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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.
| 3851. |
A wave travels in a medium according to the equation of displacement given by \[y(x,\,t)=0.03\sin \pi (2t-0.01x)\] where y and x are in metres and t in seconds. The wavelength of the wave is [EAMCET 1994; CPMT 2004] |
| A. | 200 m |
| B. | 100 m |
| C. | 20 m |
| D. | 10 m |
| Answer» B. 100 m | |
| 3852. |
A transverse wave is represented by the equation \[y={{y}_{0}}\sin \frac{2\pi }{\lambda }(vt-x)\] For what value of l, the maximum particle velocity equal to two times the wave velocity [CBSE PMT 1998; JIPMER 2001, 02; AFMC 2002] |
| A. | \[\lambda =2\pi {{y}_{0}}\] |
| B. | \[\lambda =\pi {{y}_{0}}/3\] |
| C. | \[\lambda =\pi {{y}_{0}}/2\] |
| D. | \[\lambda =\pi {{y}_{0}}\] |
| Answer» E. | |
| 3853. |
As a wave propagates [IIT-JEE 1999] |
| A. | The wave intensity remains constant for a plane wave |
| B. | The wave intensity decreases as the inverse of the distance from the source for a spherical wave |
| C. | The wave intensity decreases as the inverse square of the distance from the source for a spherical wave |
| D. | Total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times |
| Answer» B. The wave intensity decreases as the inverse of the distance from the source for a spherical wave | |
| 3854. |
The equation of a transverse wave travelling on a rope is given by \[y=10\sin \pi (0.01x-2.00t)\] where y and x are in cm and t in seconds. The maximum transverse speed of a particle in the rope is about [MP PET 1999; AIIMS 2000] |
| A. | 63 cm/s |
| B. | 75 cm/s |
| C. | 100 cm/s |
| D. | 121 cm/s |
| Answer» B. 75 cm/s | |
| 3855. |
A wave is represented by the equation \[y=7\sin \left( 7\pi t-0.04\,x\pi +\frac{\pi }{3} \right)\] x is in metres and t is in seconds. The speed of the wave is [MP PET 1996; AMU (Engg.) 1999] |
| A. | 175 m/sec |
| B. | 49 pm/sec |
| C. | 49 pm/sec |
| D. | 0.28 pm/sec |
| Answer» B. 49 pm/sec | |
| 3856. |
A wave is represented by the equation \[y=0.5\sin (10t-x)m\]. It is a travelling wave propagating along the + x direction with velocity [Roorkee 1995] |
| A. | 10 m/s |
| B. | 20 m/s |
| C. | 5 m/s |
| D. | None of these |
| Answer» B. 20 m/s | |
| 3857. |
Wave equations of two particles are given by \[{{y}_{1}}=a\sin (\omega \,t-kx)\], \[{{y}_{2}}=a\sin (kx+\omega \,t)\], then [BHU 1995] |
| A. | They are moving in opposite direction |
| B. | Phase between them is 90° |
| C. | Phase between them is 180° |
| D. | Phase between them is 0° |
| Answer» B. Phase between them is 90° | |
| 3858. |
The path difference between the two waves \[{{y}_{1}}={{a}_{1}}\sin \,\left( \omega t-\frac{2\pi x}{\lambda } \right)\] and \[{{y}_{2}}={{a}_{2}}\cos \,\left( \omega t-\frac{2\pi x}{\lambda }+\varphi \right)\] is [MP PMT 1994] |
| A. | \[\frac{\lambda }{2\pi }\varphi \] |
| B. | \[\frac{\lambda }{2\pi }\left( \varphi +\frac{\pi }{2} \right)\] |
| C. | \[\frac{2\pi }{\lambda }\left( \varphi -\frac{\pi }{2} \right)\] |
| D. | \[\frac{2\pi }{\lambda }\varphi \] |
| Answer» C. \[\frac{2\pi }{\lambda }\left( \varphi -\frac{\pi }{2} \right)\] | |
| 3859. |
A plane wave is described by the equation \[y=3\cos \left( \frac{x}{4}-10t-\frac{\pi }{2} \right)\]. The maximum velocity of the particles of the medium due to this wave is [MP PMT 1994] |
| A. | 30 |
| B. | \[\frac{3\pi }{2}\] |
