JEE Main Practice — Physics Set 1

In the hydrogen spectrum, $\lambda_L$ is the wavelength of the first (longest-wavelength) line of the Lyman series and $\lambda_B$ that of the first line of the Balmer series. The ratio $\lambda_L/\lambda_B$ is

1. A.$27/5$
2. B.$5/27$✓
3. C.$3/20$
4. D.$4/9$

Correct answer: B

The activity of a radioactive sample falls to $\frac{1}{16}$ of its initial value in 20 days. The half-life of the sample is

1. A.2.5 days
2. B.10 days
3. C.5 days✓
4. D.4 days

Correct answer: C

A nucleus of mass number 240 with binding energy per nucleon 7.6 MeV splits into two identical nuclei of mass number 120, each with binding energy per nucleon 8.5 MeV. The energy released in the process is

1. A.216 MeV✓
2. B.108 MeV
3. C.204 MeV
4. D.432 MeV

Correct answer: A

The ionisation energy of a hydrogen-like ion (from its ground state) is 122.4 eV. The wavelength of the photon emitted when its electron makes a transition from $n=3$ to $n=2$ is (take $hc=1240$ eV nm)

1. A.656.5 nm
2. B.218.8 nm
3. C.91.2 nm
4. D.72.9 nm✓

Correct answer: D

The nucleus $^{234}_{90}\mathrm{Th}$ undergoes a series of $\alpha$ and $\beta^-$ decays to become $^{214}_{83}\mathrm{Bi}$. The numbers of $\alpha$ and $\beta^-$ particles emitted are respectively

1. A.4 and 1
2. B.5 and 2
3. C.5 and 3✓
4. D.10 and 3

Correct answer: C

A hydrogen atom in an excited state returns to the ground state by emitting two successive photons of energies 2.55 eV and 10.2 eV. The ratio of the de Broglie wavelength of the electron in the initial excited state to that in the ground state is

1. A.16
2. B.2
3. C.4✓
4. D.$1/4$

Correct answer: C

The radius of an $^{27}\mathrm{Al}$ nucleus is 3.6 fm. Using $R=R_0A^{1/3}$, the radius of a $^{125}\mathrm{Te}$ nucleus in fm is ______.

Correct answer: 6

Two radioactive samples A and B have half-lives 2 h and 3 h respectively and initially contain equal numbers of nuclei. After 12 h, the ratio of the activity of B to that of A is $\frac{x}{3}$. The value of $x$ is ______.

Correct answer: 8

A wire of resistance $5\,\Omega$ is uniformly stretched so that its length doubles (volume unchanged). Its new resistance is

1. A.$10\,\Omega$
2. B.$20\,\Omega$✓
3. C.$2.5\,\Omega$
4. D.$40\,\Omega$

Correct answer: B

A battery of emf 12 V and internal resistance $0.5\,\Omega$ is connected across an external resistor of $5.5\,\Omega$. The terminal potential difference of the battery is

1. A.10.5 V
2. B.12 V
3. C.6 V
4. D.11 V✓

Correct answer: D

In a metre bridge, an unknown resistance $X$ in the left gap and $12\,\Omega$ in the right gap give a balance point at 40 cm from the left end. What resistance must be connected in parallel with the $12\,\Omega$ resistor so that the balance point shifts to 50 cm?

1. A.$24\,\Omega$✓
2. B.$8\,\Omega$
3. C.$12\,\Omega$
4. D.$36\,\Omega$

Correct answer: A

Two bulbs rated 100 W, 220 V and 60 W, 220 V are connected in series across a 220 V supply. Assuming constant resistances, the total power drawn and the brighter bulb are

1. A.37.5 W; the 60 W bulb✓
2. B.37.5 W; the 100 W bulb
3. C.160 W; the 100 W bulb
4. D.62.5 W; the 60 W bulb

Correct answer: A

A copper wire of cross-sectional area $2\ \mathrm{mm^2}$ carries a current of 3.2 A. If the free-electron density of copper is $8\times10^{28}\ \mathrm{m^{-3}}$, the drift speed of electrons is ($e=1.6\times10^{-19}$ C)

