PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

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

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

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

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

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

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

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

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

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

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:

Find the mean and variance of frequency distribution given below:

The weight of coffee in 70 jars is shown in the following table:                                                  

Determine the variance and standard deviation of the above distribution.  

Mean and standard deviation of 100 observations were found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.      

Two plants A and B of a factory show following results about the number of workers and the wages paid to them 

The means and standard deviations of heights ans weights of 50 students of a class are as follows: