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Chapter 1-4

MTH001 Elementary Maths

1 / 47

Which logical connective is represented by the symbol “∨”?

 

2 / 47

What does a negation (~) do to the truth value of a proposition p?

 

3 / 47

What is the result of a conjunction (p ∧ q) in a truth table when both p and q are false?

 

4 / 47

What is the truth value of the compound statement (h ∧ w) ∧ (~s) if h, w, and s represent “Zia is healthy”, “Zia is wealthy”, and “Zia is wise”, respectively, and Zia is healthy, wealthy but not wise?

 

5 / 47

How is the disjunction of p and q symbolically represented, if p states “Islamabad is the capital of Pakistan” and q states “17 is divisible by 3”?

 

6 / 47

What symbol is used in logical operations to represent “and”?

 

7 / 47

Which of the following is NOT a proposition?

 

8 / 47

What is the main focus of Discrete Mathematics?

 

9 / 47

Using logical laws, what is the simplified form of the expression 𝑝∨[∼(∼𝑝∧𝑞)]p∨[∼(∼p∧q)]?

 

10 / 47

What is the symbolic representation for the statement “It is not hot but sunny”?

 

11 / 47

 

In the statement translation, if m = “Ali is good in Mathematics” and c = “Ali is a Computer Science student”, how would you represent “Ali is a Computer Science student or good in Maths” in symbolic form?

 

12 / 47

What outcome is specified in a truth table for the disjunction of p and q when both p and q are false?

 

13 / 47

 

Which of the following statements best describes the construction of a truth table for a compound statement?

 

14 / 47

What is the result of the truth table for the expression ~(p ∧ q)?

 

15 / 47

Which of the following statements correctly applies De Morgan’s Laws to the statement p ∨ q?

 

16 / 47

Which of the following expressions is tautology?

 

17 / 47

How would you write the negation of the inequality -1 < x ≤ 4 using De Morgan’s Laws?

 

18 / 47

Which of the following expressions accurately represents the logical equivalence of ∼(𝑝∧𝑞)∼(p∧q)?

 

19 / 47

Evaluate the logical equivalence for the expression (𝑝∧𝑞)∨𝑟(p∧q)∨r compared to 𝑝∧(𝑞∨𝑟)p∧(q∨r).

 

20 / 47

What is the truth value of the expression (𝑝∨𝑞)∧∼(𝑝∧𝑞)(p∨q)∧∼(p∧q) when 𝑝p is true and 𝑞q is false?

 

21 / 47

Using the double negative property, what does the expression ∼(∼𝑝)∼(∼p) simplify to?

 

22 / 47

What is the correct negation for the statement “The fan is slow or it is very hot” using De Morgan’s Laws?

 

23 / 47

Identify the statement that is always false, known as a contradiction.

 

24 / 47

Which logical equivalence is demonstrated by the expression ∼(∼𝑝∧𝑞)∧(𝑝∨𝑞)≡𝑝∼(∼p∧q)∧(p∨q)≡p?

 

25 / 47

What is the simplified English version of the logical expression (𝑝∧𝑞)∨(𝑝∧𝑟)(p∧q)∨(p∧r)?

 

26 / 47

What is the simplified English version of the logical expression (𝑝∧𝑞)∨(𝑝∧𝑟)(p∧q)∨(p∧r)?

 

27 / 47

What is the correct contrapositive of the statement “If you earn an A in Math, then I’ll buy you a computer”?

 

28 / 47

Using truth tables, which statement proves 𝑝→𝑞≡∼𝑞→∼𝑝p→q≡∼q→∼p?

 

29 / 47

What is the logical equivalence used to simplify the negation of the conditional statement 𝑝→𝑞p→q?

 

30 / 47

Given the statement “If it is raining, I have forgotten my umbrella or I have forgotten my hat,” how can it be simplified using logical equivalence?

 

31 / 47

Which of the following is the correct inverse of the conditional statement “If P is a square, then P is a rectangle”?

 

32 / 47

What is the correct translation of the symbolic proposition ∼𝑞→𝑟∼q→r?

 

33 / 47

Determine the truth value of the statement “If today is not Friday, then 2 + 3 ≠ 5.”

 

34 / 47

Which expression accurately represents the contrapositive of the statement “If my car is in the repair shop, then I cannot get to class”?

