HSC Commerce (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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.

In a test that has 5 true/false questions, no student has got all correct answers and no sequence of answers is repeated. What is the maximum number of students for this to be possible?

How many four-digit numbers Will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?

How many numbers formed with digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?

A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?

A fair die is thrown two times. Find the chance that product of the numbers on the upper face is 12.

A fair die is thrown two times. Find the chance that sum of the numbers on the upper face is 10.

A fair die is thrown two times. Find the chance that Sum of the numbers on the upper face is at least 10.