 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2007

If ${M_O}$ is the mass of an oxygen isotope ${}_8{O^{17}}$ , ${M_p}$ and ${M_N}$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is
A
$\left( {{M_O} - 17{M_N}} \right){C^2}$
B
$\left( {{M_O} - 8{M_P}} \right){C^2}$
C
$\left( {{M_O} - 8{M_P} - 9{M_N}} \right){C^2}$
D
${{M_O}{c^2}}$

Explanation

Binding energy

$= \left[ {Z{M_p} + \left( {A - Z} \right){M_N} - M} \right]{c^2}$

$= \left[ {8{M_p} + \left( {17 - 8} \right){M_N} - M} \right]{c^2}$

$= \left[ {8{M_p} + 9{M_N} - M} \right]{c^2}$

$= \left[ {8{M_p} + 9{M_N} - {M_O}} \right]{c^2}$
2

AIEEE 2006

The energy spectrum of $\beta$-particles [ number $N(E)$ as a function of $\beta$-energy $E$ ] emitted from a radioactive source is
A B C D Explanation

The range of energy of $\beta$-particles is from zero to some maximum value.
3

AIEEE 2006

The $'rad'$ is the correct unit used to report the measurement of
A
the ability of a beam of gamma ray photons to produce ions in a target
B
the energy delivered by radiation to a target
C
D
the rate of decay of radioactive source

Explanation

The risk posed to a human being by any radiation exposure depends partly upon the absorbed dose, the amount of energy absorbed per gram of tissue. Absorbed dose is expressed in rad. A rad is equal to $100$ $ergs$ of energy absorbed by $1$ gram of tissue. The more modern, internationally adopted unit is the gray (named after the English medical physicist $L.$ $H.$ Gray); one gray equals $100$ rad.
4

AIEEE 2006

If the binding energy per nucleon in ${}_3^7Li$ and ${}_2^4He$ nuclei are $5.60$ $MeV$ and $7.06$ $MeV$ respectively, then in the reaction $$p + {}_3^7Li \to 2\,{}_2^4He$$
energy of proton must be
A
$28.24$ $MeV$
B
$17.28$ $MeV$
C
$1.46$ $MeV$
D
$39.2$ $MeV$

Explanation

Let $E$ be the energy of proton, then

$E + 7 \times 5.6 = 2 \times \left[ {4 \times 7.06} \right]$

$\Rightarrow E = 56.48 - 39.2 = 17.28MeV$