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

Show that `(−1+ sqrt3 i)^3` is a real number.

Evaluate the following limit:

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

Show that `(−1+ sqrt3 i)^3` is a real number.

Show that `(−1 + sqrt(3) i)^3` is a real number.

Show that `(-1 + sqrt3"i")^3` is a real number.

Evaluate the following:

`i^35`

Show that `(-1 + sqrt3i)^3` is a real number. 

Show that `(- 1 + sqrt3 i)^3` is a real number.

Simplify the following and express in the form a+ib.

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`

Mean and standard deviation of two distributions of 100 and 150 items are 50, 5 and 40, 6 respectively. Find the mean and standard deviations of all the 250 items taken together.

For certain bivariate data, the following information is available.

Obtain the combined standard deviation.

For a distribution, mean = 100, mode = 127 and SD = 60. Find the Pearson coefficient of skewness Sk_p.

The mean and variance of the distribution is 60 and 100 respectively. Find the mode and the median of the distribution if Sk_p = – 0.3.

Find Sk_p for the following set of observations.
17, 17, 21, 14, 15, 20, 19, 16, 13, 17, 18

Draw scatter diagram for the data given below and interpret it.

For the following data of marks of 7 students in physics (x) and Mathematics (y), draw scatter diagram and state the type of correlation.

Draw scatter diagram for the data given below. Is there any correlation between Aptitude score and Grade points?

A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can he select a student if the monitor can be a boy or a girl?

A teacher wants to select the class monitor in a class of 30 boys and 20 girls, in how many ways can the monitor be selected if the monitor must be a boy? What is the answer if the monitor must be a girl?

How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?