HSC Commerce (Marathi Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

State whether the following statement is True or False:

The idle time for a machine is the when machine is available but is not waiting for any job to be processed

State whether the following statement is True or False: 

In sequencing problem each job once started on any machine must be processed still its completion

State whether the following statement is True or False:

In sequencing problem each machine is of different type

Find the sequence that minimizes total elapsed time to complete the following jobs in the order XY. Find the total elasped time and idle times for each machine.

If p ∨ q is true, then the truth value of ∼ p ∧ ∼ q is ______.

If x = `sqrt(1 + u^2)`, y = `log(1 + u^2)`, then find `(dy)/(dx).`

For certain bivariate data on 5 pairs of observations given:

∑x = 20, ∑y = 20, ∑x² = 90, ∑y² = 90, ∑xy = 76 then b_xy = ______.

Obtain the trend values for the following data using 5 yearly moving averages:

Following table shows the amount of sugar production (in lakh tonnes) for the years 1931 to 1941:

Complete the following activity to fit a trend line by method of least squares:

Find `dy/dx`  if,  `x = e^(3t) , y = e^sqrtt`

Find `dy/dx` if, x = e^3t, y = `e^((4t+5))`

Find `dy/dx if, x = e^(3t),y=e^((4t+5))`

 Find `dy/dx` if,

`x = e ^(3^t), y = e^((4t + 5))`

Find `dy/dx` if, `x=e^(3t), y=e^((4t+5))`

 Find `dy/dx if,x = e^(3^T), y = e^((4t + 5)`

If x² + 6xy + y² = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.

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.

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