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1
JEE Main 2026 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The heat of atomisation of methane and ethane are ' x ' $\mathrm{kJ} \mathrm{mol}^{-1}$ and ' y ' $\mathrm{kJ} \mathrm{mol}^{-1}$ respectively. The longest wavelength ( $\lambda$ ) of light capable of breaking the $\mathrm{C}-\mathrm{C}$ bond can be expressed in SI unit as :

A

$\frac{\mathrm{N}_{\mathrm{A}} \mathrm{hc}}{250(y-6 x)}$

B

$\mathrm{N}_{\mathrm{A}} \mathrm{hc}\left(y-\frac{6 x}{4}\right)^{-1}$

C

$\frac{\mathrm{hc}}{1000}\left(\frac{y-6 x}{4}\right)^{-1}$

D

$\frac{\mathrm{N}_{\mathrm{A}} \mathrm{hc}}{250(4 y-6 x)}$

2
JEE Main 2026 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Match the LIST-I with LIST-II } $$

List-I Isothermal process for ideal gas system List-II Work done ( 
<mi>V</mi>

<mi>f</mi>
> 
<mi>V</mi>

<mi>i</mi>


<mi>V</mi>

<mi>f</mi>
> 
<mi>V</mi>

<mi>i</mi>
V_(f) > V_(i) )
A. Reversible expansion I. 
<mi mathvariant="normal">w</mi>
= 0 
<mi mathvariant="normal">w</mi>
= 0 w=0
B. Free expansion II. 
<mi mathvariant="normal">w</mi>
= − 
<mi data-mjx-auto-op="false">nR</mi>
T ln ⁡ 
<msub>

  <mrow data-mjx-texclass="ORD">

    <mtext> </mtext>

    <mi mathvariant="normal">V</mi>

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  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>


<mi mathvariant="normal">w</mi>
= − 
<mi data-mjx-auto-op="false">nR</mi>
T ln ⁡ 
<msub>

  <mrow data-mjx-texclass="ORD">

    <mtext></mtext>

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>
w=-nRT ln((V_(f))/(V_(i)))
C. Irreversible expansion III. 
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= − 
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  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>


<mo data-mjx-texclass="OPEN">(</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<mo>−</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>

<mo data-mjx-texclass="CLOSE">)</mo>


<mi mathvariant="normal">w</mi>
= − 
<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>


<mrow>

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

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    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">f</mi>

      </mrow>

    </mrow>

  </msub>  

  <mo>−</mo>  

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">i</mi>

      </mrow>

    </mrow>

  </msub>  

</mrow>
w=-p_(ex)(V_(f)-V_(i))
D. Irreversible compression IV. 
<mi mathvariant="normal">w</mi>
= − 
<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>


<mo data-mjx-texclass="OPEN">(</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>

<mo>−</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<mo data-mjx-texclass="CLOSE">)</mo>


<mi mathvariant="normal">w</mi>
= − 
<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>


<mrow>

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">i</mi>

      </mrow>

    </mrow>

  </msub>  

  <mo>−</mo>  

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">f</mi>

      </mrow>

    </mrow>

  </msub>  

</mrow>
w=-p_(ex)(V_(i)-V_(f))

Choose the correct answer from the options given below:

A

A-IV, B-I, C-III, D-II

B

A-I, B-III, C-II, D-IV

C

A-II, B-I, C-III, D-IV

D

A-IV, B-II, C-III, D-I

3
JEE Main 2026 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A cup of water at $5^{\circ} \mathrm{C}$ (system) is placed in a microwave oven and the oven is turned on for one minute during which the water begins to boil. Which of the following option is true?

A

$q=+v e, w=-v e, \Delta U=+v e$

B

$q=+v e, w=0, \Delta U=-v e$

C

$q=+v e, w=-v e, \Delta U=-v e$

D

$q=-v e, w=-v e, \Delta U=-v e$

4
JEE Main 2026 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Match the LIST-I with LIST-II } $$

List-I Thermodynamic Process List-II Magnitude in kJ
A. Work done in reversible, isothermal expansion of 2 mol of ideal gas from 2 
<mrow data-mjx-texclass="ORD">

  <mi data-mjx-auto-op="false">dm</mi>

</mrow>

<mn>3</mn>
2 
<mrow data-mjx-texclass="ORD">

  <mi data-mjx-auto-op="false">dm</mi>

</mrow>

<mn>3</mn>
2dm^(3) to 20 
<mrow data-mjx-texclass="ORD">

  <mi data-mjx-auto-op="false">dm</mi>

</mrow>

<mn>3</mn>
20 
<mrow data-mjx-texclass="ORD">

  <mi data-mjx-auto-op="false">dm</mi>

</mrow>

<mn>3</mn>
20dm^(3) at 300 K .		 I. 4
B. Work done in irreversible isothermal expansion of 1 mol ideal gas from 1 
<mrow data-mjx-texclass="ORD">

  <mtext> </mtext>

  <mi mathvariant="normal">m</mi>

</mrow>

<mn>3</mn>
1 
<mrow data-mjx-texclass="ORD">

  <mtext></mtext>

  <mi mathvariant="normal">m</mi>

</mrow>

<mn>3</mn>
1m^(3) to 3 
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  <mtext> </mtext>

  <mi mathvariant="normal">m</mi>

</mrow>

<mn>3</mn>
3 
<mrow data-mjx-texclass="ORD">

  <mtext></mtext>

  <mi mathvariant="normal">m</mi>

</mrow>

<mn>3</mn>
3m^(3) at 300 K against a constant pressure of 3 kPa .		 II. 11.5
C. Change in internal energy for adiabatic expansion of a 1 mol ideal gas with change of temperature = 320 
<mtext> </mtext>

<mi mathvariant="normal">K</mi>
= 320 
<mtext></mtext>

<mi mathvariant="normal">K</mi>
=320K and 
<mover>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">C</mi>

  </mrow>

  <mo accent="true">―</mo>

</mover>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

</mrow>
= 
<mn>3</mn>

<mn>2</mn>

<mi mathvariant="normal">R</mi>

<mover accentunder="false">

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">C</mi>

  </mrow>

  <mo>¯</mo>

</mover>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

</mrow>
= 
<mn>3</mn>

<mn>2</mn>

<mi mathvariant="normal">R</mi>
bar(C)_(V)=(3)/(2)R.		 III. 6
D. Change in enthalpy at constant pressure of 1 mol ideal gas with change of temperature = 337 
<mtext> </mtext>

<mi mathvariant="normal">K</mi>
= 337 
<mtext></mtext>

<mi mathvariant="normal">K</mi>
=337K and 
<mover>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">C</mi>

  </mrow>

  <mo accent="true">―</mo>

</mover>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">p</mi>

  </mrow>

</mrow>
= 
<mn>5</mn>

<mn>2</mn>

<mi mathvariant="normal">R</mi>

<mover accentunder="false">

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">C</mi>

  </mrow>

  <mo>¯</mo>

</mover>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">p</mi>

  </mrow>

</mrow>
= 
<mn>5</mn>

<mn>2</mn>

<mi mathvariant="normal">R</mi>
bar(C)_(p)=(5)/(2)R.		 IV. 7
A

A-I, B-II, C-III, D-IV

B

A-III, B-II, C-IV, D-I

C

A-II, B-I, C-III, D-IV

D

A-II, B-III, C-I, D-IV

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