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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2901. |
The current density varies with radial distance r as\[j=a{{r}^{2}}\], in a cylindrical wire of radius R. The current passing through the wire between radial distance R/3 and R/2 is |
| A. | \[\frac{65\pi a{{R}^{4}}}{2592}\] |
| B. | \[\frac{25\pi a{{R}^{4}}}{72}\] |
| C. | \[\frac{65\pi {{a}^{2}}{{R}^{3}}}{2938}\] |
| D. | \[\frac{81\pi {{a}^{2}}{{R}^{4}}}{144}\] |
| Answer» B. \[\frac{25\pi a{{R}^{4}}}{72}\] | |
| 2902. |
The circuit diagram shown in figure consists of a very large (infinite) number of elements. The resistances of the resistors in each subsequent element differ by a factor of k from the resistances of the resistors in the previous elements. Determine the resistance \[{{R}_{AB}}\] between points A and B if the resistances of the first element are \[{{R}_{1}}\] and\[{{R}_{2}}\]. (k=1/2) |
| A. | \[\frac{{{R}_{1}}-{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\] |
| B. | \[\frac{{{R}_{1}}+{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\] |
| C. | \[\frac{{{R}_{1}}-{{R}_{2}}-\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\] |
| D. | None of these |
| Answer» B. \[\frac{{{R}_{1}}+{{R}_{2}}+\sqrt{R_{1}^{2}+R_{2}^{2}+6{{R}_{1}}{{R}_{2}}}}{2}\] | |
| 2903. |
Six identical resistors are connected as shown in the figure. The equivalent resistance will be |
| A. | maximum between P and R |
| B. | maximum between Q and R |
| C. | maximum between P and Q |
| D. | All are equal |
| Answer» D. All are equal | |
| 2904. |
A wire of resistance 12 ohms per meter is bent to from a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the figure, is |
| A. | \[3\Omega \] |
| B. | \[6\pi \Omega \] |
| C. | \[6\Omega \] |
| D. | \[0.6\pi \Omega \] |
| Answer» B. \[6\pi \Omega \] | |
| 2905. |
The current in the \[1\Omega \] resistor shown in the circuit is |
| A. | \[\frac{2}{3}A\] |
| B. | \[3A\] |
| C. | \[6A\] |
| D. | \[2A\] |
| Answer» E. | |
| 2906. |
Six equal resistances are connected between points P, Q and R as shown in figure. Then net resistance will be maximum between: |
| A. | P and R |
| B. | P and Q |
| C. | Q and R |
| D. | any two points |
| Answer» C. Q and R | |
| 2907. |
The equivalent resistance between points A and B is |
| A. | 2R |
| B. | (3/4)R |
| C. | (4/3)R |
| D. | (3/5)R |
| Answer» E. | |
| 2908. |
A wire has a resistance \[12\Omega \]. It is bent in the form of a circle. The effective resistance between two points on any diameter is |
| A. | \[6\Omega \] |
| B. | \[3\Omega \] |
| C. | \[\,12\Omega \] |
| D. | \[24\Omega \] |
| Answer» C. \[\,12\Omega \] | |
| 2909. |
A uniform wire of length l and radius r has a resistance of \[100\Omega \]. It is recast into a wire of radius\[\frac{r}{2}\]. The resistance of new wire will be: |
| A. | \[1600\Omega \] |
| B. | \[400\Omega \] |
| C. | \[200\Omega \] |
| D. | \[100\Omega \] |
| Answer» B. \[400\Omega \] | |
| 2910. |
The masses of the three wires of copper are in the ratio of 1 : 3 : 5 and their lengths are in the ratio of 5 : 3 : 1. The ratio of their electrical resistance is |
| A. | 0.0438078703703704 |
| B. | 0.210428240740741 |
| C. | 0.060474537037037 |
| D. | 5.23961805555556 |
| Answer» E. | |
| 2911. |
A 4 ohm resistance wire is bent through \[180{}^\circ C\] at its mid-point and the two halves are twisted together. Then the resistance is |
