The shortest wavelength of H atom in the Lyman series is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mn>1</mn></msub></math>&nbsp;.&nbsp;The longest wavelength in the Balmer series of He+ is :

The combined equation of pair of lines passing through the point&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math>&nbsp;and parallel to the pair of lines&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>xy</mi><mo>+</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></math>

If the lines represented by the equations&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mi>mxy</mi><mo>+</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi>ly</mi><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn></math>&nbsp;are parallel to each other, which of the following is correct.&nbsp;

The distance between the pair of parallel lines represented by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>−</mo><mn>5</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn></math>&nbsp;is

The lines <math><mrow><mn>10</mn><mi>x</mi><mo>+</mo><mn>5</mn><mi>y</mi><mo>−</mo><mn>20</mn><mo>=</mo><mn>0</mn></mrow></math><xml> </xml>and <math><mrow><mi>y</mi><mtext> </mtext><mo>=</mo><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>20</mn></mrow></math><xml> </xml>are

The shortest wavelength of H atom in the Lyman series is $λ_{1}$ .
The longest wavelength in the Balmer series of He⁺ is :

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The shortest wavelength of H atom in the Lyman series is λ1 . The longest wavelength in the Balmer series of He+ is :

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The shortest wavelength of H atom in the Lyman series is $λ_{1}$ .
The longest wavelength in the Balmer series of He⁺ is :