HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following limit:

`lim_(x->5)[(x^3 -125)/(x^5 - 3125)]`

Evaluate the following limit:

`lim_(x ->7)[((root3x - root3(7))(root3x + root3(7)))/(x - 7)]`

Evaluate the following limit:

`lim_(x->-2)[(x^7 + x^5 + 160)/(x^3 + 8)]`

Find the various and S.D. for the following set of numbers.

7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6

Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129

Compute variance and standard deviation for the following data:

Compute the variance and S.D.

Following data gives age of 100 students in a school. Calculate variance and S.D.

The mean and variance of 5 observations are 3 and 2 respectively. If three of the five observations are 1, 3 and 5, find the values of other two observations.

Obtain standard deviation for the following date:

The following distribution was obtained change of origin and scale of variable X.

If it is given that mean and variance are 59.5 and 413 respectively, determine actual class intervals.

Following tale gives income (X) and expenditure (Y) of 25 families:

Find Conditional frequency distribution of X when Y is between 300 – 400.

Following tale gives income (X) and expenditure (Y) of 25 families:

Find Conditional frequency distribution of Y when X is between 200 – 300.

Following data gives height in cm (X) and weight in kgs (Y) of 20 boys. Prepare a bivariate frequency table taking class intervals 150-154, 155-159...etc. for X and 35-39, 40-44 ...etc. for Y. Also find conditional frequency distribution of Y when 155 ≤ X ≤ 159
(152, 40) (160, 54) (163, 52) (150, 35) (154, 36) (160, 49) (166, 54) (157, 38) (159, 43) (153, 48) (152, 41) (158, 51) (155, 44) (156, 47) (156, 43) (166, 53) (160, 50) (151, 39) (153, 50) (158, 46)

Find correlation coefficient between x and y series for the following data.
n = 15, `bar"x"` = 25, `bar"y"` = 18, σ_x = 3.01, σ_y = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122

The correlation coefficient between two variables x and y are 0.48. The covariance is 36 and the variance of x is 16. Find the standard deviation of y.

In the following data one of the value y of is missing. Arithmetic means of x and y series are 6 and 8 respectively. `(sqrt(2) = 1.4142)`

Calculate the correlation coefficient

Find correlation coefficient from the following data. `["Given:" sqrt(3) = 1.732]`

Correlation coefficient between x and y is 0.3 and their covariance is 12. The variance of x is 9, Find the standard deviation of y.

A letter lock has 3 rings and each ring has 5 letters. Determine the maximum number of trials that may be required to open the lock.