| A. | \[1\Omega \] |
| B. | \[2\Omega \] |
| C. | \[5\Omega \] |
| D. | \[8\Omega \] |
| Answer» B. \[2\Omega \] | |
| 2912. |
A wire of a certain material is stretched slowly by ten per cent. Its new resistance and specific resistance become respectively: |
| A. | 1.2 times, 1.3 times |
| B. | 1.21 times, same |
| C. | both remain the same |
| D. | 1.1 times, 1.1 times |
| Answer» C. both remain the same | |
| 2913. |
An electron beam has an aperture \[1.0m{{m}^{2}}.\] A total of \[6\times {{10}^{6}}\] electrons go through any perpendicular cross section per second. Find the current density in the beam. (in \[A/{{m}^{2}}\]) |
| A. | \[9.1\times {{10}^{13}}\] |
| B. | \[9.6\times {{10}^{3}}\] |
| C. | \[6.6\times {{10}^{5}}\] |
| D. | \[8.6\times {{10}^{11}}\] |
| Answer» C. \[6.6\times {{10}^{5}}\] | |
| 2914. |
At room temperature, copper has free electron density of \[8.4\times {{10}^{28}}\] per \[{{m}^{3}}.\] The copper conductor has a cross-section of \[{{10}^{-6}}m\] and velocity in copper is |
| A. | \[36{}^\circ C\] |
| B. | \[83{}^\circ C\] |
| C. | \[63{}^\circ C\] |
| D. | \[33{}^\circ C\] |
| Answer» D. \[33{}^\circ C\] | |
| 2915. |
The resistance of a wire at room temperature \[30{}^\circ C\]is found to be \[10\Omega .\] Now to be increase the resistance by 10%, the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is 0.002 per \[{}^\circ C\]] |
| A. | \[36{}^\circ C\] |
| B. | \[83{}^\circ C\] |
| C. | \[63{}^\circ C\] |
| D. | \[33{}^\circ C\] |
| Answer» C. \[63{}^\circ C\] | |
| 2916. |
If negligibly small current is passed through a wire of length 15 m and resistance of \[5\Omega \], having uniform cross section of \[6\times {{10}^{-7}}{{m}^{2}}\], then coefficient of resistivity of material is |
| A. | \[1\times {{10}^{-7}}\Omega -m\] |
| B. | \[2\times {{10}^{-7}}\Omega -m\] |
| C. | \[3\times {{10}^{-7}}\Omega -m\] |
| D. | \[4\times {{10}^{-7}}\Omega -m\] |
| Answer» C. \[3\times {{10}^{-7}}\Omega -m\] | |
| 2917. |
If the resistance of a conductor is \[5\Omega \] at \[50{}^\circ C\]& \[7\Omega \] at \[100{}^\circ C,\] then mean temperature coefficient |
| A. | \[0.013/{}^\circ C~\] |
| B. | \[0.004/{}^\circ C\] |
| C. | \[0.006/{}^\circ C\] |
| D. | \[0.008/{}^\circ C\] |
| Answer» B. \[0.004/{}^\circ C\] | |
| 2918. |
The resistance of a wire is R. It is bent at the middle by \[180{}^\circ \] and both the ends are twisted together to make a shorter wire. The resistance of the new wire is |
| A. | 2R |
| B. | R/2 |
| C. | R/4 |
| D. | R/8 |
| Answer» D. R/8 | |
| 2919. |
When a current I is set up in a wire of radius r, the drift velocity is \[{{v}_{d}}.\] If the same current is set up through a wire of radius 2 r, the drift velocity will be |
| A. | \[4{{v}_{d}}\] |
| B. | \[2{{v}_{d}}\] |
| C. | \[{{v}_{d}}/2\] |
| D. | \[{{v}_{d}}/4\] |
| Answer» E. | |
| 2920. |
At what temperature will the resistance of a copper wire becomes three times its value at \[0{}^\circ C\]? (Temperature coefficient of resistance of copper is \[4\times {{10}^{-3}}/{}^\circ C\] ) |
| A. | \[550{}^\circ C\] |
| B. | \[500{}^\circ C\] |
| C. | \[450{}^\circ C\] |
| D. | \[400{}^\circ C\] |
| Answer» C. \[450{}^\circ C\] | |
| 2921. |
The resistance of a wire is R. It is bent at the middle by \[180{}^\circ \] and both the ends are twisted together to make a shorter wire. The resistance of the new wire is copper wire becomes three times its value at \[0{}^\circ C\]? |
