# An electron and an alpha particle are accelerated by the same potential difference. Let $$\lambda_\mathrm{e}$$ and $$\lambda_\mathrm{\alpha}$$ denote the de-Broglie wavelengths of the electron and the alpha particle, respectively, then: 1. $$\lambda_{\mathrm{e}}>\lambda_{\alpha}$$ 2. $$\lambda_{\mathrm{e}}=4\lambda_{\alpha}$$ 3. $$\lambda_{\mathrm{e}}=\lambda_{\alpha}$$ 4. $$\lambda_{\mathrm{e}}<\lambda_{\alpha}$$

Subtopic:  De-broglie Wavelength |
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An object moving along a horizontal $$x\text-$$direction with kinetic energy $$10~\text J$$ is displaced through $$x=\left(3\hat{i}\right)\text{m}$$ by the force $$\vec{{{F}}}=\left(-2\hat{i}+3\hat{j}\right)~\text N.$$ The kinetic energy of the object at the end of the displacement $$x$$ is:
 1 $$10~\text J$$ 2 $$16~\text J$$ 3 $$4~\text J$$ 4 $$6~\text J$$
Subtopic:  Work Energy Theorem |
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NEET - 2024
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An object falls from a height of $$10~\text m$$ above the ground. After striking the ground it loses $$50\%$$ of its kinetic energy. The height up to which the object can re-bounce from the ground is:
 1 $$7.5~\text m$$ 2 $$10~\text m$$ 3 $$2.5~\text m$$ 4 $$5~\text m$$
Subtopic:  Gravitational Potential Energy |
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In the circuit shown below, the inductance $$L$$ is connected to a source. The current flowing in the circuit is $${I=I_{0}\sin\omega t.}$$ The voltage drop $$(V_L)$$ across $$L$$ is:

1. $$\omega L~I_0\sin\omega t$$
2. $$\frac{{I}_0}{\omega{L}}\sin\omega t$$
3. $$\frac{{I}_0}{\omega{L}}\cos\omega t$$
4. $$\omega L~I_0\cos\omega t$$
Subtopic:  Different Types of AC Circuits |
From NCERT
NEET - 2024
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A $$12~\text{pF}$$ capacitor is connected to a $$50~\text V$$ battery, and the electrostatic energy stored in the capacitor in $$\text{nJ}$$ is:
1. $$15$$
2. $$7.5$$
3. $$0.3$$
4. $$150$$
Subtopic:  Energy stored in Capacitor |
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A uniform wire of diameter $$d$$ carries a current of $$100~\text{mA}$$ when the mean drift velocity of electrons in the wire is $$v.$$ For a wire of diameter $${\dfrac{d}{2}}$$ of the same material to carry a current of $$200~\text{mA},$$ the mean drift velocity of electrons in the wire is:
 1 $$4v$$ 2 $$8v$$ 3 $$v$$ 4 $$2v$$
Subtopic:  Current & Current Density |
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In an electrical circuit, the voltage is measured as $${V}=(200\pm4)$$ volts and the current is measured as $${I}=(20\pm0.2)~\text A.$$ The value of the resistance is:
1. $$(10\pm4.2)~\Omega$$
2. $$(10\pm0.3)~\Omega$$
3. $$(10\pm0.1)~\Omega$$
4. $$(10\pm0.8)~\Omega$$
Subtopic:  Derivation of Ohm's Law |
From NCERT
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A step-up transformer is connected to an AC mains supply of $$220~\text V$$ to operate at $$11000~\text V, 88$$ watt. The current in the secondary circuit, ignoring the power loss in the transformer, is:
 1 $$8~\text{mA}$$ 2 $$4~\text{mA}$$ 3 $$0.4~\text{A}$$ 4 $$4~\text{A}$$
Subtopic:  Transformer |
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A particle is moving along the $$x\text-$$axis with its position $$(x)$$ varying with time $$(t)$$ as $$x=\alpha t^{4}+\beta t^{2}+\gamma t+\delta.$$ The ratio of its initial velocity to its initial acceleration, respectively, is:
1. $$2\alpha:\delta$$
2. $$\gamma:2\delta$$
3. $$4\alpha:\beta$$
4. $$\gamma:2\beta$$
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
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NEET - 2024
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The radius of gyration of a solid sphere of mass $$5~\text{kg}$$ about $$XY$$ is $$5~\text m$$ as shown in the figure. The radius of the sphere is $$\frac{5x}{\sqrt{7}}~\text m,$$then the value of $$x$$ is:

1. $$5$$
2. $$\sqrt{2}$$
3. $$\sqrt{3}$$
4. $$\sqrt{5}$$

Subtopic:  Moment of Inertia |
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From NCERT
NEET - 2024