# At any instant, two elements X1 and X2 have the same number of radioactive atoms. If the decay constant of X1 and X2 are 10 $$\lambda$$ and $$\lambda$$ respectively, then the time when the ratio of their atoms becomes $$\frac1e$$ will be: 1.  $$\frac{1}{11\lambda}$$ 2.  $$\frac{1}{9\lambda}$$ 3.  $$\frac{1}{6\lambda}$$ 4.  $$\frac{1}{5\lambda}$$

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Six charges $$+q,$$ $$-q,$$ $$+q,$$ $$-q,$$ $$+q$$ and $$-q$$ are fixed at the corners of a hexagon of side $$d$$ as shown in the figure. The work done in bringing a charge $$q_0$$ to the centre of the hexagon from infinity is:
($$\varepsilon_0\text-$$permittivity of free space)
 1 zero 2 $$\dfrac{-q^2}{4\pi\varepsilon_0d}$$ 3 $$\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)$$ 4 $$\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)$$
Subtopic:  Electric Potential Energy |
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An organ pipe filled with a gas at $$27^\circ \text{C}$$ resonates at $$400$$ Hz in its fundamental mode. If it is filled with the same gas at $$90^\circ \text{C},$$ the resonance frequency at the same mode will be:
 1 $$420$$ Hz 2 $$440$$ Hz 3 $$484$$ Hz 4 $$512$$ Hz
Subtopic:  Standing Waves |
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The position-time $$(x\text-t)$$ graph for positive acceleration is:
 1 2 3 4
Subtopic:  Graphs |
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NEET - 2022
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The collector current in a common base amplifier using n-p-n transistor is $$24$$ mA. If $$80\text{%}$$ of the electrons released by the emitter are accepted by the collector, then the base current is numerically:
1. $$6$$ mA and leaving the base.
2. $$3$$ mA and leaving the base.
3. $$6$$ mA and entering the base.
4. $$3$$ mA and entering the base.
Subtopic:  Applications of Transistor (OLD NCERT) |
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NEET - 2022
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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following, is:
 1 all vessels contain unequal number of respective molecules. 2 the root mean square speed of molecules is same in all the three cases. 3 the root mean square speed of helium is the largest. 4 the root mean square speed of sulfur hexafluoride is the largest.
Subtopic:  Types of Velocities |
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In a gravitational field, the gravitational potential is given by, $$V=-\frac{K}{x}~\text{J/kg}$$. The gravitational field intensity at point $$(2,0,3)$$ m is:
 1 $$+\frac K2$$ 2 $$-\frac{K}{2}$$ 3 $$-\frac{K}{4}$$ 4 $$+\frac K4$$
Subtopic:  Gravitational Field |
From NCERT
NEET - 2022
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Two very long, straight, parallel conductor $$\mathrm{A}$$ and $$\mathrm{B}$$ carry current of $$5~\text{A}$$  and $$10~\text{A}$$ respectively and are at a distance of $$10~\mathrm{cm}$$ from each other. The direction of the current in the two conductors is the same. The force acting per unit length between two conductors is:
($$\mu_0=4\pi \times 10^{-7}$$ SI unit)
 1 $$2\times10^{-4}~\text{Nm}^{-1}$$  and is attractive 2 $$2\times10^{-4}~\text{Nm}^{-1}$$  and is repulsive 3 $$1\times10^{-4}~\text{Nm}^{-1}$$ and is attractive 4 $$1\times10^{-4}~\text{Nm}^{-1}$$  and is repulsive
Subtopic:  Force between Current Carrying Wires |
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The magnetic field on the axis of a circular loop of radius $$100~\text{cm}$$ carrying current $$I=\sqrt{2}~\text{A},$$ at a point $$1~\text{m}$$ away from the centre of the loop is given by:
1. $$3.14 \times 10^{-7} ~\text{T}$$
2. $$6.28 \times 10^{-7} ~\text{T}$$
3. $$3.14 \times 10^{-4} ~\text{T}$$
4. $$6.28 \times 10^{-4} ~\text{T}$$
Subtopic:  Magnetic Field due to various cases |
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NEET - 2022
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Two rods, one made of copper and other made of steel, of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $$385~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}$$ and $$50~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}$$ respectively. The free ends of copper and steel are held at $$100^\circ \text{C}$$ and $$0^\circ \text{C}$$ respectively. The temperature at the junction is, nearly:
1. $$12^\circ \text{C}$$
2. $$50^\circ \text{C}$$
3. $$73^\circ \text{C}$$
4. $$88.5^\circ \text{C}$$
Subtopic:  Conduction |
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NEET - 2022
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