The minimum rate of change of the function&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>7</mn></math>&nbsp;is

On the curve&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>=</mo><mn>12</mn><mi>y</mi></math>, the values of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&nbsp;</mo></math>for which the abscissa changes at a faster rate than the ordinate is

The total revenue in Rupees received from the sale of x units of a product is given by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo>(</mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>=</mo><mn>3</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mn>36</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>5</mn></math>. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant

A kite flying at a height ‘h’ mts has 
<math >
 <m:semantics>
 <m:mrow>
 <m:mo>&#x0022;</m:mo><m:mi>x</m:mi><m:mo>&#x0022;</m:mo></m:mrow>
 </m:semantics></math>&nbsp; meters of string paid out at a time t seconds. If the kite moves horizontally with constant velocity V mts/sec. Then the rate at which the string is paid out is <pstyle="margin-top:0pt;margin-bottom:0pt;line-height:normal"><spanstyle="-aw-import:ignore">

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

$\frac{{Sin}^{2} A + Sin A + 1}{Sin A} \geq k t h e n k =$

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Sin2⁡A+Sin⁡A+1Sin⁡A≥k then k =

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$\frac{{Sin}^{2} A + Sin A + 1}{Sin A} \geq k t h e n k =$