 

35 / 47

What is the truth value of the biconditional statement “1+1 = 3 if and only if the Earth is flat”?

 

36 / 47

Which logical operation best describes the expression (𝑝↔𝑞)≡(𝑝→𝑞)∧(𝑞→𝑝)(p↔q)≡(p→q)∧(q→p)?

 

37 / 47

Translate the following logical form into English using the concept of biconditional: 𝑝∧∼𝑟↔𝑞∨𝑟p∧∼r↔q∨r

 

38 / 47

Which statement shows that ∼(𝑝⊕𝑞)∼(p⊕q) and 𝑝↔𝑞p↔q are logically equivalent?

 

39 / 47

Rewrite the statement form ∼𝑝∨𝑞→𝑟∨∼𝑞∼p∨q→r∨∼q to a logically equivalent form using only ∼∼ and ∧∧.

 

40 / 47

Suppose that 𝑝→𝑞p→q is false. What is the truth value of 𝑝∨𝑞p∨q?

 

41 / 47

What is the truth value of the biconditional statement “Sky is blue if and only if 1 = 0”?

 

42 / 47

How can you express the logical form 𝑝∧∼𝑟↔𝑞∨𝑟p∧∼r↔q∨r using the concept of implication and equivalence?

 

43 / 47

Identify the correct logical equivalence for the biconditional operation expressed as 𝑝↔𝑞p↔q.

 

44 / 47

What is the contrapositive of the statement 𝑝→𝑞p→q?

 

45 / 47

Which of the following statements is always false, known as a contradiction?

 

46 / 47

Rewrite the statement form 𝑝∧∼𝑞→𝑟p∧∼q→r using only logical equivalences without the implication operator.

 

47 / 47

Determine the truth value of the biconditional 𝑝↔𝑞p↔q when both 𝑝p and 𝑞q are false.

 

Your score is

The average score is 46%

0%

Lecture 7 MCQs

MTH-001 Lecture 7

1 / 20

Which of the following sets are disjoint?

2 / 20

Which of the following is true about the difference of sets 𝐴 and 𝐵?

3 / 20

If 𝐴∪𝐵=𝑈 and 𝐴∩𝐵=𝜙, what can be said about sets 𝐴 and 𝐵?

4 / 20

If 𝐴∩𝐵=𝐴, which of the following must be true?

5 / 20

Which membership table corresponds to the intersection of sets 𝐴 and 𝐵?

6 / 20

If 𝑈={𝑎,𝑏,𝑐,𝑑,𝑒,𝑓,𝑔}, 𝐴={𝑎,𝑐,𝑒,𝑔}, and 𝐵={𝑑,𝑒,𝑓,𝑔}, what is 𝐴−𝐵?

7 / 20

If 𝐴∪𝐵=𝐴, what can be inferred about sets 𝐴 and 𝐵?

8 / 20

If 𝑈={𝑎,𝑏,𝑐,𝑑,𝑒,𝑓,𝑔}, 𝐴={𝑎,𝑐,𝑒,𝑔}, and 𝐵={𝑑,𝑒,𝑓,𝑔}, what is 𝐴∩𝐵?

9 / 20

Which of the following is true about the union of sets 𝐴 and 𝐵?

10 / 20

Which Venn diagram correctly represents 𝐴∪𝐵?

11 / 20

Which of the following is true about the complement of set 𝐴?

12 / 20

If 𝑈={𝑎,𝑏,𝑐,𝑑,𝑒,𝑓,𝑔} and 𝐴={𝑎,𝑐,𝑒,𝑔}, what is 𝐴𝑐?

13 / 20

If 𝐴∪𝐵=𝐴, what can be inferred about sets 𝐴 and 𝐵?

14 / 20

Which Venn diagram correctly represents 𝐴∩𝐵?

15 / 20

Given 𝑈={1,2,3,4,5,6,7,8,9,10} and 𝐴={2,3,5,7}, what is 𝐴∪𝐴𝑐?

16 / 20

Which of the following is true about the intersection of sets 𝐴 and 𝐵?

17 / 20

If 𝐴={1,2,3} and 𝐵={4,5,6}, what is 𝐴∪𝐵?