| C. | 3/4 |
| D. | 40 |
| Answer» B. \[\frac{3\pi }{2}\] | |
| 3860. |
A travelling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and [MP PMT 1990] |
| A. | The wavelength is 5 m |
| B. | The frequency is 5 Hz |
| C. | The velocity of propagation is 5 m/s |
| D. | The wavelength is 0.2 m |
| Answer» C. The velocity of propagation is 5 m/s | |
| 3861. |
A wave represented by the given equation \[Y=A\sin \left( 10\,\pi \,x+15\,\pi \,t+\frac{\pi }{3} \right)\], where x is in meter and t is in second. The expression represents [IIT 1990] |
| A. | A wave travelling in the positive X direction with a velocity of 1.5 m/sec |
| B. | A wave travelling in the negative X direction with a velocity of 1.5 m/sec |
| C. | A wave travelling in the negative X direction with a wavelength of 0.2 m |
| D. | A wave travelling in the positive X direction with a wavelength of 0.2 m |
| Answer» D. A wave travelling in the positive X direction with a wavelength of 0.2 m | |
| 3862. |
Which one of the following does not represent a travelling wave [NCERT 1984] |
| A. | \[y=\sin (x-v\,t)\] |
| B. | \[y={{y}_{m}}\sin k(x+v\,t)\] |
| C. | \[y={{y}_{m}}\log (x-v\,t)\] |
| D. | \[y=f({{x}^{2}}-v\,{{t}^{2}})\] |
| Answer» E. | |
| 3863. |
The displacement of a particle is given by \[y=5\times {{10}^{-4}}\sin (100t-50x)\], where x is in meter and t in sec, find out the velocity of the wave [CPMT 1982] |
| A. | 5000 m/sec |
| B. | 2 m/sec |
| C. | 0.5 m/sec |
| D. | 300 m/sec |
| Answer» C. 0.5 m/sec | |
| 3864. |
A transverse wave of amplitude 0.5 m and wavelength 1 m and frequency 2 Hz is propagating in a string in the negative x-direction. The expression for this wave is [AIIMS 1980] |
| A. | \[y(x,\,t)=0.5\sin (2\pi x-4\pi t)\] |
| B. | \[y(x,\,t)=0.5\cos (2\pi x+4\pi t)\] |
| C. | \[y(x,\,t)=0.5\sin (\pi x-2\pi t)\] |
| D. | \[y(x,\,t)=0.5\cos (2\pi x+2\pi t)\] |
| Answer» C. \[y(x,\,t)=0.5\sin (\pi x-2\pi t)\] | |
| 3865. |
A wave equation which gives the displacement along the Y direction is given by the equation \[y={{10}^{4}}\sin (60t+2x)\], where x and y are in metres and t is time in seconds. This represents a wave [MNR 1983; IIT 1982; RPMT 1998; MP PET 2001] |
| A. | Travelling with a velocity of 30 m/sec in the negative X direction |
| B. | Of wavelength p metre |
| C. | Of frequency 30/p Hz |
| D. | Of amplitude \[{{10}^{4}}\]metre travelling along the negative X direction |
| Answer» B. Of wavelength p metre | |
| 3866. |
A transverse wave is described by the equation \[Y={{Y}_{0}}\sin 2\pi \left( ft-\frac{x}{\lambda } \right)\]. The maximum particle velocity is four times the wave velocity if [IIT 1984; MP PMT 1997; EAMCET; 1998; CBSE PMT 2000; AFMC 2000; MP PMT/PET 1998; 01; KCET 1999, 04; Pb. PET 2001; DPMT 2005] |
| A. | \[\lambda =\frac{\pi {{Y}_{0}}}{4}\] |
| B. | \[\lambda =\frac{\pi {{Y}_{0}}}{2}\] |
| C. | \[\lambda =\pi {{Y}_{0}}\] |
| D. | \[\lambda =2\pi {{Y}_{0}}\] |
| Answer» C. \[\lambda =\pi {{Y}_{0}}\] | |
| 3867. |
The equation of a wave travelling in a string can be written as \[y=3\cos \pi (100\,t-x)\]. Its wavelength is [MNR 1985; CPMT 1991; MP PMT 1994, 97; Pb. PET 2004] |
| A. | 100 cm |
| B. | 2 cm |
| C. | 5 cm |
| D. | None of the above |
| Answer» C. 5 cm | |
| 3868. |
The displacement y (in cm) produced by a simple harmonic wave is \[y=\frac{10}{\pi }\sin \left( 2000\pi t-\frac{\pi x}{17} \right)\]. The periodic time and maximum velocity of the particles in the medium will respectively be [CPMT 1986] |
