HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Mean of x = 25

Mean of y = 20

`sigma_x` = 4

`sigma_y` = 3

r = 0.5

b_yx = `square`

b_xy = `square`

when x = 10,

`y - square = square (10 - square)`

∴ y = `square`

The regression equation of y on x is 2x – 5y + 60 = 0

Mean of x = 18

`2 square -  5 bary + 60` = 0

∴ `bary = square`

`sigma_x : sigma_y` = 3 : 2

∴ b_yx = `square/square`

∴ b_yx = `square/square`

∴ r = `square`

b_xy = `square/square`

b_yx = `square/square`

∴ Regression equation of x on y is `square`

∴ Regression equation of y on x is `square`

State whether the following statement is True or False:

Purchasing power of money = `1/"Cost of Living Index Number"`

The Cost of Living Index Numbers for years 2003 and 2008 are 150 and 200 respectively. A person earned ₹ 18,000 per month in year 2003. What should be his earning per month in year 2008, so as to maintain same standard of living as 2003?

Choose the correct alternative:

In sequencing, an optimal path that minimizes ______

The optimum sequence for the above data is ______

State whether the following statement is true or false.

The integrating factor of the differential equation `(dy)/(dx) + y/x` = x³ is – x.

b_XY . b_YX = ______.

Five jobs are performed first on machine M₁ and then on machine M₂. Time taken in hours by each job on each machine is given below:

Determine the optimal sequence of jobs and total elapsed time. Also, find the idle time for two machines.

Draw Venn diagram for the following:

No policeman is thief

Draw Venn diagram for the following:

Some doctors are rich

Draw Venn diagram for the following:

Some students are not scholars

If b_yx > 1 then b_xy is _______.

The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.

`sum(x_i - barx)(y_i - bary)` = 1170

|b_xy + b_yz| ≥ ______.

For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

Find: 

1. b_yx
2. b_xy
3. Correlation coefficient between x and y.

Six jobs are performed on Machines M₁ and M₂ respectively. Time in hours taken by each job on each machine is given below:

Determine the optimal sequence of jobs and find total elapsed time. Also find the idle time for machines M₁ and M₂.

Solution:

Given jobs can be arranged in optimal sequence as,

Total Elapsed time = `square` hrs.

Idle time for Machine M₁ = 43 – 42 = 1 hour.

Idle time for Machine M₂ = `square` hrs.

`"Find"  (d^2y)/(dx^2)  "if"  y=e^((2x+1))`

Find `(d^2y)/dx^2 if, y = e^((2x + 1))`