Match List-I with List-II

List-I	List-II
A. Impedance of a series LCR circuit at resonance	(I) Voltage across L and C are 180 degree out of phase
B. For a series LC Circuit	(II) Current in L and C are 180 degree out of phase
C. For a parallel LC circuit	(III) Minimum
D. Reactance of a capacitor in a DC circuit	(IV) Infinite

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A charged particle moving with a certain velocity enters a uniform electric field perpendicular to its direction. In this context, which of the following statements are correct?
(A) Force acting on the particle is constant
(B) Acceleration of the particle is constant
(C) Velocity of the particle is constant
(D) Displacement of the particle follows a parabolic path
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Two cylindrical wires of the same material have their lengths in the ratio 2: 1 and their diameters in the ratio \(1: 3\). The ratio of the resistance of thinner wire to that of thicker wire is:

The electrical resistance to the diffusion current in the depletion layer in a p-n junction is large due to the presence of

A magnetic field energy of \( 34 \times 10^{-6} \) J is stored in an inductor of inductance 1.7 mH in an LC circuit. The current flowing in the inductor is:

Find the true statement:

In a semiconductor, there are :
(A) no free electrons at any temperature
(B) no free electrons at 0 K
(C) number of free electrons increase with temperature
(D) number of free electrons decrease with temperature
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Integrating factor of the differential equation \(x \frac{d y}{d x}-y=3 x^2\) 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 comple: to yield three orbitals of lower energy, \(t_{2 g}\) 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 paring 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.
Which of the following complex is not expected to be coloured?

The nuclear force is a short range force, this can be explained by fact that the binding energy per nucleon versus mass number curve:

Consider the following hypothesis test :
\( H_0 : \mu=18 \)
\( H_1 : \mu \neq 18 \)
If a sample of 48 provided a sample mean \(\bar{x}=17\),
and a sample standard deviation \(\sigma=4.5\),
then the value of the \(t\)-test statistic is :

You must have seen the weed Calotropis growing in abandoned fields. The plant produces highly poisonous _________ and that is why you never see any cattle or goats browsing on this plant.

Arrange the given compounds in order of decreasing oxidation state of nitrogen:
A. \(N_2\)
B. \(NO\)
C. \(HNO_3\)
D. \(NH_4Cl\)
Choose the correct answer from the options given below: