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Important Questions for HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Maharashtra State Board - Mathematics and Statistics

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The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class.
Also prepare marginal distributions :

(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )

Appears in 2 question papers
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Probability Distribution > Distribution Function of a Continuous Random Variable

If a random variable X follows Poisson distribution sucli that P(X = 1) = P(X = 2), find:
(a) the mean and
(b) P(X = 0). [Given: e-2 = 0.1353)

Appears in 2 question papers
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Probability Distribution > Distribution Function of a Continuous Random Variable

The negation of p ∧ (q → r) is ______________.

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

Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p → q) ∧ q] → p

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

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”

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

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "

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

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)

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

Express the truth of each of the following statements by Venn diagram:

(a) Some hardworking students are obedient.

(b) No circles are polygons.

(c) All teachers are scholars and scholars are teachers. 

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Venn Diagrams

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Mathematical Logic > Logical Connectives

Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)

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

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`

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

Write the dual of the following statements: (p ∨ q) ∧ T

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

If A = {2, 3, 4, 5, 6}, then which of the following is not true?

(A) ∃ x ∈ A such that x + 3 = 8

(B) ∃ x ∈ A such that x + 2 < 5

(C) ∃ x ∈ A such that x + 2 < 9

(D) ∀ x ∈ A such that x + 6 ≥ 9

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

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.

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

Draw a Venn diagram for the truth of the following statement : 

All rational number are real numbers. 

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Venn Diagrams

Draw Venn diagram for the truth of the following statements : 

Some rectangles are squares. 

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Venn Diagrams

Write the truth values of the following statements:
(1) 2 is a rational number and`sqrt2` is an irrational number. .
(2) 2 + 3 = 5 or `sqrt 2 +sqrt3 = sqrt5`

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Mathematical Logic > Statements - Introduction in Logic

 Find the symbolic form of the given switching circuit. Construct its switching table and interpret yout result. diagram 

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Mathematical Logic > Statements - Introduction in Logic

Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 

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

Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )

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