MCQOPTIONS
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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.
| 8001. |
A fully charged capacitor has a capacitance ?C?. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity ?s? and mass ?m?. If the temperature of the block is raised by ?\[\Delta T\]?, the potential difference ?V? across the capacitance is [AIEEE 2005] |
| A. | \[\frac{ms\Delta T}{C}\] |
| B. | \[\sqrt{\frac{2ms\Delta T}{C}}\] |
| C. | \[\sqrt{\frac{2mC\Delta T}{s}}\] |
| D. | \[\frac{mC\Delta T}{s}\] |
| Answer» C. \[\sqrt{\frac{2mC\Delta T}{s}}\] | |
| 8002. |
There is an equiconvex glass lens with radius of each face as R and \[_{a}{{\mu }_{g}}=3/2\] and \[_{a}{{\mu }_{w}}=4/3\]. If there is water in object space and air in image space, then the focal length is |
| A. | 2R |
| B. | R |
| C. | 3 R/2 |
| D. | \[{{R}^{2}}\] |
| Answer» D. \[{{R}^{2}}\] | |
| 8003. |
If one starts with one curie of radioactive substance (T1/2 = 12 hrs) the activity left after a period of 1 week will be about |
| A. | 1 curie |
| B. | 120 micro curie |
| C. | 60 micro curie |
| D. | 8 mili curie |
| Answer» D. 8 mili curie | |
| 8004. |
The plates of a parallel plate condenser are pulled apart with a velocity \[v\]. If at any instant their mutual distance of separation is \[d\], then the magnitude of the time of rate of change of capacity depends on \[d\] as follows [MP PET 1991] |
| A. | \[\frac{1}{d}\] |
| B. | \[\frac{1}{{{d}^{2}}}\] |
| C. | \[{{d}^{2}}\] |
| D. | \[d\] |
| Answer» C. \[{{d}^{2}}\] | |
| 8005. |
Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place |
| A. | 6 cm |
| B. | 9 cm |
| C. | 12 cm |
| D. | 15 cm |
| Answer» B. 9 cm | |
| 8006. |
The ratio of radii of nuclei \[_{13}A{{l}^{27}}\] and \[_{52}{{X}^{A}}\] is 3 : 5. The number of neutrons in the nuclei of X will be |
| A. | 52 |
| B. | 73 |
| C. | 125 |
| D. | 13 |
| Answer» C. 125 | |
| 8007. |
The plates of a capacitor are charged to a potential difference of 320 volts and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After 1 second the potential difference between the plates of the capacitor is 240 volts, then after 2 and 3 seconds the potential difference between the plates will be [MP PET 1996] |
| A. | 200 and 180 V |
| B. | 180 and 135 V |
| C. | 160 and 80 V |
| D. | 140 and 20 V |
| Answer» C. 160 and 80 V | |
| 8008. |
A beam of electron is used in an YDSE experiment. The slit width is d. When the velocity of electron is increased, then [IIT-JEE (Screening) 2005] |
| A. | No interference is observed |
| B. | Fringe width increases |
| C. | Fringe width decreases |
| D. | Fringe width remains same |
| Answer» C. Fringe width decreases | |
| 8009. |
A radioactive nucleus is being produced at a constant rate a per second. Its decay constant is l. If N0 are the number of nuclei at time t = 0, then maximum number of nuclei possible are |
| A. | \[\frac{\alpha }{\lambda }\] |
| B. | \[{{N}_{0}}+\frac{\alpha }{\lambda }\] |
| C. | N0 |
| D. | \[\frac{\lambda }{\alpha }+{{N}_{0}}\] |
| Answer» B. \[{{N}_{0}}+\frac{\alpha }{\lambda }\] | |
| 8010. |
In the given figure each plate of capacitance C has partial value of charge [MP PMT 2003] |
| A. | CE |
| B. | \[\frac{CE{{R}_{1}}}{{{R}_{2}}-r}\] |
| C. | \[\frac{CE{{R}_{2}}}{{{R}_{2}}+r}\] |
| D. | \[\frac{CE{{R}_{1}}}{{{R}_{1}}-r}\] |
| Answer» D. \[\frac{CE{{R}_{1}}}{{{R}_{1}}-r}\] | |
| 8011. |
In Young's double slit experiment intensity at a point is (1/4) of the maximum intensity. Angular position of this point is [IIT-JEE (Screening) 2005] |
