HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Important Questions for Mathematics and Statistics

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

(p ∧ ~ q) → (~ p ∧ ~ q)

Write the converse, inverse, and contrapositive of the following statement.

"If it snows, then they do not drive the car"

Find MPC, MPS, APC and APS, if the expenditure E_c of a person with income I is given as E_c = (0.0003) I² + (0.075) I ; When I = 1000.

Choose the correct alternative:

`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?

If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? `("Given" sqrt(3/2) = 1.2247)`

The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.

1. Obtain trend values for the above data using 5-yearly moving averages.
2. Plot the original time series and trend values obtained above on the same graph.

Four new machines M₁, M₂, M₃ and M₄ are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M₂ cannot be placed at C and M₃ cannot be placed at A. The cost matrix is given below:

Find the optimal assignment schedule.

The false statement in the following is ______.

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 5 comment on the result.

If the elasticity of demand η = 1, then demand is ______.

`int(x + 1/x)^3 dx` = ______.

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

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.

b_XY . b_YX = ______.

In a cattle breeding firm, it is prescribed that the food ration for one animal must contain 14, 22, and 1 unit of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following amounts of these three nutrients:

The cost of fodder 1 is ₹ 3 per unit and that of fodder ₹ 2 per unit. Formulate the L.P.P. to minimize the cost.

A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.

Solve the problem for minimizing the total elapsed time.

Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.

Negation of “Some men are animal” is ______.