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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.
| 3501. |
Two thin lenses of focal lengths f1 and f2 are in contact. The focal length of this combination is [MP PET 2002] |
| A. | \[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}-{{f}_{2}}}\] |
| B. | \[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\] |
| C. | \[\frac{2{{f}_{1}}{{f}_{2}}}{{{f}_{1}}-{{f}_{2}}}\] |
| D. | \[\frac{2{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\] |
| Answer» C. \[\frac{2{{f}_{1}}{{f}_{2}}}{{{f}_{1}}-{{f}_{2}}}\] | |
| 3502. |
The focal length of lens of refractive index 1.5 in air is 30 cm. When it is immersed in a liquid of refractive index \[\frac{4}{3}\], then its focal length in liquid will be [BHU 2002] |
| A. | 30 cm |
| B. | 60 cm |
| C. | 120 cm |
| D. | 240 cm |
| Answer» D. 240 cm | |
| 3503. |
A point object O is placed in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at [Orissa JEE 2002] |
| A. | 30 cm left |
| B. | Infinity |
| C. | 1 cm to the right |
| D. | 18 cm to the left |
| Answer» B. Infinity | |
| 3504. |
If convex lens of focal length 80cm and a concave lens of focal length 50 cm are combined together, what will be their resulting power [AFMC 2002] |
| A. | + 6.5 D |
| B. | ? 6.5 D |
| C. | + 7.5 D |
| D. | ? 0.75 D |
| Answer» E. | |
| 3505. |
An object is placed 12 cm to the left of a converging lens of focal length 8 cm. Another converging lens of 6 cm focal length is placed at a distance of 30 cm to the right of the first lens. The second lens will produce [KCET 2002] |
| A. | No image |
| B. | A virtual enlarged image |
| C. | A real enlarged image |
| D. | A real smaller image |
| Answer» D. A real smaller image | |
| 3506. |
A convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis, the number of images formed are [KCET 2002] |
| A. | 1 |
| B. | 5 |
| C. | 4 |
| D. | 3 |
| Answer» E. | |
| 3507. |
A convex lens produces a real image m times the size of the object. What will be the distance of the object from the lens [JIPMER 2002] |
| A. | \[\left( \frac{m+1}{m} \right)f\] |
| B. | (m ?1)f |
| C. | \[\left( \frac{m-1}{m} \right)f\] |
| D. | \[\frac{m+1}{f}\] |
| Answer» B. (m ?1)f | |
| 3508. |
Figure given below shows a beam of light converging at point P. When a convex lens of focal length 16 cm is introduced in the path of the beam at a place O shown by dotted line such that OP becomes the axis of the lens, the beam converges at a distance x from the lens. The value x will be equal to [AMU (Med.) 2002] |
| A. | 12 cm |
| B. | 24 cm |
| C. | 36 cm |
| D. | 48 cm |
| Answer» E. | |
| 3509. |
The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit S and the collimating lens L is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure [CPMT 1986] |
| A. | 1 |
| B. | 3 |
| C. | 2 |
| D. | None of the figures |
| Answer» D. None of the figures | |
| 3510. |
A concave and convex lens have the same focal length of 20 cm and are put into contact to form a lens combination. The combination is used to view an object of 5 cm length kept at 20 cm from the lens combination. As compared to the object, the image will be [CPMT 1986; RPMT 1997] |
| A. | Magnified and inverted |
| B. | Reduced and erect |
| C. | Of the same size as the object and erect |
| D. | Of the same size as the object but inverted |
| Answer» D. Of the same size as the object but inverted | |
| 3511. |
If in a plano-convex lens, the radius of curvature of the convex surface is 10 cm and the focal length of the lens is 30 cm, then the refractive index of the material of lens will be [CPMT 1986; MNR 1988; MP PMT 2002; UPSEAT 2000] |
| A. | 1.5 |
| B. | 1.66 |
| C. | 1.33 |
| D. | 3 |
| Answer» D. 3 | |
| 3512. |