| A. | 2R |
| B. | R/2 |
| C. | R/4 |
| D. | R/8 |
| Answer» D. R/8 | |
| 2922. |
A conductor carries a current of \[50\mu A.\] If the area of cross-section of the conductor is \[50m{{m}^{2}}\], then value of the current density in \[A{{m}^{-2}}\]is |
| A. | 0.5 |
| B. | 1 |
| C. | \[{{10}^{-3}}\] |
| D. | \[{{10}^{-6}}\] |
| Answer» C. \[{{10}^{-3}}\] | |
| 2923. |
The amount of charge Q passed in time t through a cross-section of a wire is \[Q=5{{t}^{2}}+3t+1.\] The value of current at time t=5 s is |
| A. | 9 A |
| B. | 49 A |
| C. | 53 A |
| D. | None of these |
| Answer» D. None of these | |
| 2924. |
The voltage V and current I graphs for a conductor at two different temperatures \[{{T}_{1}}\]and \[{{T}_{2}}\]are shown in the figure. The relation between \[{{T}_{1}}\]and \[{{T}_{2}}\]is |
| A. | \[{{T}_{1}}>{{T}_{2}}\] |
| B. | \[{{T}_{1}}<{{T}_{2}}\] |
| C. | \[{{T}_{1}}={{T}_{2}}\] |
| D. | \[{{T}_{1}}=\frac{1}{{{T}_{2}}}\] |
| Answer» B. \[{{T}_{1}}<{{T}_{2}}\] | |
| 2925. |
A wire X is half the diameter and half the length of a wire Y of similar material. The ratio of resistance of X to that of Y is |
| A. | 8 : 1 |
| B. | 0.167361111111111 |
| C. | 2 : 1 |
| D. | 0.0423611111111111 |
| Answer» D. 0.0423611111111111 | |
| 2926. |
A battery of emf \[{{E}_{0}}=6V\] is connected across a 2m long uniform wire having resistance \[4\Omega /m.\] The cell of small emf \[{{\varepsilon }_{1}}=2V\] and \[{{\varepsilon }_{2}}=3V\] having internal resistance \[2\Omega \,\And \,1\Omega \] respectively are connected as show in the figure. The null point will be obtained at |
| A. | 0.10m |
| B. | 0.25m |
| C. | 0.50m |
| D. | 0.75m |
| Answer» E. | |
| 2927. |
If N, e, \[\tau \]and m are representing electron density, charge, relaxation time and mass of an electron respectively, then the resistance of wire of length l and cross-sectional area A is given by |
| A. | \[\frac{ml}{N{{e}^{2}}{{A}^{2}}\tau }\] |
| B. | \[\frac{2m\tau A}{N{{e}^{2}}l}\] |
| C. | \[\frac{N{{e}^{2}}\tau A}{2ml}\] |
| D. | \[\frac{N{{e}^{2}}}{2m\tau l}\] |
| Answer» B. \[\frac{2m\tau A}{N{{e}^{2}}l}\] | |
| 2928. |
The total momentum of electrons in a straight wire of length 1000m carrying a current of 70A is closest to |
| A. | \[40\times {{10}^{-8}}N-\sec \] |
| B. | \[30\times {{10}^{-8}}N-\sec \] |
| C. | \[50\times {{10}^{-8}}N-\sec \] |
| D. | \[70\times {{10}^{-8}}N-\sec \] |
| Answer» B. \[30\times {{10}^{-8}}N-\sec \] | |
| 2929. |
Determine the modulation index \[({{m}_{f}})\] and carrier swing (S) of an FM carrier having a frequency deviation of \[25\text{ }kHz\] and a modulating signal of\[5\text{ }kHz\]. |
| A. | \[{{m}_{f}}=3\] |
| B. | \[{{m}_{f}}=5\] |
| C. | \[S=80\,kHz\] |
| D. | \[S=60\,kHz\] |
| Answer» C. \[S=80\,kHz\] | |
| 2930. |
The area of the region covered by the TV broadcast by a TV tower of 100 m height is (Radius of the earth \[=6.4\times {{10}^{6}}m\]). |
| A. | \[1.28\pi \times {{10}^{3}}k{{m}^{2}}\] |
| B. | \[2\pi \times {{10}^{4}}k{{m}^{2}}\] |
| C. | \[3.1\times {{10}^{4}}k{{m}^{2}}\] |
| D. | \[6\pi \times {{10}^{4}}k{{m}^{2}}\] |
| Answer» B. \[2\pi \times {{10}^{4}}k{{m}^{2}}\] | |
| 2931. |
If \[{{E}_{c}}=20\,\sin \,{{10}^{5}}\pi t\] and \[{{E}_{m}}=10\,\sin \,400\,\pi t\] are carrier and modulating signals, the modulation index is: |
| A. | \[56\,%\] |
| B. | \[30\,%\] |
| C. | \[50\,%\] |
| D. | \[48\,%\] |
