HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

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

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

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

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

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the value of x for which Total cost is decreasing.

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the values of x for which Revenue is increasing.

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)`

Obtain the differential equation by eliminating arbitrary constants from the following equation:

y = Ae^3x + Be^–3x

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.

The probability distribution of X is as follows:

Find:

1. k
2. P[X < 2]
3. P[X ≥ 3]
4. P[1 ≤ X < 4]
5. P(2)

If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of  `dy/dx `at t = `pi/4`

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the value of x for which Total cost is decreasing.

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the values of x for which Revenue is increasing.

A bill of Rs.7,500 was discounted for Rs. 7,290 at a bank on 28^th October 2006. If the rate of interest was 14% p.a., what is the legal due date ?

From the following table which relates to the number of animals of a certain
species at age x. complete the life table :

The probability distribution of X is as follows:

Find:

1. k
2. P[X < 2]
3. P[X ≥ 3]
4. P[1 ≤ X < 4]
5. P(2)

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

(p ∧ ~ q) → (~ p ∧ ~ q)

The false statement in the following is ______.

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

Which of the following is not a statement?

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

(p ∧ ~ q) → (~ p ∧ ~ q)