Science (English Medium) Class 11 - CBSE Question Bank Solutions

\[\lim_{x \to 0} \frac{\sqrt{1 + x + x^2} - \sqrt{x + 1}}{2 x^2}\] 

\[\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}\]

\[\lim_{x \to a} \frac{x - a}{\sqrt{x} - \sqrt{a}}\]

\[\lim_{x \to 0} \frac{\sqrt{1 + 3x} - \sqrt{1 - 3x}}{x}\]

\[\lim_{x \to 0} \frac{\sqrt{2 - x} - \sqrt{2 + x}}{x}\] 

\[\lim_{x \to 1} \frac{\sqrt{3 + x} - \sqrt{5 - x}}{x^2 - 1}\] 

\[\lim_{x \to 1} \frac{\left( 2x - 3 \right) \left( \sqrt{x} - 1 \right)}{3 x^2 + 3x - 6}\]

\[\lim_{x \to 0} \frac{\sqrt{1 + x^2} - \sqrt{1 + x}}{\sqrt{1 + x^3} - \sqrt{1 + x}}\] 

\[\lim_{x \to 1} \frac{ x^2 - \sqrt{x}}{\sqrt{x} - 1}\]

\[\lim_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}, x \neq 0\] 

\[\lim_{x \to \sqrt{10}} \frac{\sqrt{7 + 2x} - \left( \sqrt{5} + \sqrt{2} \right)}{x^2 - 10}\] 

\[\lim_{x \to \sqrt{6}} \frac{\sqrt{5 + 2x} - \left( \sqrt{3} + \sqrt{2} \right)}{x^2 - 6}\] 

\[\lim_{x \to \sqrt{2}} \frac{\sqrt{3 + 2x} - \left( \sqrt{2} + 1 \right)}{x^2 - 2}\] 

Find the mean, variance and standard deviation for the data:

 2, 4, 5, 6, 8, 17.

Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.

Find the mean, variance and standard deviation for the data:

 227, 235, 255, 269, 292, 299, 312, 321, 333, 348.

Find the mean, variance and standard deviation for the data 15, 22, 27, 11, 9, 21, 14, 9.

The variance of 15 observations is 4. If each observation is increased by 9, find the variance of the resulting observations.

The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.