| A. | sin-1(l/d) |
| B. | sin-1(l/2d) |
| C. | sin-1(l/3d) |
| D. | sin-1(l/4d) |
| Answer» D. sin-1(l/4d) | |
| 8012. |
A radioactive sample is a-emitter with half life 138.6 days is observed by a student to have 2000 disintegration/sec. The number of radioactive nuclei for given activity are |
| A. | 3.45 ´ 1010 |
| B. | 1 ´ 1010 |
| C. | 3.45 ´ 1015 |
| D. | 2.75 ´ 1011 |
| Answer» B. 1 ´ 1010 | |
| 8013. |
A capacitor of capacitance \[{{C}_{\text{1}}}=\text{ 1}\mu F\] can with stand maximum voltage \[{{V}_{\text{1}}}=\text{ 6}kV\left( kilo-volt \right)\] and another capacitor of capacitance \[{{C}_{\text{2}}}=\text{3}\mu F\] can withstand maximum voltage \[{{V}_{\text{2}}}=\text{ 4}kV\]. When the two capacitors are connected in series, the combined system can withstand a maximum voltage of [MP PET 2001] |
| A. | \[4\,kV\] |
| B. | \[6\,kV\] |
| C. | \[8\,kV\] |
| D. | \[10\,kV\] |
| Answer» D. \[10\,kV\] | |
| 8014. |
If \[{{I}_{0}}\] is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled [AIEEE 2005] |
| A. | \[{{I}_{0}}\] |
| B. | \[\frac{{{I}_{0}}}{2}\] |
| C. | \[2{{I}_{0}}\] |
| D. | \[4\,{{I}_{0}}\] |
| Answer» E. | |
| 8015. |
Consider a hydrogen like atom whose energy in nth exicited state is given by \[{{E}_{n}}=-\frac{13.6{{Z}^{2}}}{{{n}^{2}}}\] when this excited atom makes a transition from excited state to ground state, most energetic photons have energy Emax = 52.224 eV and least energetic photons have energy Emin = 1.224 eV. The atomic number of atom is |
| A. | 2 |
| B. | 5 |
| C. | 4 |
| D. | None of these |
| Answer» B. 5 | |
| 8016. |
Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is [IIT-JEE (Screening) 2001] |
| A. | Zero |
| B. | \[q/2\] |
| C. | q |
| D. | \[2q\] |
| Answer» B. \[q/2\] | |
| 8017. |
There are two wires of same material and same length while the diameter of second wire is 2 times the diameter of first wire, then ratio of extension produced in the wires by applying same load will be [DCE 2000; Roorkee 2000; DCE 2003] |
| A. | 1 : 1 |
| B. | 2 : 1 |
| C. | 1 : 2 |
| D. | 4 : 1 |
| Answer» E. | |
| 8018. |
A force \[F=-K(yi+xj)\] (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is [IIT 1998] |
| A. | \[-2K{{a}^{2}}\] |
| B. | \[2K{{a}^{2}}\] |
| C. | \[-K{{a}^{2}}\] |
| D. | \[K{{a}^{2}}\] |
| Answer» D. \[K{{a}^{2}}\] | |
| 8019. |
A string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/p revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is [BHU 2002; DPMT 2004] |
| A. | ML |
| B. | 2 ML |
| C. | 4 ML |
| D. | 16 ML |
| Answer» E. | |
| 8020. |
A highly rigid cubical block \[A\] of small mass \[M\] and side \[L\] is fixed rigidly onto another cubical block \[B\]of the same dimensions and of low modulus of rigidity \[\eta \] such that the lower face of \[A\] completely covers the upper face of \[B\]. The lower face of \[B\]is rigidly held on a horizontal surface. A small force \[F\] is applied perpendicular to one of the side faces of \[A\]. After the force is withdrawn block \[A\] executes small oscillations. The time period of which is given by [IIT 1992] |
| A. | \[2\pi \sqrt{\frac{M\eta }{L}}\] |
| B. | \[2\pi \sqrt{\frac{L}{M\eta }}\] |
| C. | \[2\pi \sqrt{\frac{ML}{\eta }}\] |
| D. | \[2\pi \sqrt{\frac{M}{\eta L}}\] |
| Answer» E. | |
| 8021. |
