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

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

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

Appears in 3 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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

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

Appears in 3 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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 = ?

Appears in 3 question papers
Chapter: [0.015] Integration
Concept: Methods of Integration: Integration Using Partial Fractions

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)`

Appears in 3 question papers
Chapter: [0.018000000000000002] Differential Equation and Applications
Concept: Application of Differential Equations

The difference between face value and present worth is called ______.

Appears in 3 question papers
Chapter: [0.021] Commission, Brokerage and Discount
Concept: Discount

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Appears in 2 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

The false statement in the following is ______.

Appears in 2 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Appears in 2 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

The false statement in the following is ______.

Appears in 2 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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

Appears in 2 question papers
Chapter: [0.018000000000000002] Differential Equation and Applications
Concept: Differential Equations

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.

Appears in 2 question papers
Chapter: [0.023] Linear Regression
Concept: Properties of Regression Coefficients

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

Year 1962 1963 1964 1965 1966 1967 1968 1969
Production
(million barrels)
0 0 1 1 2 3 4 5
Year 1970 1971 1972 1973 1974 1975 1976  
Production
(million barrels)
6 7 8 9 8 9 10  
  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.
Appears in 2 question papers
Chapter: [0.024] Time Series
Concept: Measurement of Secular Trend

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:

Nutrient\Fodder Fodder 1 Fodder2
Nutrient A 2 1
Nutrient B 2 3
Nutrient C 1 1

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.

Appears in 2 question papers
Chapter: [0.026000000000000002] Linear Programming
Concept: Linear Programming Problem (L.P.P.)

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.

Type 1 2 3 4 5
Machine A 16 20 12 14 22
Machine B 10 12 4 6 8
Machine C 8 18 16 12 10

Solve the problem for minimizing the total elapsed time.

Appears in 2 question papers
Chapter: [0.027000000000000003] Assignment Problem and Sequencing
Concept: Types of Sequencing Problem

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements

Examine whether the statement pattern

[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Complete the truth table.

p q r q → r r → p (q → r) ˅ (r → p)
T T T T `square` T
T T F F `square` `square`
T F T T `square` T
T F F T `square` `square`
F T T `square` F T
F T F `square` T `square`
F F T `square` F T
F F F `square` T `square`

The given statement pattern is a `square`

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Algebra of Statements

Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements
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