A convex lens of focal length \[f\] is placed somewhere in between an object and a screen. The distance between the object and the screen is \[x\]. If the numerical value of the magnification produced by the lens is \[m,\], then the focal length of the lens is |
| A. | \[\frac{mx}{{{(m+1)}^{2}}}\] |
| B. | \[\frac{mx}{{{(m-1)}^{2}}}\] |
| C. | \[\frac{{{(m+1)}^{2}}}{m}x\] |
| D. | \[\frac{{{(m-1)}^{2}}}{m}x\] |
| Answer» B. \[\frac{mx}{{{(m-1)}^{2}}}\] | |
| 3513. |
The radius of curvature for a convex lens is 40 cm, for each surface. Its refractive index is 1.5. The focal length will be [MP PMT 1989] |
| A. | 40 cm |
| B. | 20 cm |
| C. | 80 cm |
| D. | 30 cm |
| Answer» B. 20 cm | |
| 3514. |
An atomic nucleus \[_{90}T{{h}^{232}}\] emits several a and b radiations and finally reduces to \[_{82}P{{b}^{208}}\]. It must have emitted [MP PET 2003] |
| A. | 4a and 2b |
| B. | 6a and 4b |
| C. | 8a and 24b |
| D. | 4a and 16b |
| Answer» C. 8a and 24b | |
| 3515. |
Plutonium decays with a half-life of 24000 years. If the plutonium is stored for 72000 years, then the fraction of plutonium that remains is [CPMT 1999; MH CET 2003] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{8}\] |
| Answer» E. | |
| 3516. |
A radioactive substance emits [CPMT 1999] |
| A. | a-rays |
| B. | b-rays |
| C. | g-rays |
| D. | All of these |
| Answer» E. | |
| 3517. |
3.8 days is the half-life period of a sample. After how many days, the sample will become 1/8th of the original substance [DCE 1999] |
| A. | 11.4 |
| B. | 3.8 |
| C. | 3 |
| D. | None of these |
| Answer» B. 3.8 | |
| 3518. |
A nucleus of an element \[_{84}{{X}^{202}}\]emits an a-particle first, a b-particle next and then a gamma photon. The final nucleus formed has an atomic number [JIPMER 1999] |
| A. | 200 |
| B. | 199 |
| C. | 83 |
| D. | 198 |
| Answer» D. 198 | |
| 3519. |
The activity of a sample is 64 × 10?5 Ci. Its half-life is 3 days. The activity will become 5 × 10?6 Ci after [MP PET 2003] |
| A. | 12 days |
| B. | 7 days |
| C. | 18 days |
| D. | 21 days |
| Answer» E. | |
| 3520. |
Consider the following two statements A. Energy spectrum of a-particles emitted in radioactive decay is discrete B. Energy spectrum of b-particles emitted in radioactive decay is continuous [AMU (Med.) 1999] |
| A. | Only A is correct |
| B. | Only B is correct |
| C. | A is correct but B is wrong |
| D. | Both A and B are correct |
| Answer» C. A is correct but B is wrong | |
| 3521. |
An artificial radioactive decay series begins with unstable \[_{94}^{241}Pu\]. The stable nuclide obtained after eight \[\alpha -\]decays and five \[\beta -\]decays is [SCRA 1998] |
| A. | \[_{83}^{209}Bi\] |
| B. | \[_{82}^{209}Pb\] |
| C. | \[_{82}^{205}Ti\] |
| D. | \[_{82}^{201}Hg\] |
| Answer» B. \[_{82}^{209}Pb\] | |
| 3522. |
Beta rays emitted by a radioactive material are [IIT 1983; ISM Dhanbad 1994; AFMC 1997; BHU 2000; AIEEE 2002] |
| A. | Electromagnetic radiation |
| B. | The electrons orbiting around the nucleus |
| C. | Charged particles emitted by nucleus |
| D. | Neutral particles |
| Answer» D. Neutral particles | |
| 3523. |
The activity of a radioactive sample is measured as 9750 counts per minute at t = 0 and as 975 counts per minute at t = 5 minutes. The decay constant is approximately [CBSE PMT 1997] |
| A. | 0.230 per minute |
| B. | 0.461 per minute |
| C. | 0.691 per minute |
| D. | 0.922 per minute |
| Answer» C. 0.691 per minute | |
| 3524. |
A radio isotope has a half life of 75 years. The fraction of the atoms of this material that would decay in 150 years will be [BHU 1997] |
| A. | 66.6% |
| B. | 85.5% |
| C. | 62.5% |
| D. | 75% |
| Answer» E. | |
| 3525. |
A radioactive element \[_{90}{{X}^{238}}\]decay into\[_{83}{{Y}^{222}}\]. The number of \[\beta -\]particles emitted are [BHU 1997; JIPMER 2001, 02] |
