An electron moving with velocity of \(5.4 \times 10^6\) m/sec. What is the de-Broglie wavelength associated with them (\(h = 6.63 \times 10^{-34}\) J/s)

A body of mass 20 g and charge \( +50 \text{ }\mu\text{C} \) is suspended from the ceiling by a string. A horizontal electric field of 10 kV/m is applied.
The angle between the string and the vertical direction is :

A sinusoidal voltage with peak value 220 V and variable frequency is applied to a series LCR circuit in which \( R = 10 \, \Omega \), \( L = 4 \, \text{mH} \), and \( C = 100 \, \text{mF} \). Consider the following:
(A) Resonant angular frequency \(\left(w_o\right)=50 rad / s\)
(B) Resonant frequency \(\left(v_o\right)=25 / n Hz\)
(C) Resonant frequency \(\left(v_o\right)=50 / n Hz\)
(D) The rms current at resonance is 15.5 A
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Match List-I with List-II

List-I (Parameter of Magnetic Dipole)	List-II (Formula)
(A) Magnetic moment	(I) \( \mu_0 2m / (4\pi x^3) \)
(B) Magnetic field on the equatorial line	(II) \( m \times B \)
(C) Magnetic field on axial line	(III) \( IA \)
(D) External torque in magnetic field	(IV) [Missing/Constant]

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The core of a transformer is laminated to:

In which of the following transitions will the wavelength of light emitted be minimum?

Two capacitors of capacitances 2 \( \mu\text{F} \) and 4 \( \mu\text{F} \) are connected in parallel. A charge of 6 \( \mu\text{C} \) is given to the combination which gets shared. The ratio of the charges on the two capacitors, respectively will be

An infinite plane sheet of charge density \(10^{-8} \text{ C m}^{-2}\) is held in air. In this situation, the distance between two equipotential surfaces, whose potential difference is 10 V, will be (Given: Permittivity of vacuum\(\epsilon_0 \approx 8.85 \times 10^{-12} F / m\))

Let a relation \(R=\{(a, b): a\) is a factor of \(b, a, b \in N\}\). Then, \(R\) is __________.

The structures present in human sperm are-
(A). Nucleus
(B). Zona pellucida
(C). Acrosome
(D). Mitochondria
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If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(x\)-axis, \(y\)-axis, \(z\)-axis respectively, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is equal to:

The sequencing of fragments using automated DNA sequencers in HGP, worked on the principle of the method that was developed by:

Read the given paragraph and answer the given question :
Parasitism has evolved in many taxonomic groups from plants to higher vertebrates. Many parasites have evolved to be host specific in such a way that both host and the parasite tend to co-evolve. In accordance with their life styles, parasite evolve special adaptations and complex life cycle. Identify the statements which are not correct regarding host–parasite relationship:
(A) Host and parasite co-evolve.
(B) Parasite develops a main nervous system to survive.
(C) If host rejects parasite, parasite evolves counter-mechanisms to neutralize host defenses.
(D) If host rejects parasite, parasite succeeds by shifting to another host.
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