| A. | \[{{10}^{-3}}\]sec and 330 m/sec |
| B. | \[{{10}^{-4}}\]sec and 20 m/sec |
| C. | \[{{10}^{-3}}\]sec and 200 m/sec |
| D. | \[{{10}^{-2}}\]sec and 2000 m/sec |
| Answer» D. \[{{10}^{-2}}\]sec and 2000 m/sec | |
| 3869. |
A plane wave is represented by \[x=1.2\sin (314\,t+12.56y)\] Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has [MP PET 1991] |
| A. | A wavelength of 0.25 m and travels in + ve x direction |
| B. | A wavelength of 0.25 m and travels in + ve y direction |
| C. | A wavelength of 0.5 m and travels in ? ve y direction |
| D. | A wavelength of 0.5 m and travels in ? ve x direction |
| Answer» D. A wavelength of 0.5 m and travels in ? ve x direction | |
| 3870. |
The relation between time and displacement for two particles is given by \[{{y}_{1}}=0.06\sin 2\pi (0.04t+{{\varphi }_{1}})\], \[{{y}_{2}}=0.03\sin 2\pi (1.04t+{{\varphi }_{2}})\] The ratio of the intensity of the waves produced by the vibrations of the two particles will be [MP PMT 1991] |
| A. | 2 : 1 |
| B. | 1 : 2 |
| C. | 4 : 1 |
| D. | 1 : 4 |
| Answer» D. 1 : 4 | |
| 3871. |
A wave is reflected from a rigid support. The change in phase on reflection will be [MP PMT 1990; RPMT 2002] |
| A. | \[\pi /4\] |
| B. | \[\pi /2\] |
| C. | \[\pi \] |
| D. | \[2\pi \] |
| Answer» D. \[2\pi \] | |
| 3872. |
Equation of a progressive wave is given by \[y=0.2\cos \pi \left( 0.04t+.02x-\frac{\pi }{6} \right)\] The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of \[\pi /2\] |
| A. | 4 cm |
| B. | 8 cm |
| C. | 25 cm |
| D. | 12.5 cm |
| Answer» D. 12.5 cm | |
| 3873. |
If amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be [MP PMT 1985] |
| A. | 2A |
| B. | A |
| C. | A/2 |
| D. | A/4 |
| Answer» D. A/4 | |
| 3874. |
The equation of a wave is\[y=2\sin \pi (0.5x-200t)\], where x and y are expressed in cm and t in sec. The wave velocity is [MP PMT 1986] |
| A. | 100 cm/sec |
| B. | 200 cm/sec |
| C. | 300 cm/sec |
| D. | 400 cm/sec |
| Answer» E. | |
| 3875. |
The pressure of air in a soap bubble of 0.7cm diameter is 8 mm of water above the pressure outside. The surface tension of the soap solution is [MP PET 1991; MP PMT 1997] |
| A. | \[100dyne/cm\] |
| B. | \[68.66dyne/cm\] |
| C. | \[137dyne/cm\] |
| D. | \[150dyne/cm\] |
| Answer» C. \[137dyne/cm\] | |
| 3876. |
The excess of pressure inside a soap bubble than that of the outer pressure is [MP PMT 1989; BHU 1995; MH CET 2002; RPET 2003; AMU (Engg.) 2000] |
| A. | \[\frac{2T}{r}\] |
| B. | \[\frac{4T}{r}\] |
| C. | \[\frac{T}{2r}\] |
| D. | \[\frac{T}{r}\] |
| Answer» C. \[\frac{T}{2r}\] | |
| 3877. |
If the surface tension of a soap solution is 0.03 MKS units, then the excess of pressure inside a soap bubble of diameter 6 mm over the atmospheric pressure will be |
| A. | Less than\[40N/{{m}^{2}}\] |
| B. | Greater than \[40N/{{m}^{2}}\] |
| C. | Less than\[20N/{{m}^{2}}\] |
| D. | Greater than \[20N/{{m}^{2}}\] |
| Answer» C. Less than\[20N/{{m}^{2}}\] | |
| 3878. |
A long cylindrical glass vessel has a small hole of radius 'r' at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension T) without any water entering inside is [MP PMT 1990] |
| A. | \[4T/\rho rg\] |
| B. | \[3T/\rho rg\] |
| C. | \[2T/\rho rg\] |
| D. | \[T/\rho rg\] |
| Answer» D. \[T/\rho rg\] | |
| 3879. |