| A. | 4 |
| B. | 6 |
| C. | 2 |
| D. | 1 |
| Answer» E. | |
| 3526. |
If half-life of a radioactive atom is 2.3 days, then its decay constant would be [AFMC 1997; JIPMER 2000] |
| A. | 0.1 |
| B. | 0.2 |
| C. | 0.3 |
| D. | 2.3 |
| Answer» D. 2.3 | |
| 3527. |
At any instant the ratio of the amount of radioactive substances is 2 : 1. If their half lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances [RPMT 1996] |
| A. | 1 : 1 |
| B. | 2 : 1 |
| C. | 1 : 2 |
| D. | 1 : 4 |
| Answer» B. 2 : 1 | |
| 3528. |
An element A decays into element C by a two-step process : \[A\to B+{{\ }_{2}}H{{e}^{4}}\]\[B\to C+\ 2{{e}^{-}}\] Then [CBSE PMT 1994; AMU 2002; KCET 2003] |
| A. | A and C are isotopes |
| B. | A and C are isobars |
| C. | A and B are isotopes |
| D. | A and B are isobars |
| Answer» B. A and C are isobars | |
| 3529. |
A radioactive sample with a half-life of 1 month has the label: ?Activity=2 micro curies on 1.8.1991.'' What will be its activity two months later [CBSE PMT 1992] |
| A. | 1.0 micro curies |
| B. | 0.5 micro curies |
| C. | 4 micro curies |
| D. | 8 micro curies |
| Answer» C. 4 micro curies | |
| 3530. |
The nucleus \[_{48}^{115}Cd\] after two successive \[{{\beta }^{-}}\] decays will give [CBSE PMT 1992; JIPMER 2000] |
| A. | \[_{46}^{115}Pa\] |
| B. | \[_{49}^{114}In\] |
| C. | \[_{50}^{113}Sn\] |
| D. | \[_{50}^{115}Sn\] |
| Answer» E. | |
| 3531. |
What percentage of original radioactive atoms is left after five half lives [AFMC 1996; RPMT 1996] |
| A. | 0.3% |
| B. | 1% |
| C. | 31% |
| D. | 3.125% |
| Answer» E. | |
| 3532. |
In the given nuclear reaction A, B, C, D, E represents \[_{92}{{U}^{238}}{{\xrightarrow{\alpha }}_{B}}T{{h}^{A}}{{\xrightarrow{\beta }}_{D}}P{{a}^{C}}{{\xrightarrow{E}}_{92}}{{U}^{234}}\] [RPET 1997] |
| A. | A = 234, B = 90, C = 234, D = 91, E = \[\beta \] |
| B. | A = 234, B = 90, C = 238, D = 94, E = \[\alpha \] |
| C. | A = 238, B = 93, C = 234, D = 91, E = \[\beta \] |
| D. | A = 234, B = 90, C = 234, D = 93, E = \[\alpha \] |
| Answer» B. A = 234, B = 90, C = 238, D = 94, E = \[\alpha \] | |
| 3533. |
Half-life of a radioactive element is 10 days. The time during which quantity remains 1/10 of initial mass will be [RPET 1997] |
| A. | 100 days |
| B. | 50 days |
| C. | 33 days |
| D. | 16 days |
| Answer» D. 16 days | |
| 3534. |
In the disintegration series\[_{92}^{238}U\xrightarrow{\alpha }X\xrightarrow{\beta -}_{Z}^{A}Y\]the values of Z and A respectively will be [MP PMT 2003] |
| A. | 92, 236 |
| B. | 88, 230 |
| C. | 90, 234 |
| D. | 91, 234 |
| Answer» E. | |
| 3535. |
Which of the following statements are true regarding radioactivity (I) All radioactive elements decay exponentially with time (II) Half life time of a radioactive element is time required for one half of the radioactive atoms to disintegrate (III) Age of earth can be determined with the help of radioactive dating (IV) Half life time of a radioactive element is 50% of its average life period Select correct answer using the codes given below Codes: [SCRA 1994] |
| A. | I and II |
| B. | I, III and IV |
| C. | I, II and III |
| D. | II and III |
| Answer» D. II and III | |
| 3536. |
An atom of mass number 15 and atomic number 7 captures an \[\alpha -\]particle and then emits a proton. The mass number and atomic number of the resulting product will respectively be [SCRA 1994] |
| A. | 14 and 2 |
| B. | 15 and 3 |
| C. | 16 and 4 |
| D. | 18 and 8 |
| Answer» E. | |
| 3537. |
Age of a tree is determined using radio-isotope of [EAMCET (Engg.) 1995] |
| A. | Carbon |
| B. | Cobalt |
| C. | Iodine |
| D. | Phosphorus |
| Answer» B. Cobalt | |
| 3538. |
The half-life of \[^{131}I\]is 8 days. Given a sample of \[^{131}I\]at time t = 0, we can assert that [IIT 1998] |