18 / 20

If 𝐴∩𝐵=𝐵, what can be inferred about sets 𝐴 and 𝐵?

19 / 20

Given 𝑈={1,2,3,4,5,6,7,8,9,10} and 𝐴={2,4,6,8,10}, what is 𝐴𝑐?

20 / 20

Which membership table corresponds to the union of sets 𝐴 and 𝐵?

Your score is

Lecture 8 MCQs

MTH-001 Lecture 8

1 / 23

Which of the following is not an ordered pair?

2 / 23

Find the values of x and y if (2x, x + y) = (6, 2).

3 / 23

What is the domain of the relation R = {(1, 2), (2, 3), (3, 4)}?

4 / 23

How many elements are there in the Cartesian product of two sets A and B, where |A| = 2 and |B| = 3?

5 / 23

What is the matrix representation of the relation R = {(1, y), (2, x), (2, y), (3, x)} from A = {1, 2, 3} to B = {x, y}?

6 / 23

The matrix representation of a relation R from A = {1, 2, 3} to B = {x, y} is given as 100111101​011​. What is the relation R?

7 / 23

The matrix representation of a relation R from A = {1, 2, 3} to B = {x, y} is given as 100111101011. What is the relation R?

8 / 23

The range of the relation R = {(1, 2), (2, 3), (3, 4)} is:

9 / 23

If A = {0, 1} and B = {1}, what is the total number of binary relations from A to B?

10 / 23

Which of the following is the Cartesian product A × A for A = {1, 2}?

11 / 23

The Cartesian product of sets A and B is denoted by:

12 / 23

Given sets A = {1, 2} and B = {a, b, c}, which of the following is a binary relation from A to B?

13 / 23

If A = {1, 2, 3} and R = {(1, 2), (2, 1), (2, 3), (3, 2)}, what type of relation is R?

14 / 23

Let R be a binary relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}. What is the range of R?

15 / 23

If 𝐴={1,2,3} and 𝐵={4,5,6}, what is 𝐴∪𝐵?

16 / 23

Which of the following is the universal relation on set A = {1, 2, 3}?

17 / 23

The range of the relation R = {(2, 4), (3, 6), (4, 8)} is:

18 / 23

Which of the following statements is true about Cartesian products?

19 / 23

Given the ordered pairs (a, b) and (c, d), when are they equal?

20 / 23

If A = {1, 2} and B = {a, b, c}, what is A × B?

21 / 23

Which of the following is an ordered triple?

22 / 23

Given sets A = {1, 2} and B = {a, b, c}, which of the following is a binary relation from A to B?

23 / 23

Let R be a binary relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}. What is the domain of R?

Your score is

Lecture 9 MCQs

MTH-001 Lecture-9

1 / 20

For the set 𝐴={1,2,3,4}, which relation is transitive?

2 / 20

Which of the following is a transitive relation on set 𝐴={1,2,3}?

3 / 20

Which statement is true for a symmetric relation on set 𝐴?

4 / 20

Which of the following statements is true about a transitive relation?

5 / 20

Which of the following is not a characteristic of a symmetric relation?

6 / 20

A relation 𝑅 on set 𝐴 is transitive if:

7 / 20

The matrix representation of a transitive relation on set 𝐴={1,2,3} must satisfy which condition?

8 / 20

For the set 𝐴={1,2,3}, the relation 𝑅={(1,2),(2,1),(2,3),(3,2),(3,3)} is:

9 / 20

A relation R on set A is symmetric if:

10 / 20

Which matrix representation corresponds to a reflexive relation on set A = {1, 2, 3}?

11 / 20

A directed graph representing a reflexive relation always includes:

12 / 20

Which of the following relations on set 𝐴={1,2,3,4} is neither reflexive, symmetric, nor transitive?

13 / 20

Which of the following relations on set A = {1, 2, 3} is reflexive?

14 / 20

If 𝑅 is a transitive relation on set 𝐴 and (𝑎,𝑏)∈𝑅 and (𝑏,𝑐)∈𝑅, which of the following must be true?

15 / 20

Which of the following relations on set A = {1, 2, 3} is symmetric?

16 / 20

If R is a relation on set A and R is not reflexive, then:

17 / 20

Which of the following is true for the relation 𝑅={(1,2),(2,1)} on set 𝐴={1,2,3}?