The excess pressure due to surface tension in a spherical liquid drop of radius r is directly proportional to [MP PMT 1987; KCET 2000] |
| A. | \[r\] |
| B. | \[{{r}^{2}}\] |
| C. | \[{{r}^{-1}}\] |
| D. | \[{{r}^{-2}}\] |
| Answer» D. \[{{r}^{-2}}\] | |
| 3880. |
When two soap bubbles of radius \[{{r}_{1}}\]and \[{{r}_{2}}\] \[({{r}_{2}}>{{r}_{1}})\] coalesce, the radius of curvature of common surface is [MP PMT 1996] |
| A. | \[{{r}_{2}}-{{r}_{1}}\] |
| B. | \[\frac{{{r}_{2}}-{{r}_{1}}}{{{r}_{1}}{{r}_{2}}}\] |
| C. | \[\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{2}}-{{r}_{1}}}\] |
| D. | \[{{r}_{2}}+{{r}_{1}}\] |
| Answer» D. \[{{r}_{2}}+{{r}_{1}}\] | |
| 3881. |
The excess pressure in a soap bubble is thrice that in other one. Then the ratio of their volume is [RPMT 2003; CPMT 2001] |
| A. | 1 : 3 |
| B. | 1 : 9 |
| C. | 27 : 1 |
| D. | 0.0604166666666667 |
| Answer» E. | |
| 3882. |
The surface tension of soap solution is \[25\times {{10}^{-3}}\,N{{m}^{-1}}\]. The excess pressure inside a soap bubble of diameter 1 cm is [AIIMS 1987] |
| A. | 10 Pa |
| B. | 20 Pa |
| C. | 5 Pa |
| D. | None of the above |
| Answer» C. 5 Pa | |
| 3883. |
In Jager's method, at the time of bursting of the bubble [RPET 2002] |
| A. | The internal pressure of the bubble is always greater than external pressure |
| B. | The internal pressure of the bubble is always equal to external pressure |
| C. | The internal pressure of the bubble is always less than external pressure |
| D. | The internal pressure of the bubble is always slightly greater than external pressure |
| Answer» B. The internal pressure of the bubble is always equal to external pressure | |
| 3884. |
Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement [MP PMT 2004] |
| A. | Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble |
| B. | Pressure of the larger bubble is higher than the smaller bubble |
| C. | Both bubbles have the same internal pressure |
| D. | None of the above |
| Answer» B. Pressure of the larger bubble is higher than the smaller bubble | |
| 3885. |
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm, then the surface tension of soap solution will be (r = 1 cm and density d = 0.8 gm/cc) [J & K CET 2004] |
| A. | 3.9 N/m |
| B. | \[3.9\text{ }\times {{10}^{2}}N/m\] |
| C. | \[3.9\text{ }\times {{10}^{3}}N/m\] |
| D. | 3.9 dyne/m |
| Answer» C. \[3.9\text{ }\times {{10}^{3}}N/m\] | |
| 3886. |
Two bubbles A and B \[(A>B)\] are joined through a narrow tube. Then [UPSEAT 2001; Kerala (Med.) 2002] |
| A. | The size of A will increase |
| B. | The size of B will increase |
| C. | The size of B will increase until the pressure equals |
| D. | None of these |
| Answer» B. The size of B will increase | |
| 3887. |
The pressure inside a small air bubble of radius 0.1 mm situated just below the surface of water will be equal to [Take surface tension of water \[70\times {{10}^{-3}}N{{m}^{-1}}\] and atmospheric pressure = \[1.013\times {{10}^{5}}N{{m}^{-2}}\]] [AMU (Med.) 2002] |
| A. | \[2.054\times {{10}^{3}}Pa\] |
| B. | \[1.027\times {{10}^{3}}Pa\] |
| C. | \[1.027\times {{10}^{5}}Pa\] |
| D. | \[2.054\times {{10}^{5}}Pa\] |
| Answer» D. \[2.054\times {{10}^{5}}Pa\] | |
| 3888. |
Two soap bubbles of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] equal to 4 cm and 5 cm are touching each other over a common surface \[{{S}_{1}}{{S}_{2}}\] (shown in figure). Its radius will be [MP PMT 2002] |