1. A.1.25 mm/s
2. B.0.0125 mm/s
3. C.0.125 mm/s✓
4. D.12.5 mm/s

Correct answer: C

Two cells, one of emf 6 V and internal resistance $1\,\Omega$ and the other of emf 4 V and internal resistance $2\,\Omega$, are connected in parallel with like terminals joined. This combination is connected across a $4\,\Omega$ resistor. The current through the $4\,\Omega$ resistor is

1. A.$10/7$ A
2. B.$8/7$ A✓
3. C.1 A
4. D.$5/3$ A

Correct answer: B

On a potentiometer, a cell gives a balancing length of 360 cm. When the cell is shunted by a $15\,\Omega$ resistor, the balancing length becomes 300 cm. The internal resistance of the cell (in $\Omega$) is ______.

Correct answer: 3

A uniform wire of resistance $36\,\Omega$ is bent into a circle. The equivalent resistance (in $\Omega$) between two points on the circle that subtend an angle of $120^\circ$ at the centre is ______.

Correct answer: 8

Photons of energy 4.1 eV fall on a metal surface of work function 2.3 eV. The stopping potential for the emitted photoelectrons is

1. A.2.3 V
2. B.6.4 V
3. C.1.8 V✓
4. D.4.1 V

Correct answer: C

An electron accelerated from rest through a potential difference $V$ has de Broglie wavelength $\lambda$. If the accelerating potential is made $9V$, the de Broglie wavelength becomes

1. A.$\lambda/3$✓
2. B.$\lambda/9$
3. C.$3\lambda$
4. D.$\lambda/\sqrt3$

Correct answer: A

When light of wavelength $\lambda$ falls on a metal, the stopping potential is $V$. When light of wavelength $\lambda/2$ is used, the stopping potential becomes $3V$. The threshold wavelength of the metal is

1. A.$3\lambda$
2. B.$4\lambda$
3. C.$2\lambda$✓
4. D.$3\lambda/2$

Correct answer: C

A proton and an $\alpha$-particle are each accelerated from rest through the same potential difference. The ratio of the de Broglie wavelength of the proton to that of the $\alpha$-particle is (take $m_\alpha=4m_p$)

1. A.$\sqrt2$
2. B.2
3. C.$\frac{1}{2\sqrt2}$
4. D.$2\sqrt2$✓

Correct answer: D

A 60 W lamp converts 40% of its electrical power into light of wavelength 600 nm. The number of photons emitted per second is approximately (take $hc=1240$ eV nm, $1\ \mathrm{eV}=1.6\times10^{-19}$ J)

1. A.$7.3\times10^{19}$✓
2. B.$1.8\times10^{20}$
3. C.$2.9\times10^{19}$
4. D.$7.3\times10^{18}$

Correct answer: A

Light of wavelength 248 nm falls on a metal of work function 3.0 eV. The most energetic photoelectrons enter a uniform magnetic field perpendicular to their velocity. The field needed to make them move in a circle of radius 5 mm is approximately ($hc=1240$ eV nm, $m_e=9.1\times10^{-31}$ kg, $e=1.6\times10^{-19}$ C)

1. A.1.9 mT
2. B.0.95 mT✓
3. C.0.48 mT
4. D.9.5 mT

Correct answer: B

Light of wavelength 200 nm is incident on a metal surface of work function 2.2 eV. The stopping potential (in volt) is ______. (Take $hc=1240$ eV nm.)

Correct answer: 4

The threshold frequency of a metal is $\nu_0$. Light of frequency $2\nu_0$ ejects photoelectrons with maximum speed $v_1$, and light of frequency $10\nu_0$ ejects them with maximum speed $v_2$. The value of $v_2/v_1$ is ______.

Correct answer: 3

A coil of 200 turns and area $0.05\ \mathrm{m^2}$ is placed with its plane perpendicular to a magnetic field. The field changes uniformly from 0.2 T to 0.8 T in 0.3 s. The magnitude of the average induced emf is

1. A.10 V
2. B.2 V
3. C.40 V
4. D.20 V✓

Correct answer: D