In a Young's double slit experiment the source S and the two slits A and B are vertical with slit A above slit B. The fringes are observed on a vertical screen K. The optical path length from S to B is increased very slightly (by introducing a transparent material of higher refractive index) and the optical path length from S to A is not changed, as a result the fringe system on K moves [NCERT 1984] |
| A. | Vertically downwards slightly |
| B. | Vertically upwards slightly |
| C. | Horizontally, slightly to the left |
| D. | Horizontally, slightly to the right |
| Answer» B. Vertically upwards slightly | |
| 8022. |
A ray of light falls on the surface of a spherical glass paper weight making an angle \[\alpha \] with the normal and is refracted in the medium at an angle \[\beta \]. The angle of deviation of the emergent ray from the direction of the incident ray [NCERT 1982] |
| A. | \[(\alpha -\beta )\] |
| B. | \[2(\alpha -\beta )\] |
| C. | \[(\alpha -\beta )/2\] |
| D. | \[(\beta -\alpha )\] |
| Answer» C. \[(\alpha -\beta )/2\] | |
| 8023. |
A 2V battery is connected across the points A and B as shown in the figure given below. Assuming that the resistance of each diode is zero in forward bias and infinity in reverse bias, the current supplied by the battery when its positive terminal is connected to A is [UPSEAT 2002] |
| A. | 0.2 A |
| B. | 0.4 A |
| C. | Zero |
| D. | 0.1 A |
| Answer» B. 0.4 A | |
| 8024. |
The antenna current of an AM transmitter is 8 A when only carrier is sent but increases to 8.96 A when the carrier is sinusoidally modulated. The percentage modulation is |
| A. | 50% |
| B. | 60% |
| C. | 65% |
| D. | 71% |
| Answer» E. | |
| 8025. |
A hydrogen atom in its ground state absorbs 10.2 eV of energy. The orbital angular momentum is increased by [MP PET 1995; MP PMT 1997] |
| A. | \[1.05\times {{10}^{-34}}\]J-sec |
| B. | \[3.16\times {{10}^{-34}}\]J-sec |
| C. | \[2.11\times {{10}^{-34}}\]J-sec |
| D. | \[4.22\times {{10}^{-34}}\]J-sec (Given Planck constant \[h=6.6\times {{10}^{-34}}J-\]sec) |
| Answer» B. \[3.16\times {{10}^{-34}}\]J-sec | |
| 8026. |
When an inert gas is filled in the place vacuum in a photo cell, then [MP PMT 1997] |
| A. | Photo-electric current is decreased |
| B. | Photo-electric current is increased |
| C. | Photo-electric current remains the same |
| D. | Decrease or increase in photo-electric current does not depend upon the gas filled |
| Answer» C. Photo-electric current remains the same | |
| 8027. |
A bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased, while keeping the voltage of the source constant, then [Roorkee 1999] |
| A. | Bulb will give more intense light |
| B. | Bulb will give less intense light |
| C. | Bulb will give light of same intensity as before |
| D. | Bulb will stop radiating light |
| Answer» B. Bulb will give less intense light | |
| 8028. |
A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position MNQ, the speed of the ring is V and the potential difference developed across the ring is [IIT JEE 1996] |
| A. | Zero |
| B. | \[B\nu \pi {{R}^{2}}/2\] and M is at higher potential |
| C. | \[\pi RBV\]and Q is at higher potential |
| D. | 2RBV and Q is at higher potential |
| Answer» E. | |
| 8029. |
The true value of angle of dip at a place is 60o, the apparent dip in a plane inclined at an angle of 30o with magnetic meridian is [AIEEE 2002] |
| A. | \[{{\tan }^{-1}}\frac{1}{2}\] |
| B. | \[{{\tan }^{-1}}(2)\] |
| C. | \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\] |
| D. | None of these |
| Answer» C. \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\] | |
| 8030. |
