\vec{a}||\vec{b}|}\)

Choose the Correct answer from the options given below :

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4, 18) and (6, 12). If objective function is Z = 30x + 20y then the sum of the maximum and the minimum values of Z is

The points of discontinuity of the function \(f\) defined by \(f(x)=\begin{cases} x + 2 & x \leq 1 \\x - 2 & 1 < x < 2\text { are: } \\0 & x \geq 2 \end{cases}\)

The number of equivalence relation on the set {1, 2, 3} containing (1, 2) and (2, 1) is

The point on the curve \(y^2=x\), where the tangent makes an angle of \(\frac{\pi}{4}\) with x-axis is:

If we double the number of turns of coil in a moving coil galvanometer, its voltage sensitivity will :

Match List - I with List - II.

List - I	List - II (Physical Quantity) (S.I. Unit)
(A) Electric Field intensity	(I) Coulomb/metre
(B) Electric dipole moment	(II) Newton (metre)\(^2\)/Coulomb
(C) Linear charge density	(III) Newton/Coulomb
(D) Electric flux	(IV) Coulomb - metre

Choose the correct answer from the options given below :

A parallel plate air capacitor is charged, and then the battery is disconnected. Now on inserting a dielectric between the plates of the capacitor, which of the following change:
1. potential difference between the plates
2. charge on the plates
3. electric field between the plates
4. energy stored in the capacitor
Choose the correct answer from the options given below:

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:

The derivative of \(\sqrt{e^{\sqrt{x}}}\) with respect to \(x\) is :

Alkyl halides react with sodium to give alkanes with double number of carbon atoms in