| Answer» D. \[48\,%\] | |
| 2932. |
In optical communication system operating at \[1200\text{ }nm,\] only \[2%\] of the source frequency is available for TV transmission having a bandwidth of \[5\text{ }MHz\]. What is the number of TV channels that can be transmitted? |
| A. | 1 million |
| B. | 50 million |
| C. | 1 thousand |
| D. | 50 thousand |
| Answer» B. 50 million | |
| 2933. |
Given the electric field of a complete amplitude modulated wave as \[\vec{E}=\hat{i}{{E}_{C}}\left( 1+\frac{{{E}_{m}}}{{{E}_{C}}}\cos {{\omega }_{m}}t \right)\,\cos {{\omega }_{C}}t.\] Where the subscript c stands for the carrier wave and m for the modulating signal. The frequencies present in the modulated wave are |
| A. | \[{{\omega }_{C}}\] and \[\sqrt{\omega _{C}^{2}+\omega _{m}^{2}}\] |
| B. | \[{{\omega }_{C}},\,{{\omega }_{C}}+{{\omega }_{m}}\] and \[{{\omega }_{C}}-{{\omega }_{m}}\] |
| C. | \[{{\omega }_{C}}\] and \[{{\omega }_{m}}\] |
| D. | \[{{\omega }_{C}}\] and \[\sqrt{{{\omega }_{C}}{{\omega }_{m}}}\] |
| Answer» C. \[{{\omega }_{C}}\] and \[{{\omega }_{m}}\] | |
| 2934. |
Determine the modulation index and carrier swing of an FM carrier having a frequency deviation of \[56\text{ }kHz\] and a modulating signal of\[8\text{ }kHz\]. |
| A. | \[9,\,\,580\,kHz\] |
| B. | \[3,\,101\,kHz\] |
| C. | \[7,112\,kHz\] |
| D. | \[8,\,\,80\,kHz\] |
| Answer» D. \[8,\,\,80\,kHz\] | |
| 2935. |
The maximum range \[{{d}_{\max }},\] of radar is |
| A. | proportional to the cube root of the peak transmitted power |
| B. | proportional to the fourth root of the peak transmitted power |
| C. | proportional to the square root of the peak transmitted power |
| D. | Not related to the peak transmitted power at all |
| Answer» C. proportional to the square root of the peak transmitted power | |
| 2936. |
A signal of \[5\text{ }kHz\] frequency modulates a carrier of frequency \[1\text{ }MHz\] and peak voltage \[25\,V\]. If the amplitude at the side bands of the amplitude modulated signal is \[5V,\] then the modulation index is: |
| A. | \[0.8\] |
| B. | \[0.6\] |
| C. | \[0.5\] |
| D. | \[0.4\] |
| Answer» E. | |
| 2937. |
An audio signal consists of two distinct sounds: one a human speech signal in the frequency band of \[200\text{ }Hz\] to \[2700\text{ }Hz,\] while the other is a high frequency music signal in the frequency band of \[10200\text{ }Hz\] to \[15200\text{ }Hz\]. The ratio of the AM signal bandwidth required to send both the signals together to the AM signal bandwidth required to send just the human speech is: |
| A. | \[2\] |
| B. | \[5\] |
| C. | \[6\] |
| D. | \[3\] |
| Answer» D. \[3\] | |
| 2938. |
The T.V. transmission tower in Delhi has a height of\[240\text{ }m\]. The distance upto which the broadcast can be received. (Radius of earth is \[6.4\times {{10}^{6}}m\]) |
| A. | \[60\,km\] |
| B. | \[100\,km\] |
| C. | \[50\,km\] |
| D. | \[55\,km\] |
| Answer» E. | |
| 2939. |
A transmitter radiates \[10\text{ }kW\] of power with the carrier unmodulated and \[11.8\text{ }kW\] with the carrier sinusoidally modulated. The modulation factor is |
| A. | \[56%\] |
| B. | \[60%\] |
| C. | \[72%\] |
| D. | \[84%\] |
| Answer» C. \[72%\] | |
| 2940. |
The frequency deviation in a FM transmission is\[18.75\text{ }KHz\]. If it broadcasts in \[88-108\text{ }MHz\] band, then the percent modulation is |
| A. | \[10%\] |
| B. | \[25%\] |
| C. | \[50%\] |
| D. | \[75%\] |
| Answer» C. \[50%\] | |