In the circuit as shown in the figure, the heat produced by 6 ohm resistance due to current flowing in it is 60 calorie per second. The heat generated across 3 ohm resistance per second will be [MP PET 1996] |
| A. | 30 calorie |
| B. | 60 calorie |
| C. | 100 calorie |
| D. | 120 calorie |
| Answer» E. | |
| 8031. |
In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. when this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction [IIT-JEE (Screening) 2003] |
| A. | 0.012m |
| B. | 0.025m |
| C. | 0.05m |
| D. | 0.024m |
| Answer» C. 0.05m | |
| 8032. |
A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be |
| A. | \[2\pi \sqrt{\left( \frac{\left( R-r \right)1.4}{g} \right)}\] |
| B. | \[2\pi \sqrt{\left( \frac{R-r}{g} \right)}\] |
| C. | \[2\pi \sqrt{\left( \frac{rR}{a} \right)}\] |
| D. | \[2\pi \sqrt{\left( \frac{R}{gr} \right)}\] |
| Answer» C. \[2\pi \sqrt{\left( \frac{rR}{a} \right)}\] | |
| 8033. |
A room is maintained at \[{{20}^{o}}C\] by a heater of resistance 20 ohm connected to 200 volt mains. The temperature is uniform throughout the room and heat is transmitted through a glass window of area \[1{{m}^{2}}\] and thickness 0.2 cm. What will be the temperature outside? Given that thermal conductivity K for glass is \[320\ kcal/{{m}^{2}}\ min\] and J = 4.2 J/cal [IIT 1978] |
| A. | \[{{15.24}^{o}}C\] |
| B. | 15.00°C |
| C. | \[{{24.15}^{o}}C\] |
| D. | None of the above |
| Answer» B. 15.00°C | |
| 8034. |
A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is \[\omega \], then the difference in the heights of the liquid at the centre of the vessel and the edge is |
| A. | \[\frac{r\omega }{2g}\] |
| B. | \[\frac{{{r}^{2}}{{\omega }^{2}}}{2g}\] |
| C. | \[\sqrt{2gr\omega }\] |
| D. | \[\frac{{{\omega }^{2}}}{2g{{r}^{2}}}\] |
| Answer» C. \[\sqrt{2gr\omega }\] | |
| 8035. |
In the figure shown, the capacity of the condenser C is \[2\,\mu F\]. The current in \[2\,\Omega \] resistor is [IIT 1982] |
| A. | 9 A |
| B. | 0.9 A |
| C. | \[\frac{1}{9}A\] |
| D. | \[\frac{1}{0.9}A\] |
| Answer» C. \[\frac{1}{9}A\] | |
| 8036. |
A closed hollow insulated cylinder is filled with gas at \[{{0}^{o}}C\] and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \[{{100}^{o}}C.\] If the piston moves \[5\,cm,\] the length of the hollow cylinder is [EAMCET 2001] |
| A. | 13.65 cm |
| B. | 27.3 cm |
| C. | 38.6 cm |
| D. | 64.6 cm |
| Answer» E. | |
| 8037. |
Two equal charges \[q\] of opposite sign separated by a distance \[2a\] constitute an electric dipole of dipole moment \[p\]. If \[P\] is a point at a distance \[r\] from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle \[\theta \] with the axis of the dipole, then the potential at \[P\] is given by \[(r>>2a)\] (Where\[p=2qa\]) [MP PET 1997] |
| A. | \[V=\frac{p\cos \theta }{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\] |
| B. | \[V=\frac{p\cos \theta }{4\pi {{\varepsilon }_{0}}r}\] |
| C. | \[V=\frac{p\sin \theta }{4\pi {{\varepsilon }_{0}}r}\] |
| D. | \[V=\frac{p\cos \theta }{2\pi {{\varepsilon }_{0}}{{r}^{2}}}\] |
| Answer» B. \[V=\frac{p\cos \theta }{4\pi {{\varepsilon }_{0}}r}\] | |
| 8038. |
A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is [AIEEE 2005] |
| A. | Straight line |
| B. | Parabola |
| C. | Hyperbola |
| D. | Circle |
| Answer» D. Circle | |
| 8039. |
The wavelength Ka X-rays produced by an X-ray tube is 0.76 Å. The atomic number of anticathode material is |
| A. | 82 |
| B. | 41 |
| C. | 20 |
| D. | 10 |
| Answer» C. 20 | |
| 8040. |
For the circuit shown, which of the following statements is true [IIT-JEE 1999; UPSEAT 2003] |
