A cylindrical bar magnet is kept along the axis of circular coil. If the magnet is rotated about its axis, then :

The speed of an electromagnetic wave in a medium of dielectric constant 2.25 and relative permeability 4 is:

Match List I with List - II.

List - I	List - II
(A) Interference experiment	(I) Maxwell
(B) Electromagnetic theory of light	(II) Christian Huygens
(C) Wave theory of light	(III) Isaac Newton
(D) Particle theory of light	(IV) Thomas Young

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Match the electromagnetic waves in Column-l with production methods in Column-II

List-I (Electromagnetic Waves)	List-II (Production Methods)
(A) Microwaves	(I) LC oscillator
(B) Infrared	(II) Magnetron
(C) X-rays	(III) Vibration of atoms/molecules
(D) Radio waves	(IV) Bombarding large atomic number metal target with fast-moving electrons

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The ratio of the radius of the third orbit to that of the second orbit in a hydrogen atom is

The kinetic energy of an electron in the ground state of hydrogen atom is \(1 3 . 6 ~ e V\). The potential energy (P.E) and total energy ( E ) of electron in this state is :

A series combination of two capacitors \( C_1 = 3 \, \mu\text{F} \) and \( C_2 = 6 \, \mu\text{F} \) is connected in parallel with a third capacitor \( C_3 = 4 \, \mu\text{F} \). This system is connected to a 10 V battery. The total energy stored in the system is:

Which of the following is not correct about the Central Limit Theorem?

The \(K H\) values of \(HCOOH > CH _4> Ar\) and CO _2 > at \(2 9 8 K\) are \(1 . 8 3 \times 1 0 - 5 ~ k b a r\), \(0.413 kbar , 40 kbar\) and 1.67 kbar respectively. Arrange them in the order of their decreasing solubility at constant pressure :

"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
Arrange the following acids in order of their increasing \(\text{pKa}\) value:
(A) Benzoic acid
(B) 2-nitrobenzoic acid
(C) 4-nitrobenzoic acid
(D) 4-methoxybenzoic acid
Choose the correct answer from the options given below:"

If matrix\(A_p=\left[\begin{array}{ll}p & (p+1) \\ p & (p-1)\end{array}\right], p \in \mathbb{N}\) (where \(\mathbb{N}\) is the set of natural numbers), then the value of \(\left|A_1\right|+\left|A_2\right|+\left|A_3\right|+\cdots+\left|A_{2025}\right|\) is:

If the solubility of the given gases in water decreases in the order of formaldehyde, methane, vinyl chloride, argon.
Match List-I with List-II.

List-I(Gas)	List-II(\((\mathrm{K})_{\mathbf{H}} / \mathrm{k}\) bar)
(A) Formaldehyde	(I) 40.3
(B) Vinyl Chloride	(II) 0.413
(C) Argon	(III) 1.83 x \(\mathrm{10}^{-5}\)
(D) Methane	(IV) 0.611

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Match List - I with List - II

List - I (Complex)	List - II (Hybridisation)
(A) \([CoF_6]^{3-}\)	(I) \(sp^3\)
(B) \([Co(NH_3)_6]^{3+}\)	(II) \(dsp^2\)
(C) \([NiCl_4]^{2-}\)	(III) \(d^2sp^3\)
(D) \([Ni(CN)_4]^{2-}\)	(IV) \(sp^3d^2\)

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