HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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:

Which of the following is not a statement?

The complicated but efficient method of measuring trend of time series is ______.

The following table shows gross capital information (in Crore ₹) for years 1966 to 1975:

Obtain trend values using 5-yearly moving values.

The publisher of a magazine wants to determine the rate of increase in the number of subscribers. The following table shows the subscription information for eight consecutive years:

Fit a trend line by graphical method.

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

The management of a large furniture store would like to determine sales (in thousands of ₹) (X) on a given day on the basis of number of people (Y) that visited the store on that day. The necessary records were kept, and a random sample of ten days was selected for the study. The summary results were as follows:

`sumx_i = 370 , sumy_i = 580, sumx_i^2 = 17200 , sumy_i^2 = 41640, sumx_iy_i = 11500, n = 10`

Without using truth table, prove that:

[p ∧ (q ∨ r)] ∨ [∼r ∧ ∼q ∧ p] ≡ p

Fit a trend line to the following data by the method of least square :

The processing times required for four jobs A, B, C and D on machine M₁ are 5, 8, 10 and 7 hours and on machine M₂ it requires 7, 4, 3 and 6 hours respectively. The jobs are processed in the order M_l, M₂. The sequence that minimises total elapsed time is ______

A publisher produces 5 books on Mathematics. The books have to go through composing, printing and binding done by 3 machines A, B, C. The time schedule for the entire task in proper unit is as follows :

Determine the optimum time required to finish the entire task. Also, find idle time for machines A, B, C.

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

Solution:

Here n = 9. We transform year t to u by taking u = t - 1979. We construct the following table for calculation :

The equation of trend line is x_t= a' + b'u.

The normal equations are,

`sumx_t = na^' + b^' sumu`              ...(1)

`sumux_t = a^'sumu + b^'sumu^2`      ...(2)

Here, n = 9, `sumx_t = 47, sumu= 0, sumu^2 = 60`

By putting these values in normal equations, we get

47 = 9a' + b' (0)       ...(3)

40 = a'(0) + b'(60)      ...(4)

From equation (3), we get a' = `square`

From equation (4), we get b' = `square`

∴ the equation of trend line is x_t = `square`

Without using truth table, prove that : [(p ∨ q) ∧ ∼p] →q is a tautology.