| A. | With \[{{S}_{1}}\]closed, \[{{V}_{1}}=15\,V,\ {{V}_{2}}=20\ V\] |
| B. | With \[{{S}_{3}}\] closed \[{{V}_{1}}={{V}_{2}}=25V\] |
| C. | With \[{{S}_{1}}\] and \[{{S}_{2}}\] closed \[{{V}_{1}}={{V}_{2}}=0\] |
| D. | With\[{{S}_{1}}\]and \[{{S}_{3}}\]closed, \[{{V}_{1}}=30\,V,\ {{V}_{2}}=20\,V\] |
| Answer» E. | |
| 8041. |
The k line of singly ionised calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, this spectral line is located at 401.8 nm. The speed with which the galaxy is moving away from us, will be [Pb. PET 2003] |
| A. | 6480 km/s |
| B. | 3240 km/s |
| C. | 4240 km/sec |
| D. | None of these |
| Answer» B. 3240 km/s | |
| 8042. |
A radioactive sample of U238 decay to Pb through a process for which half life is 4.5 ´ 109 years. The ratio of number of nuclei of Pb to U238 after a time of 1.5 ´ 109 years (given 21/3 = 1.26) [Based on IIT-JEE (Mains) 2004] |
| A. | 0.12 |
| B. | 0.26 |
| C. | 1.2 |
| D. | 0.37 |
| Answer» C. 1.2 | |
| 8043. |
In an isolated parallel plate capacitor of capacitance C, the four surface have charges \[{{Q}_{1}}\], \[{{Q}_{2}}\], \[{{Q}_{3}}\] and \[{{Q}_{4}}\] as shown. The potential difference between the plates is [IIT-JEE 1999] |
| A. | \[\frac{{{Q}_{1}}+{{Q}_{2}}+{{Q}_{3}}+{{Q}_{4}}}{2C}\] |
| B. | \[\frac{{{Q}_{2}}+{{Q}_{3}}}{2C}\] |
| C. | \[\frac{{{Q}_{2}}-{{Q}_{3}}}{2C}\] |
| D. | \[\frac{{{Q}_{1}}+{{Q}_{4}}}{2C}\] |
| Answer» D. \[\frac{{{Q}_{1}}+{{Q}_{4}}}{2C}\] | |
| 8044. |
The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young?s double-slit experiment is [AIEEE 2004] |
| A. | Infinite |
| B. | Five |
| C. | Three |
| D. | Zero |
| Answer» C. Three | |
| 8045. |
A hydrogen like atom of atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204 eV. If it makes a transition to quantum state n, a photon of energy 40.8 eV is emitted. The value of n will be [Based onIIT-JEE (Mains) 2000] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 8046. |
A finite ladder is constructed by connecting several sections of \[2\mu F,\ 4\mu F\] capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between [MP PMT 1999; KCET (Engg./Med.) 1999] |
| A. | \[4\mu F\] |
| B. | \[2\mu F\] |
| C. | \[18\mu F\] |
| D. | \[6\mu F\] |
| Answer» B. \[2\mu F\] | |
| 8047. |
In a YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1m. The minimum distance between two successive regions of complete darkness is [IIT JEE (Screening) 2004] |
| A. | 4 mm |
| B. | 5.6 mm |
| C. | 14 mm |
| D. | 28 mm |
| Answer» E. | |
| 8048. |
Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is |
| A. | 1.1 |
| B. | 1.2 |
| C. | 1.3 |
| D. | 1.4 |
| Answer» D. 1.4 | |
| 8049. |
A small quantity of solution containing Na24 radio nuclide of activity 1 microcurie is injected into the blood of a person. A sample of the blood of volume 1 cm3 taken after 5 hours shows an activity of 296 disintegration per minute. What will be the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person (Take 1 curie = 3.7 ´ 1010 disintegration per second and \[{{e}^{-\lambda t}}=0.7927;\] where l = disintegration constant) |
| A. | 5.94 litre |
| B. | 2 litre |
| C. | 317 litre |
| D. | 1 litre |
| Answer» B. 2 litre | |
| 8050. |
In the given circuit if point C is connected to the earth and a potential of \[+\,2000\,V\] is given to the point A, the potential at B is [MP PET 1997; Pb. PET 2003] |
| A. | \[1500\,V\] |
| B. | \[1000\ V\] |
| C. | \[500\ V\] |
| D. | \[400\ V\] |
| Answer» D. \[400\ V\] | |