Q27. To determine the resistance $( R )$ of a wire, a circuit is designed below. The $V - I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is $\_\_\_\_$ $\Omega$. [Figure] [Figure]

Q28. A alternating current at any instant is given by $i = [ 6 + \sqrt { 56 } \sin ( 100 \pi t + \pi / 3 ) ]$ A. The $r m s$ value of the current is $\_\_\_\_$ A.

Q28. A rod of length 60 cm rotates with a uniform angular velocity $20 \mathrm { rads } ^ { - 1 }$ about its perpendicular bisector, in a uniform magnetic filed $0.5 T$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is $\_\_\_\_$ V.

Q28. An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of [Figure]
$$\mathrm { V } = 50 \sqrt { 2 } \sin 100 \mathrm { t } \text { volt }$$
$20 \mu \mathrm {~F}$ is $\_\_\_\_$ V.

Q28. The current in an inductor is given by $\mathbf { I } = ( 3 \mathbf { t } + 8 )$ where $\mathbf { t }$ is in second. The magnitude of induced emf produced in the inductor is 12 mV . The self-inductance of the inductor $\_\_\_\_$ mH .

Q28. When a $d c$ voltage of 100 V is applied to an inductor, a $d c$ current of 5 A flows through it. When an ac voltage of 200 V peak value is connected to inductor, its inductive reactance is found to be $20 \sqrt { 3 } \Omega$. The power dissipated in the circuit is $\_\_\_\_$ W.

Q28. For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 25 nF . If resistance of $200 \Omega$ and 100 mH inductor is being used in the given circuit. The frequency of ac source is $\_\_\_\_$ $\times 10 ^ { 3 } \mathrm {~Hz}$. (given $\pi ^ { 2 } = 10$ )

Q28. A square loop PQRS having 10 turns, area $3.6 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 }$ and resistance $100 \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $\mathrm { B } = 0.5 \mathrm {~T}$ as shown. Work done in pulling the loop out of [Figure] the field in 1.0 s is $\_\_\_\_$ $\times 10 ^ { - 6 } \mathrm {~J}$.

Q28. An alternating emf $\mathrm { E } = 110 \sqrt { 2 } \sin 100 \mathrm { t }$ volt is applied to a capacitor of $2 \mu \mathrm {~F}$, the rms value of current in the circuit is $\_\_\_\_$ mA ,

Q28. When a coil is connected across a 20 V dc supply, it draws a current of 5 A . When it is connected across $20 \mathrm {~V} , 50 \mathrm {~Hz}$ ac supply, it draws a current of 4 A . The self inductance of the coil is $\_\_\_\_$ mH. ( Take $\pi = 3$ )

Q28. A straight magnetic strip has a magnetic moment of $44 \mathrm { Am } ^ { 2 }$. If the strip is bent in a semicircular shape, its magnetic moment will be $\_\_\_\_$ $\mathrm { Am } ^ { 2 }$. (given $\left. \pi = \frac { 22 } { 7 } \right)$

Q29. Two wavelengths $\lambda _ { 1 }$ and $\lambda _ { 2 }$ are used in Young's double slit experiment. $\lambda _ { 1 } = 450 \mathrm {~nm}$ and $\lambda _ { 2 } = 650 \mathrm {~nm}$. The minimum order of fringe produced by $\lambda _ { 2 }$ which overlaps with the fringe produced by $\lambda _ { 1 }$ is $n$. The value of $n$ is $\_\_\_\_$ .

Q29. A light ray is incident on a glass slab of thickness $4 \sqrt { 3 } \mathrm {~cm}$ and refractive index $\sqrt { 2 }$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is $\_\_\_\_$ $\mathrm { cm } . \left( \right.$ Given $\left. \sin 15 ^ { \circ } = 0.25 \right)$

Q29. In Young's double slit experiment, carried out with light of wavelength $5000 \backslash \mathrm { AA }$, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x = 0 \mathrm {~cm}$. The value of $x$ for third maxima is $\_\_\_\_$ mm .

Q29. In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm . The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x \times 10 ^ { - 5 } \mathrm {~m}$. The value of $x$ is :

Q29. The refractive index of prism is $\mu = \sqrt { 3 }$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is $\_\_\_\_$ .

Q29. Two coherent monochromatic light beams of intensities I and 4 I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $x \mathrm { I }$. The value of $x$ is $\$$ $\_\_\_\_$ .

Q29. A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be $\_\_\_\_$ $\times 10 ^ { - 3 } \mathrm { rad }$.

Q29. Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is $\_\_\_\_$ $\times 10 ^ { - 4 } \mathrm {~m}$

Q29. In a Young's double slit experiment, the intensity at a point is $\left( \frac { 1 } { 4 } \right) ^ { \text {th } }$ of the maximum intensity, the minimum distance of the point from the central maximum is $\_\_\_\_$ $\mu \mathrm { m }$. (Given : $\lambda = 600 \mathrm {~nm} , \mathrm {~d} = 1.0 \mathrm {~mm} , \mathrm { D } = 1.0 \mathrm {~m}$ )

Q29. A capacitor of reactance $4 \sqrt { 3 } \Omega$ and a resistor of resistance $4 \Omega$ are connected in series with an ac source of peak value $8 \sqrt { 2 } \mathrm {~V}$. The power dissipation in the circuit is $\_\_\_\_$ W.

Q30. A hydrogen atom changes its state from $n = 3$ to $n = 2$. Due to recoil, the percentage change in the wave length of emitted light is approximately $1 \times 10 ^ { - n }$. The value of $n$ is $\_\_\_\_$ . [Given $\mathrm { Rhc } = 13.6 \mathrm { eV } , \mathrm { hc } = 1242 \mathrm { eVnm } , \mathrm { h } = 6.6 \times 10 ^ { - 34 } \mathrm {~J}$ s mass of the hydrogenatom $= 1.6 \times 10 ^ { - 27 } \mathrm {~kg}$ ]

Q30. The disintegration energy $Q$ for the nuclear fission of ${ } ^ { 235 } \mathrm { U } \rightarrow { } ^ { 140 } \mathrm { Ce } + { } ^ { 94 } \mathrm { Zr } + n$ is $\_\_\_\_$ MeV. Given atomic masses of ${ } ^ { 235 } \mathrm { U } : 235.0439 u ; { } ^ { 140 } \mathrm { Ce } : 139.9054 u , { } ^ { 94 } \mathrm { Zr } : 93.9063 u ; n : 1.0086 u$, Value of $c ^ { 2 } = 931 \mathrm { MeV } / \mathrm { u }$

Q30. If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is $\_\_\_\_$ $\times 10 ^ { - 2 } \mathrm { MeV }$. (Given $1 \mathrm { u } = 931 \mathrm { MeV } / \mathrm { c } ^ { 2 }$, atomic mass of helium $= 4.002603 \mathrm { u }$ )

Q30. The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915 \tilde { A } \ldots$. The longest wavelength of spectral lines in the Balmer series will be $\_\_\_\_$ $\tilde { A } \ldots$.