| 2941. |
Pre-emphasis in FM system is done to |
| A. | compress modulating signal |
| B. | expand modulating signal |
| C. | amplify lower frequency component of the modulating signal |
| D. | amplify higher frequency component of the modulating signal |
| Answer» E. | |
| 2942. |
The sky wave propagation is suitable for radio- waves of frequency |
| A. | upto \[2\,MHz\] |
| B. | from \[2\,MHz\] to \[20\,MHz\] |
| C. | from \[2\,MHz\] to \[30\,MHz\] |
| D. | from \[2\,MHz\] to \[50\,MHz\] |
| Answer» D. from \[2\,MHz\] to \[50\,MHz\] | |
| 2943. |
If a carrier wave c(t) = A \[\sin {{\omega }_{c}}t\] is amplitude modulated by a modulator signal \[m(t)=A\,\sin {{\omega }_{m}}t\]then the equation of modulated signal \[[{{C}_{m}}(t)]\]and its modulation index are respectively |
| A. | \[{{C}_{m}}(t)=A(1+\sin {{\omega }_{m}}t)\,\sin {{\omega }_{c}}t\] and 2 |
| B. | \[{{C}_{m}}(t)=A(1+\sin {{\omega }_{m}}t)\,\sin {{\omega }_{m}}t\] and 1 |
| C. | \[{{C}_{m}}(t)=A(1+\sin {{\omega }_{m}}t)\,\sin {{\omega }_{c}}t\] and 1 |
| D. | \[{{C}_{m}}(t)=A(1+\sin {{\omega }_{c}}t)\,\sin {{\omega }_{m}}t\] and 2 |
| Answer» D. \[{{C}_{m}}(t)=A(1+\sin {{\omega }_{c}}t)\,\sin {{\omega }_{m}}t\] and 2 | |
| 2944. |
An audio signal represented as \[25\,\sin \,2\pi (2000\,t)\]amplitude modulated by a carrier wave: \[60\,\sin \,2\pi (100\,,\,000)t\]. The modulation index of the modulated signal is |
| A. | \[25%\] |
| B. | \[41.6%\] |
| C. | \[50%\] |
| D. | \[75%\] |
| Answer» C. \[50%\] | |
| 2945. |
A radio station has two channels. One is AM at \[1020\text{ }kHz\] and the other FM at\[89.5\text{ }MHz\]. For good results you will use |
| A. | longer antenna for the AM channel and shorter for the FM |
| B. | shorter antenna for the AM channel and longer for the FM |
| C. | same length antenna will work for both |
| D. | information given is not enough to say which one to use for which |
| Answer» C. same length antenna will work for both | |
| 2946. |
Determine the modulation index and carrier swing of an FM carrier having a frequency deviation of \[25\text{ }kHz\] and a modulating signal of\[5\text{ }kHz\]. |
| A. | \[7,\,\,70\,kHz\] |
| B. | \[8,\,\,80\,kHz\] |
| C. | \[5,\,\,50\,kHz\] |
| D. | \[10,\,\,100\,kHz\] |
| Answer» D. \[10,\,\,100\,kHz\] | |
| 2947. |
If level of modulation is increased........power is increased. |
| A. | carrier |
| B. | sideband |
| C. | carrier as well as sideband |
| D. | none of the above |
| Answer» C. carrier as well as sideband | |
| 2948. |
A device with input \[x(t)\] and output \[y(t)\] is characterized by: \[y(t)={{x}^{2}}(t)\]. An FM signal with frequency deviation of \[90\text{ }kHz\] and modulating signal bandwidth of \[5\text{ }kHz\] is applied to this device. The bandwidth of the output signal is |
| A. | \[370\,kHz\] |
| B. | \[190\,kHz\] |
| C. | \[380\,kHz\] |
| D. | \[95\,kHz\] |
| Answer» D. \[95\,kHz\] | |
| 2949. |
As the modulation level is increased, the carrier power - |
| A. | is increased |
| B. | is decreased |
| C. | remains the same |
| D. | None of the above |
| Answer» D. None of the above | |
| 2950. |
A \[10\text{ }kW\] carrier is sinusoidally modulated by two carriers corresponding to a modulation index of 30% and 40% respectively then total power radiated by the modulator is |
| A. | \[10.25\,kW\] |
| B. | \[11.25\,kW\] |
| C. | \[12.75\,kW\] |
| D. | \[17\,kW\] |
| Answer» C. \[12.75\,kW\] | |