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

If X and Y are two variates connected by the relation

In a series of 20 observations, 10 observations are each equal to k and each of the remaining half is equal to − k. If the standard deviation of the observations is 2, then write the value of k.

If v is the variance and σ is the standard deviation, then

\[\lim_{x \to 0} \frac{e^{2x} - e^x}{\sin 2x}\]

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

\[\lim_{x \to 0} \frac{\log \left( a + x \right) - \log \left( a - x \right)}{x}\]

\[\lim_{x \to 0} \frac{\log \left( 2 + x \right) + \log 0 . 5}{x}\]

The standard deviation of the data:

is

\[\lim_{x \to 0} \frac{x\left( 2^x - 1 \right)}{1 - \cos x}\] 

\[\lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{\log \left( 1 + x \right)}\] 

\[\lim_{x \to 0} \frac{\log \left| 1 + x^3 \right|}{\sin^3 x}\] 

`\lim_{x \to \pi/2} \frac{a^\cot x - a^\cos x}{\cot x - \cos x}`

\[\lim_{x \to 0} \frac{e^x - 1}{\sqrt{1 - \cos x}}\]

\[\lim_{x \to 5} \frac{e^x - e^5}{x - 5}\]

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

`\lim_{x \to \pi/2} \frac{e^\cos x - 1}{\cos x}`

\[\lim_{x \to 0} \frac{e^{3 + x} - \sin x - e^3}{x}\] 

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

\[\lim_{x \to 0} \frac{e^{3x} - e^{2x}}{x}\]