A neutron star has a density equal to that of a nuclear matter.
Question: A neutron star has a density equal to that of a nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass $4.0 \times 10^{30} \mathrm{~kg}$ (twice the mass of the sun). Solution:...
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Question: Evaluate: $\int \frac{d x}{(\sqrt{x+1}+\sqrt{x+2})}$ Ans. $\frac{2}{3}(\mathrm{x}+2)^{3 / 2}-\frac{2}{3}(\mathrm{x}+1)^{3 / 2}+\mathrm{C}$ Solution:...
Read More →Assume that the mass of a nucleus is approximately given by
Question: Assume that the mass of a nucleus is approximately given by $\mathrm{M}=\mathrm{Am} \mathrm{p}_{\mathrm{p}}$ where $\mathrm{A}$ is the mass number. Estimate the density of matter in $\mathrm{kg} / \mathrm{m}^{3}$ inside a nucleus. What is the specific gravity of nuclear matter? Solution:...
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Question: Evaluate: $\int(3 \sin x+4 \operatorname{cosec} x)^{2} d x$ Ans. $\frac{57}{2} x-\frac{9}{4} \sin 2 x-16 \cot x+C$ Solution:...
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Question: Evaluate: $\int(3 \cot x-2 \tan x)^{2} d x$ Ans. $4 \tan x-9 \cos x-25 x+C$ Solution:...
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Question: Show that $\mathrm{AB}+\overline{\mathrm{AB}}$ is is always $1 .$ Solution:...
Read More →Design a logical circuit using AND,
Question: Design a logical circuit using AND, or and NOT gates to evaluate $\overline{\mathrm{ABC}}+\overline{\mathrm{BCA}}$. Solution:...
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Question: Evaluate: $\int \tan ^{-1} \sqrt{\frac{1-\sin x}{1+\sin x}} d x$ Ans. $\frac{\pi x}{4}-\frac{x^{2}}{4}+C$ Solution:...
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Question: Let $\mathrm{X}=\overline{\mathrm{ABC}}+\mathrm{B} \overline{\mathrm{CA}}+\mathrm{C} \overline{\mathrm{AB}}$ Evaluate $X$ for (a) $A=1, B=0, C=1$, (b) $A=B=C=1$ (c) $A=B=C=0$. Solution:...
Read More →A load resistor of 2kΩ connected in the collector branch of an amplifier circuit
Question: A load resistor of $2 \mathrm{k} \Omega$ connected in the collector branch of an amplifier circuit using a transistor in common-emitter mode. The current $\mathrm{B}=50$.the input resistance of the transistor is $0.50 \mathrm{k}$. If the input current is changed by $50 \mu \mathrm{A}$. (a) By what amount does the output voltage change, (b) by what amount does the input voltage change and (c) what is the power gain? Solution:...
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Question: Evaluate:. $\int \cos ^{-1}(\sin x) d x$ Ans. $\left(\frac{\pi \mathrm{X}}{2}-\frac{\mathrm{x}^{2}}{2}+\mathrm{C}\right)$ Solution: $=\frac{\pi}{2} x-\frac{x^{2}}{2}+c$...
Read More →When the base current in a transistor is changed from 30μA to 80 μA,
Question: When the base current in a transistor is changed from $30 \mu \mathrm{A}$ to $80 \mu \mathrm{A}$, the collector is changed from $1.0 \mathrm{~mA}$ to $3.5 \mathrm{~mA}$. find the current gain $\beta$. Solution:...
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Question: Evaluate: $\int \cos ^{1}\left(\frac{1-\tan ^{2} x}{1+\tan ^{2} x}\right) d x$ Ans. $\mathrm{x}^{2}+\mathrm{C}$ Solution:...
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Question: Evaluate : $\int \tan ^{-1}\left(\frac{\sin 2 x}{1+\cos 2 x}\right) d x$ Ans. $\frac{x^{2}}{2}+C$ Solution:...
Read More →Find the equivalent resistance of the network shown in figure (45-E8)
Question: Find the equivalent resistance of the network shown in figure (45-E8) between the points A and B. Solution:...
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Question: Evaluate: $\int\left(\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}\right) d x$ Ans. $\sec x-\operatorname{cosec} x+C$ Solution:...
Read More →Draw the current-voltage characteristics for the device shown
Question: Draw the current-voltage characteristics for the device shown in figure (45-E7) between the terminals A and B. Solution:...
Read More →Find the current through the resistance R is figure (45-E6)
Question: Find the current through the resistance $R$ is figure (45-E6) if (a) $R=12 \Omega$ (b) $R=48 \Omega$. Solution:...
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Question: Evaluate : i. $\int \frac{1}{(1+\cos 2 x)} d x$ ii. $\int \frac{1}{(1-\cos 2 x)} d x$ Solution: i. Given:...
Read More →Find the current through the battery in each of the circuits shown in figure (45-E5).
Question: Find the current through the battery in each of the circuits shown in figure (45-E5). Solution:...
Read More →What are the readings of the ammeters
Question: What are the readings of the ammeters $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ shown in figure (45-E4). Neglect the resistances of the meters. Solution:...
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Question: Evaluate: i. $\int \sqrt{1+\cos 2 x} d x$ ii. $\int \sqrt{1-\cos 2 x} d x$ Solution:...
Read More →Find the currents through the resistance in the circuits shown in figure (45-E3).
Question: Find the currents through the resistance in the circuits shown in figure (45-E3). Solution:...
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Question: Evaluate : i. $\int \frac{\cos x}{1+\cos x} d x$ ii. $\int \frac{\sin x}{(1-\sin x)} d x$ Solution:...
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