According to Avogadro law the correct statements area) Volume of gas is proportional to the no. of moles at constant T and P&nbsp;b) The pressure of a gas is directly proportional to temp. of the gas under all conditions&nbsp;c) Equal volumes of different gases under similar conditions consist of equal no. of molecules&nbsp;d) Equal volumes of different gases under same conditions have equal no. of atoms

If A is a square matrix of order 3 and |A|=5, then the value of |<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>A</mi><mo>'</mo></math>| is

The value of <math><mrow><mrow><mo>|</mo><mrow><mtable><mtr><mtd><mrow><msup><mn>5</mn><mn>2</mn></msup></mrow></mtd><mtd><mrow><msup><mn>5</mn><mn>3</mn></msup></mrow></mtd><mtd><mrow><msup><mn>5</mn><mn>4</mn></msup></mrow></mtd></mtr><mtr><mtd><mrow><msup><mn>5</mn><mn>3</mn></msup></mrow></mtd><mtd><mrow><msup><mn>5</mn><mn>4</mn></msup></mrow></mtd><mtd><mrow><msup><mn>5</mn><mn>5</mn></msup></mrow></mtd></mtr><mtr><mtd><mrow><msup><mn>5</mn><mn>4</mn></msup></mrow></mtd><mtd><mrow><msup><mn>5</mn><mn>5</mn></msup></mrow></mtd><mtd><mrow><msup><mn>5</mn><mn>7</mn></msup></mrow></mtd></mtr></mtable></mrow><mo>|</mo></mrow></mrow></math><xml> </xml> is

If &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced close="]" open="["><mtable><mtr><mtd><mn>1</mn><mo>+</mo><mn>2</mn><mi>m</mi></mtd><mtd><mn>4</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>+</mo><mn>3</mn><mi>m</mi></mtd><mtd><mn>6</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>+</mo><mn>4</mn><mi>m</mi></mtd><mtd><mn>8</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mtext> </mtext><mrow><mo>|</mo><mi>A</mi><mo>|</mo></mrow><mo>=</mo><mo>−</mo><mn>4</mn></math>, then &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo></math>

If&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo>&nbsp;</mo><mi mathvariant="normal">y</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo>&nbsp;</mo><mi mathvariant="normal">z</mi><mo>≠</mo><mn>0</mn></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn><mo>+</mo><mi mathvariant="normal">x</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>+</mo><mi mathvariant="normal">y</mi></mtd><mtd><mn>1</mn><mo>+</mo><mn>2</mn><mi mathvariant="normal">y</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>+</mo><mi mathvariant="normal">z</mi></mtd><mtd><mn>1</mn><mo>+</mo><mi mathvariant="normal">z</mi></mtd><mtd><mn>1</mn><mo>+</mo><mn>3</mn><mi mathvariant="normal">z</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>,</mo></math>&nbsp;then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">x</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>&nbsp;</mo><msup><mi mathvariant="normal">y</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><msup><mi mathvariant="normal">z</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>&nbsp;is equal to

The value of the determinant&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced separators="|" close="|" open="|"><mtable columnalign="left left left" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">a</mi><mo>    </mo><mn>1</mn><mo>    </mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>    </mo><mi mathvariant="normal">b</mi><mo>    </mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>    </mo><mn>1</mn><mo>    </mo><mi mathvariant="normal">c</mi></mtd></mtr></mtable></mfenced></math>&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&gt;</mo><mn>0</mn></math>&nbsp;, then (where a, b, c &gt; 0)

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