| A. | 4 cm |
| B. | 20 cm |
| C. | 5 cm |
| D. | 4.5 cm |
| Answer» C. 5 cm | |
| 3889. |
In capillary pressure below the curved surface of water will be [RPET 2001] |
| A. | Equal to atmospheric |
| B. | Equal to upper side pressure |
| C. | More than upper side pressure |
| D. | Lesser than upper side pressure |
| Answer» E. | |
| 3890. |
The pressure at the bottom of a tank containing a liquid does not depend on [Kerala (Engg.) 2001] |
| A. | Acceleration due to gravity |
| B. | Height of the liquid column |
| C. | Area of the bottom surface |
| D. | Nature of the liquid |
| Answer» D. Nature of the liquid | |
| 3891. |
If the radius of a soap bubble is four times that of another, then the ratio of their pressures will be [AIIMS 2000] |
| A. | 1 : 4 |
| B. | 4 : 1 |
| C. | 16 : 1 |
| D. | 1 : 16 |
| Answer» B. 4 : 1 | |
| 3892. |
If two soap bubbles of different radii are in communication with each other [NCERT 1980; MP PMT/PET 1988; AIEEE 2004] |
| A. | Air flows from larger bubble into the smaller one |
| B. | The size of the bubbles remains the same |
| C. | Air flows from the smaller bubble into the large one and the larger bubble grows at the expense of the smaller one |
| D. | The air flows from the larger |
| Answer» D. The air flows from the larger | |
| 3893. |
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake [RPET 2000] |
| A. | 10m |
| B. | 20m |
| C. | 60m |
| D. | 30m |
| Answer» C. 60m | |
| 3894. |
The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is [AMU 1995] |
| A. | 5 m |
| B. | 10 m |
| C. | 15 m |
| D. | 20 m |
| Answer» D. 20 m | |
| 3895. |
Excess pressure of one soap bubble is four times more than the other. Then the ratio of volume of first bubble to another one is [CPMT 1997; MH CET 2000] |
| A. | 1 : 64 |
| B. | 1 : 4 |
| C. | 64 : 1 |
| D. | 1 : 2 |
| Answer» B. 1 : 4 | |
| 3896. |
There are two liquid drops of different radii. The excess pressure inside over the outside is [JIPMER 1999] |
| A. | More in the big drop |
| B. | More in the small drop |
| C. | Equal in both drops |
| D. | There is no excess pressure inside the drops |
| Answer» C. Equal in both drops | |
| 3897. |
A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. If the two bubbles coalesce under isothermal condition, then the radius of the new bubble is [MP PMT/PET 1998; JIPMER 2000] |
| A. | 2.3 cm |
| B. | 4.5 cm |
| C. | 5 cm |
| D. | 7 cm |
| Answer» D. 7 cm | |
| 3898. |
When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is [AIIMS 1995; AFMC 1997] |
| A. | H |
| B. | 2H |
| C. | 7H |
| D. | 8H |
| Answer» D. 8H | |
| 3899. |
The radii of two soap bubbles are r1 and r2. In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by [MP PMT 2001; RPET 1999; EAMCET 2003] |
| A. | \[R=({{r}_{1}}+{{r}_{2}})/2\] |
| B. | \[R={{r}_{1}}({{r}_{1}}{{r}_{2}}+{{r}_{2}})\] |
| C. | \[{{R}^{2}}=r_{1}^{2}+r_{2}^{2}\] |
| D. | \[R={{r}_{1}}+{{r}_{2}}\] |
| Answer» D. \[R={{r}_{1}}+{{r}_{2}}\] | |
| 3900. |
A capillary tube of radius r is dipped in a liquid of density r and surface tension S. If the angle of contact is q, the pressure difference between the two surfaces in the beaker and the capillary |
| A. | \[\frac{S}{r}\cos \theta \] |
| B. | \[\frac{2S}{r}\cos \theta \] |
| C. | \[\frac{S}{r\cos \theta }\] |
| D. | \[\frac{2S}{r\cos \theta }\] |
| Answer» C. \[\frac{S}{r\cos \theta }\] | |