| A. | No nucleus will decay before t = 4 days |
| B. | No nucleus will decay before t = 8 days |
| C. | All nuclei will decay before t = 16 days |
| D. | A given nucleus may decay at any time after t = 0 |
| Answer» E. | |
| 3539. |
If the radioactive decay constant of radium is \[1.07\times {{10}^{-4}}\]per year, then its half life period is approximately equal to [AIIMS 1998] |
| A. | 8,900 years |
| B. | 7,000 years |
| C. | 6,476 years |
| D. | 2,520 years |
| Answer» D. 2,520 years | |
| 3540. |
The half-life period of radium is 1600 years. Its average life time will be [MP PET/PMT 1988] |
| A. | 3200 years |
| B. | 4800 years |
| C. | 2319 years |
| D. | 4217 years |
| Answer» D. 4217 years | |
| 3541. |
Half lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes. Initially the sample of A and B have equal number of nuclei. After 80 minutes, the ratio of remaining number of A and B nuclei is [CBSE PMT 1998; JIPMER 2000] |
| A. | 1 : 16 |
| B. | 4 : 1 |
| C. | 1 : 4 |
| D. | 1 : 1 |
| Answer» D. 1 : 1 | |
| 3542. |
\[^{22}Ne\]nucleus after absorbing energy decays into two \[\alpha -\]particles and an unknown nucleus. The unknown nucleus is [IIT 1999; UPSEAT 2002] |
| A. | Nitrogen |
| B. | Carbon |
| C. | Boron |
| D. | Oxygen |
| Answer» C. Boron | |
| 3543. |
Which of the following is a correct statement [IIT 1999; DPMT 2000; UPSEAT 2003] |
| A. | Beta rays are same as cathode rays |
| B. | Gamma rays are high energy neutrons |
| C. | Alpha particles are singly ionized helium atoms |
| D. | Protons and neutrons have exactly the same mass |
| Answer» B. Gamma rays are high energy neutrons | |
| 3544. |
After \[1\alpha \]and \[2\beta \]emissions [CBSE PMT 1999] |
| A. | Mass number reduces by 3 |
| B. | Mass number reduces by 4 |
| C. | Mass number reduces by 6 |
| D. | Atomic number remains unchanged |
| Answer» C. Mass number reduces by 6 | |
| 3545. |
In the uranium radioactive series, the initial nucleus is \[_{92}{{U}^{238}}\]and the final nucleus is \[_{82}P{{b}^{206}}\]. When the uranium nucleus decays to lead, the number of \[\alpha -\]particles emitted will be [MP PMT 1999] |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 8 |
| Answer» E. | |
| 3546. |
Decay constant of radium is\[\lambda \]. By a suitable process its compound radium bromide is obtained. The decay constant of radium bromide will be [MP PET 1999; JIPMER 2001, 02] |
| A. | \[\lambda \] |
| B. | More than \[\lambda \] |
| C. | Less than \[\lambda \] |
| D. | Zero |
| Answer» B. More than \[\lambda \] | |
| 3547. |
Radon (Ra) decays into Polonium (\[{{P}_{0}}\]) by emitting an \[\alpha -\]particle with half-life of 4 days. A sample contains \[6.4\times {{10}^{10}}\]atoms of\[Rn\]. After 12 days, the number of atoms of \[{{R}_{n}}\]left in the sample will be [MP PET 1999, Pb. PMT 2004] |
| A. | \[3.2\times {{10}^{10}}\] |
| B. | \[0.53\times {{10}^{10}}\] |
| C. | \[2.1\times {{10}^{10}}\] |
| D. | \[0.8\times {{10}^{10}}\] |
| Answer» E. | |
| 3548. |
The half-life period of a radioactive substance is 5 min. The amount of substance decayed in 20 min will be [MP PMT/PET 1998] |
| A. | 93.75% |
| B. | 75% |
| C. | 25% |
| D. | 6.25% |
| Answer» B. 75% | |
| 3549. |
The half-life (T) and the disintegration constant \[(\lambda )\]of a radioactive substance are related as [MP PMT/PET 1998] |
| A. | \[\lambda T=1\] |
| B. | \[\lambda T=0.693\] |
| C. | \[\frac{T}{\lambda }=0.693\] |
| D. | \[\frac{\lambda }{T}=0.693\] |
| Answer» C. \[\frac{T}{\lambda }=0.693\] | |
| 3550. |
Which can pass through 20 cm thickness of the steel [MNR 1985; CPMT 1990; RPET 2000] |
| A. | \[\alpha -\]particles |
| B. | \[\beta -\]particles |
| C. | \[\gamma -\]rays |
| D. | Ultraviolet rays |
| Answer» D. Ultraviolet rays | |