Solve this following
Question: If $y=\sec x-\tan x .$ show that $(\cos x) \frac{d^{2} y}{d x^{2}}=y^{2}$ Solution:...
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Question: If $y=e^{-} \cos x$, show that $\frac{d^{2} y}{d x^{2}}=2 e^{-x} \sin x$ Solution:...
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Question: If $y=3 \cos (\log x)+4 \sin (\log x)$, prove that $x^{2} y_{2}+x y_{1}+y=0$ Solution:...
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Question: If $y=2 \sin x+3 \cos x$, s how that $y+\frac{d^{2} y}{d x^{2}}=0$ Solution:...
Read More →Find the equivalent resistance of the circuits shown in figure (32-E17)
Question: Find the equivalent resistance of the circuits shown in figure (32-E17) between the points a and $b$. Each resistor has a resistance $r$. Solution:...
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Question: If $y=x+\tan x$, show that $\cos ^{2} \cdot \frac{d^{2} y}{d x^{2}}-2 y+2 x=0$ Solution:...
Read More →What should be the value of R in figure (32-E 16)
Question: What should be the value of $R$ in figure $(32-E 16)$ for which the current in it is zero? Solution: The circuit is in wheat stone symmetry So, for all values of $R$, current=0....
Read More →Find the second derivative of:
Question: Find the second derivative of: (i) $x \sin x$ (ii) $e^{2 x} \cos 3 x$ (iii) $x^{3} \log x$ Solution:...
Read More →Consider the circuit shown in the figure (32-E8).
Question: Consider the circuit shown in the figure (32-E8). Find the current through the $10 \Omega$ resistor when the switch S is (a) Open and (b) Closed. Solution:...
Read More →A wire of resistance 15.0Ω is bent to form a regular hexagon ABCDEFA.
Question: A wire of resistance $15.0 \Omega$ is bent to form a regular hexagon ABCDEFA. Find the equivalent resistance of the loop between the points (a) $A$ and $B$, (b) $A$ and $C$ and (c) $A$ and $D$. Solution:...
Read More →Find the equivalent resistance of the network shown in figure
Question: Find the equivalent resistance of the network shown in figure ( $32-\mathrm{E} 7)$ between the points a and $b$. Solution:...
Read More →An ideal battery sends a current of 5A in a resistor.
Question: An ideal battery sends a current of $5 \mathrm{~A}$ in a resistor. When another resistor of value $10 \Omega$ is connected in parallel, the current through the battery is increased to $6 \mathrm{~A}$. Find the resistance of the first resistor. Solution:...
Read More →Find the second derivate of :
Question: Find the second derivate of : (i) $x^{11}$ (ii) $5^{x}$ (iii) $\tan x$ (iv) $\cos ^{-1} x$ Solution:...
Read More →Figure (32-E6) shows a part of a circuit.
Question: Figure (32-E6) shows a part of a circuit. If a current of $12 \mathrm{~mA}$ exists in the $5 \mathrm{k} \Omega$ resistor, find the currents in the other three resistors. What is the potential difference between the points $A$ and $B$ ? Solution:...
Read More →A bulb is made using two filaments.
Question: A bulb is made using two filaments. A switch selects whether the filaments are used individually or in parallel. When used with a $15 \mathrm{~V}$ battery, the bulb can be operated at $5 \mathrm{~W}, 10 \mathrm{~W}$ or $15 \mathrm{~W}$. What should be the resistances of the filaments? Solution:...
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Question: If $x=a(\theta-\sin \theta), y=a(1+\cos \theta)$, find $\frac{d^{2} y}{d x^{2}}$ Solution:...
Read More →Suppose you have three resistors of 20Ω, 50Ω and 100Ω.
Question: Suppose you have three resistors of $20 \Omega, 50 \Omega$ and $100 \Omega$. What minimum and maximum resistances can you obtain from these resistors? Solution:...
Read More →Three bulbs, each having a resistance of
Question: Three bulbs, each having a resistance of $180 \Omega$,are connected in parallel to an ideal battery of emf $60 \mathrm{~V}$. find the current delivered by the battery when (a) all the bulbs are switched on, (b) two of the bulbs are switched on and (c) Only one bulb is switched on. Solution:...
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Question: If $x=(2 \cos \theta-\cos 2 \theta)$ and $=(2 \sin \theta-\sin 2 \theta)$, find $\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)_{\theta=\frac{\pi}{2}} .$ Solution:...
Read More →The resistance of the rheostat shown in figure (32-E5)
Question: The resistance of the rheostat shown in figure (32-E5) is $30 \Omega$. Neglecting the meter resistance; find the minimum and maximum currents through the ammeter as the rheostat is varied. Solution:...
Read More →If the reading of ammeter A1 in figure (32-E4) is 2.4 A,
Question: If the reading of ammeter $\mathrm{A}_{1}$ in figure (32-E4) is $2.4 \mathrm{~A}$, what will the ammeters $\mathrm{A}_{2}$ and $\mathrm{A}_{3}$ read? Neglect the resistances of the ammeter. Solution:...
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Question: If $x=\frac{\sin ^{3} t}{\sqrt{\cos 2 t}}, y=\frac{\cos ^{3} t}{\sqrt{\cos 2 t}}$, find $\frac{d y}{d x}$ Solution:...
Read More →The battery of emf 100 V and a resistor of resistances 10kΩ are joined in series.
Question: The battery of emf $100 \mathrm{~V}$ and a resistor of resistances $10 \mathrm{k} \Omega$ are joined in series. This system is used as a source to supply current to an external resistance $\mathrm{R}$. If $\mathrm{R}$ is not greater than $100 \Omega$, the current through it is constant up to two significant digits. Find its value. This is the basic principle of a constant-current source Solution:...
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Question: If $x=2 \cos \theta-\cos 2 \theta$ and $y=2 \sin \theta-\sin 2 \theta$, show that $\frac{d y}{d x}=\tan \frac{3 \theta}{2}$ Solution:...
Read More →Consider N = n1n2 identical cells, each of emf ε and internal resistance r.
Question: Consider $N=n_{1} n_{2}$ identical cells, each of emf $\varepsilon$ and internal resistance $r$. Suppose $\mathrm{n}_{1}$ cells are joined in series to form a line and $\mathrm{n}_{2}$ such lines are connected in parallel. The combination drives a current in an external resistance $R$. (a) Find the current in external resistance. (b) Assuming that $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ can be continuously varied, find the relation between $\mathrm{n}_{1}, \mathrm{n}_{2}, R$ and $r$ for ...
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