18 / 20

Which of the following relations on set 𝐴={1,2,3} is transitive?

19 / 20

For set A = {1, 2, 3}, which of the following relations is not reflexive?

20 / 20

For the set 𝐴={1,2,3}, the relation 𝑅={(1,2),(2,3),(1,3)} is:

Your score is

Lecture 10 MCQs

MTH-001 Lecture-10

1 / 20

A partial order relation is:

2 / 20

The matrix representation of an antisymmetric relation R on a set A has:

3 / 20

Which of the following is true for a symmetric relation?

4 / 20

A relation R on set A is reflexive if:

5 / 20

The subset relation ⊆ on the power set P(A) is:

6 / 20

Which of the following is an example of a partial order relation?

7 / 20

For the relation 𝑅 defined on set 𝐴 as 𝑅={(𝑎,𝑏)∣𝑎>𝑏}, 𝑅 is:

8 / 20

The matrix representation of an irreflexive relation has:

9 / 20

Which of the following is a property of an antisymmetric relation 𝑅 on set 𝐴?

10 / 20

A relation 𝑅 on set 𝐴 is irreflexive if:

11 / 20

Which of the following relations is neither reflexive nor irreflexive?

12 / 20

A relation 𝑅R on a set 𝐴A is symmetric if:

13 / 20

A relation 𝑅R on set 𝐴A is transitive if:

14 / 20

The relation 𝑅={(1,1),(2,2),(3,3)}R={(1,1),(2,2),(3,3)} on the set 𝐴={1,2,3}A={1,2,3} is:

15 / 20

Which of the following statements is true for an antisymmetric relation 𝑅R?

16 / 20

If a relation 𝑅R is both symmetric and irreflexive, which of the following is true?

17 / 20

A relation 𝑅R on a set 𝐴A is called irreflexive if for all 𝑎∈𝐴a∈A:

18 / 20

If 𝑅R and 𝑆S are transitive, is 𝑅∩𝑆R∩S transitive?

19 / 20

If 𝑅R and 𝑆S are symmetric, is 𝑅∩𝑆R∩S symmetric?

20 / 20

If 𝑅R and 𝑆S are reflexive, is 𝑅∩𝑆R∩S reflexive?

Your score is

Lecture 11 MCQs

MTH001-Lecture-11

1 / 20

If a binary operation * on a set A is defined as a * b = a + b for all a, b ∈ A, then this operation is:

2 / 20

Which of the following is a function from X = {2, 4, 5} to Y = {1, 2, 4, 6}?

3 / 20

For the function f(x) = x^2 + 1, what is the range?

4 / 20

The composition of two functions f and g, denoted by g ∘ f, is defined as:

5 / 20

In the vertical line test, if any vertical line intersects the graph of a relation more than once, then the relation:

6 / 20

Which of the following is not a binary operation?

7 / 20

If the set X = {a, b, c} and the set Y = {1, 2, 3}, which of the following represents a one-to-one function from X to Y?

8 / 20

If A = {1, 2} and B = {2, 3}, which of the following is the image of A under f where f: A → B is defined by f(x) = x + 1?

9 / 20

Which of the following is true about the inverse image of a function f: X → Y?

10 / 20

If f: X → Y, and f(x) = y, where X = {a, b, c} and Y = {1, 2, 3, 4}, what is the range of f if f(a) = 2, f(b) = 4, and f(c) = 2?

11 / 20

In an arrow diagram of a function, which of the following must be true?

12 / 20

The range of the function f(x) = x^2 + 3 for x in R is:

13 / 20

What is the domain of the function f(x) = sqrt(x)?

14 / 20

For the function f: X → Y, what is the co-domain?

15 / 20

Let A = {4, 5, 6} and B = {5, 6}. Which of the following relations R from A to B is a function?

16 / 20

Which of the following relations is not a function?

17 / 20

Which of the following sets is the domain of the function f: X → Y defined by f(x) = x^2 + 1, where X and Y are real numbers?

18 / 20

The graph of y = x^2 is a:

19 / 20

The inverse image of a set C under a function f: X → Y is defined as:

20 / 20

How many functions are there from a set with three elements to a set with four elements?

