&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;A ray of light passes through a medium whose refractive index varies with distance as&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msub><mi>n</mi><mn>0</mn></msub><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mi>x</mi><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></mfenced></math>.ray enters the medium parallel to x-axis, what w be the time taken for ray to travel between x=0 an x=a ?

In a &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>△</mo><mi>ABC</mi><mo>,</mo><mi mathvariant="normal">a</mi><mo>=</mo><mn>13</mn><mo>;</mo><mi mathvariant="normal">b</mi><mo>=</mo><mn>15</mn><mo>;</mo><mi>cos</mi><mo>&nbsp;</mo><mi mathvariant="normal">C</mi><mo>=</mo><mfrac><mn>2</mn><mn>13</mn></mfrac></math>then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo></math>

In a triangle&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi><mo>,</mo><mo>&nbsp;</mo><mfrac><mrow><msub><mi mathvariant="normal">r</mi><mn>1</mn></msub><mo>-</mo><mi mathvariant="normal">r</mi></mrow><mi mathvariant="normal">a</mi></mfrac><mo>+</mo><mfrac><msub><mi mathvariant="normal">r</mi><mrow><mn>2</mn><mo>-</mo><mi mathvariant="normal">r</mi></mrow></msub><mi mathvariant="normal">b</mi></mfrac><mo>+</mo><mfrac><mrow><msub><mi mathvariant="normal">r</mi><mn>3</mn></msub><mo>-</mo><mi mathvariant="normal">r</mi></mrow><mi mathvariant="normal">c</mi></mfrac><mo>=</mo></math>

If the lengths of the sides of a triangle are 15,20,25 units. Find the circum radius of the triangle

In a triangle ABC,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∠</mi><mi mathvariant="normal">A</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mi mathvariant="normal">b</mi><mo>−</mo><mi mathvariant="normal">c</mi><mo>=</mo><mn>3</mn><msqrt><mn>3</mn></msqrt><mtext>&nbsp;and&nbsp;</mtext><mi mathvariant="normal">Δ</mi><mo>=</mo><mfrac><mrow><mn>9</mn><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><msup><mi>cm</mi><mn>2</mn></msup></math>&nbsp;then a =

In a triangle ABC,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∠</mi><mi mathvariant="normal">B</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>3</mn></mfrac><mo>,</mo><mi mathvariant="normal">∠</mi><mi mathvariant="normal">C</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac></math>&nbsp;and D divides BC internally in the ratio 1:3. Then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>sin</mi><mo>⁡</mo><mi mathvariant="normal">∠</mi><mi>BAD</mi></mrow><mrow><mi>sin</mi><mo>⁡</mo><mi mathvariant="normal">∠</mi><mi>CAD</mi></mrow></mfrac></math>&nbsp;is equal to

A ray of light passes through a medium whose refractive index varies with distance as $n = n_{0} (1 + \frac{x}{2 a})$ .ray enters the medium parallel to x-axis, what w be the time taken for ray to travel between x=0 an x=a ?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A ray of light passes through a medium whose refractive index varies with distance as n=n01+x2a.ray enters the medium parallel to x-axis, what w be the time taken for ray to travel between x=0 an x=a ?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A ray of light passes through a medium whose refractive index varies with distance as $n = n_{0} (1 + \frac{x}{2 a})$ .ray enters the medium parallel to x-axis, what w be the time taken for ray to travel between x=0 an x=a ?