### JEE Mains Previous Years Questions with Solutions

4.5
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1

### AIEEE 2003

When a ${U^{238}}$ nucleus originally at rest, decays by emitting an alpha particle having a speed $'u',$ the recoil speed of the residual nucleus is
A
${{4\mu } \over {238}}$
B
$- {{4\mu } \over {234}}$
C
${{4\mu } \over {234}}$
D
$- {{4\mu } \over {238}}$

## Explanation

Here, conservation of linear momentum can be applied

$238 \times 0 = 4u + 234v$

$\therefore$ $v = - {4 \over {234}}u$

$\therefore$ speed $= |\overrightarrow v | = {4 \over {234}}u$
2

### AIEEE 2003

Which of the following radiations has the least wavelength ?
A
$\gamma$ - rays
B
$\beta$ - rays
C
$\alpha$ - rays
D
$X$ - rays

## Explanation

The electromagnetic spectrum is as follows

$\therefore$ $\gamma$-rays has least wavelength.
3

### AIEEE 2002

If ${N_0}$ is the original mass of the substance of half-life period ${t_{1/2}} = 5$ years, then the amount of substance left after $15$ years is
A
${N_0}/8$
B
${N_0}/16$
C
${N_0}/2$
D
${N_0}/4$

## Explanation

After every half-life, the mass of the substance reduces to half its initial value.

${N_0}\mathop \to \limits^{5\,years} \,\,{{{N_0}} \over 2}\mathop \to \limits^{5\,years} {{{N_0}} \over {{2^2}}}\mathop \to \limits^{5\,years} {{{N_0}} \over 8}$
4

### AIEEE 2002

At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit
\eqalign{ & \left( i \right)\,\,\,\,\,\,\,electrons\,\,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,protons \cr & \left( {iii} \right)\,\,\,H{e^{2 + }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,neutrons \cr}

The emission at instant can be

A
$i, ii, iii$
B
$i, ii, iii, iv$
C
$iv$
D
$ii, iii$

## Explanation

Charged particles are deflected in magnetic field.