Your score is

Math Lesson 12

1 / 20

The function ℎ:𝑍→𝑍 defined by ℎ(𝑛)=2𝑛+1 is:

2 / 20

What is the image of the function 𝑔:𝑍→𝑍 defined by 𝑔(𝑛)=𝑛^2?

3 / 20

Which of the following functions is bijective?

4 / 20

If a function 𝑓:𝑋→𝑌 is both injective and surjective, it is called:

5 / 20

Which of the following is an example of a constant function?

6 / 20

Given the sequence an=2n+3, find the first 5 terms and determine if it is arithmetic or geometric.

7 / 20

How many one-to-one functions are there from a set with 3 elements to a set with 4 elements?

8 / 20

Is the function 𝑓:𝑅→𝑅 defined by 𝑓(𝑥)=2𝑥−5 surjective?

9 / 20

Given 𝑓:𝑋→𝑌 where 𝑓(𝑥)=3𝑥+2, which of the following statements is true?

10 / 20

Given the sequence an=3n-2, what are the first 5 terms?

11 / 20

Which of the following sequences converges to 0?

12 / 20

Which characteristic is true for a surjective function?

13 / 20

What is the domain of the function 𝑓(𝑥)=𝑥−1?

14 / 20

Calculate the 13th term of the Fibonacci sequence.

15 / 20

Which arrow diagram represents a one-to-one function?

16 / 20

Describe what is meant by the convergence of a sequence:

17 / 20

Explain the difference between an arithmetic and a geometric sequence:

18 / 20

Alex owns a vineyard that produces 500 barrels of wine annually. Due to a new irrigation system, the production increases by 5% each year. However, due to soil erosion, 30 barrels of wine are lost each year. Model the vineyard's production as a sequence and determine the sustainability of this plan.

19 / 20

Which of the following is true for an injective function?

20 / 20

If a function 𝑓:𝑋→𝑌 is not one-to-one, which of the following is true?

Your score is

Math Lesson 13

1 / 20

If 𝑓:𝑅→𝑅 is defined by 𝑓(𝑥)=𝑥^2+1, is it surjective?

2 / 20

Identify the geometric sequence from the following options:

3 / 20

Which term of the arithmetic sequence 4, 1, -2, …, is -77?

4 / 20

Which of the following is true for a bijective function?

5 / 20

Identify the arithmetic sequence from the following options:

6 / 20

If 𝐶𝑛=1+(−1)𝑛Cn​=1+(−1)n for all integers 𝑛≥0n≥0, what is the value of 𝐶3C3​?

7 / 20

What is the range of the function 𝑓(𝑥)=ln⁡(𝑥) where 𝑥>0?

8 / 20

Which of the following is a sequence?

9 / 20

Find the 8th term of the geometric sequence 4, 12, 36, 108, ….

10 / 20

What is the common difference of the arithmetic sequence 5, 9, 13, 17, …?

11 / 20

If 𝑓:𝑅→𝑅 is defined by 𝑓(𝑥)=∣𝑥∣, is it injective?

12 / 20

Which of the following is true for a constant function?

13 / 20

Which sequence is defined by the explicit formula 𝑎𝑛=(−1)𝑛+1𝑛an​=(−1)n+1n for all integers 𝑛≥0n≥0?

14 / 20

What is the common ratio of the geometric sequence 3, -3/2, 3/4, -3/8, …?

15 / 20

Find the 36th term of the arithmetic sequence whose 3rd term is 7 and 8th term is 17.

16 / 20

Which of the following functions is neither injective nor surjective?

17 / 20

Find the 20th term of the arithmetic sequence 3, 9, 15, 21, ….

18 / 20

Find the first four terms of the sequence defined by the formula 𝑏𝑗=1+2𝑗bj​=1+2j for all integers 𝑗≥0j≥0.

19 / 20

The function 𝑓:𝑅→𝑅 defined by 𝑓(𝑥)=𝑒^𝑥 is:

20 / 20

What does the notation 𝑎𝑛an​ represent in a sequence?

Your score is

Math Lesson 14

1 / 20

Write the series 1+2+3+...+𝑛 in summation notation.

2 / 20

Write the geometric sequence with positive terms whose second term is 9 and fourth term is 1.

3 / 20

Find the sum of the geometric series 4+12+36+108+... up to the 6th term.

