Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

\[\lim_{x \to 0} \frac{a^{mx} - 1}{b^{nx} - 1}, n \neq 0\]

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

\[\lim_{x \to 0} \frac{9^x - 2 . 6^x + 4^x}{x^2}\] 

\[\lim_{x \to 0} \frac{8^x - 4^x - 2^x + 1}{x^2}\]

\[\lim_{x \to 0} \frac{a^{mx} - b^{nx}}{x}\] 

\[\lim_{x \to 0} \frac{a^x + b^x + c^x - 3}{x}\] 

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

\[\lim_{x \to 0} \frac{5^x + 3^x + 2^x - 3}{x}\]

\[\lim_{x \to \infty} \left( a^{1/x} - 1 \right)x\]

\[\lim_{x \to 0} \frac{a^{mx} - b^{nx}}{\sin kx}\]

\[\lim_{x \to 0} \frac{a^x + b^ x - c^x - d^x}{x}\]

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

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

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

Find the standard deviation for the following data:

Calculate the mean and S.D. for the following data:

Calculate the standard deviation for the following data:

Calculate the A.M. and S.D. for the following distribution:

A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and S.D.

Calculate the mean, median and standard deviation of the following distribution: