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

In sequencing, an optimal path is one that minimizes _______.

If jobs A to D have processing times as 5, 6, 8, 4 on first machine and 4, 7, 9, 10 on second machine then the optimal sequence is ______.

Solve the following problem :

Consider the problem of assigning five operators to five machines. The assignment costs are given in following table.

Operator A cannot be assigned to machine 3 and operator C cannot be assigned to machine 4. Find the optimal assignment schedule.

Solve the following problem :

A chartered accountant’s firm has accepted five new cases. The estimated number of days required by each of their five employees for each case are given below, where - means that the particular employee cannot be assigned the particular case. Determine the optimal assignment of cases of the employees so that the total number of days required to complete these five cases will be minimum. Also find the minimum number of days.

Find the general solution of the equation `("d"y)/("d"x) - y` = 2x.

Solution: The equation `("d"y)/("d"x) - y` = 2x

is of the form `("d"y)/("d"x) + "P"y` = Q

where P = `square` and Q = `square`

∴ I.F. = `"e"^(int-"d"x)` = e^–x

∴ the solution of the linear differential equation is

ye^–x = `int 2x*"e"^-x  "d"x + "c"`

∴ ye^–x  = `2int x*"e"^-x  "d"x + "c"`

= `2{x int"e"^-x "d"x - int square  "d"x* "d"/("d"x) square"d"x} + "c"`

= `2{x ("e"^-x)/(-1) - int ("e"^-x)/(-1)*1"d"x} + "c"`

∴ ye^–x = `-2x*"e"^-x + 2int"e"^-x "d"x + "c"`

∴ e^–xy = `-2x*"e"^-x+ 2 square + "c"`

∴ `y + square + square` = ce^x is the required general solution of the given differential equation

Choose the correct alternative:

If for a bivariate data, b_YX = – 1.2 and b_XY = – 0.3, then r = ______

Choose the correct alternative:

If the regression equation X on Y is 3x + 2y = 26, then b_xy equal to 

Choose the correct alternative:

If b_yx < 0 and b_xy < 0, then r is ______

Choose the correct alternative:

|b_yx + b_xy| ≥ ______

Choose the correct alternative:

Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σ_x = 2, σ_y = 8

Choose the correct alternative:

b_xy and b_yx are ______

Choose the correct alternative:

If r = 0.5, σ_x = 3, `σ_"y"^2` = 16, then b_yx = ______

Choose the correct alternative:

If r = 0.5, σ_x = 3, σ_y² = 16, then b_xy = ______

Choose the correct alternative:

Both the regression coefficients cannot exceed 1

State whether the following statement is True or False:

If b_yx = 1.5 and b_xy = `1/3` then r = `1/2`, the given data is consistent

State whether the following statement is True or False: 

If b_xy < 0 and b_yx < 0 then ‘r’ is > 0

The following data is not consistent: b_yx + b_xy =1.3 and r = 0.75

State whether the following statement is True or False: 

If u = x – a and v = y – b then b_xy = b_uv 

State whether the following statement is True or False:

Corr(x, x) = 0

Corr(x, x) = 1