4 / 20

Find the sum of the arithmetic series 1+3+5+7+...+19.

5 / 20

Compute the summation ∑𝑗=04𝑎𝑗 for 𝑎0=2, 𝑎1=3, 𝑎2=−2, 𝑎3=1, and 𝑎4=0.

6 / 20

Find the sum of the series 5+10+15+...+100.

7 / 20

If 𝑎0=2, 𝑎1=3, 𝑎2=−2, 𝑎3=1, 𝑎4=0, find ∑𝑗=13𝑎𝑗.

8 / 20

Find the sum of the first 20 natural numbers.

9 / 20

Which of the following represents a series?

10 / 20

What symbol is commonly used to denote summation?

11 / 20

What is the sum of the arithmetic series 7+14+21+28+...+70?

12 / 20

What is the 10th term of the geometric sequence 5, 10, 20, 40, …?

13 / 20

Which term of the geometric sequence is 1/8 if the first term is 4 and the common ratio is 1/2?

14 / 20

Convert the summation notation ∑𝑘=15(2𝑘+1) to its expanded form.

15 / 20

Which of the following is the correct expanded form of the summation ∑𝑘=1𝑛𝑘?

16 / 20

Determine the sum of the infinite geometric series 13+19+127+⋯.

17 / 20

Determine the sum of the arithmetic series 2+5+8+11+...+50.

18 / 20

Which of the following is a geometric series?

19 / 20

Convert the expanded form 1+2+3+⋯+10 into summation notation.

20 / 20

Find the sum of the first 10 terms of the geometric series 3,9,27,81,...

Your score is

Math Lesson 15

1 / 23

What is the square root of 4 in exponent notation?

2 / 23

Which of the following is NOT a type of operator in Excel?

3 / 23

Which of the following is NOT one of the five basic arithmetic operations?

4 / 23

In Excel, how would you start a formula?

5 / 23

Which of the following is a correct Excel formula for addition?

6 / 23

What is the result of 12×512×5?

7 / 23

Convert 20% to a fraction in Excel.

8 / 23

In Excel, which operator is used for multiplication?

9 / 23

What is the result of 4242?

10 / 23

In Excel, what symbol is used for exponentiation?

11 / 23

What is the result of the Excel formula =5^2?

12 / 23

Which of the following is a correct Excel formula for subtraction?

13 / 23

Which of the following steps is required to enter a value into a cell in Excel?

14 / 23

What is the result of 12+512+5?

15 / 23

What is the result of the Excel formula =5*4?

16 / 23

What does the cell reference B15 indicate in Excel?

17 / 23

Which of the following steps is NOT included in starting Microsoft Excel 2000 XP?

18 / 23

What is the result of the Excel formula =20%?

19 / 23

Which Excel formula correctly divides 240 by 15?

20 / 23

What is the reference for a range that starts at A1 and ends at D15 in Excel?

21 / 23

In Excel, which symbol is used for percent?

22 / 23

What is the result of 12−512−5?

23 / 23

In Excel, what is the reference for a cell in column B and row 15?

Your score is

Math Lesson 16

1 / 20

What is the value of the investment at the end of the second year if the initial investment is 100,000 Rs. and the rate of return is 4%?

2 / 20

What is the formula to calculate percentage change?

3 / 20

How would you enter the formula to calculate the percentage change in Excel if the initial value is in cell C4 and the final value is in cell C5?

4 / 20

How do you calculate the percentage change if the original weight of cotton is 3 kg and it increases to 15 kg?

5 / 20

In Excel, how would you write the formula to calculate the value of the investment at the end of the fourth year if the value at the end of the third year is in cell C52 and the rate of return is in cell C53?

6 / 20

In Excel, how would you write the formula to calculate the value of the investment at the end of the second year if the initial investment is in cell C46 and the rate of return is in cell C47?

7 / 20

In Excel, how would you calculate the percentage change for fruit shrinking from 15 kg to 3 kg?

8 / 20

If 15 kg of fresh fruit shrinks to 3 kg of dried fruit, what is the percentage change?

9 / 20

If an investment has rates of return of 4%, 8%, -10%, and 9% over four years, what will be the value of the investment at the end of the fourth year if the initial investment is 100,000 Rs.?

10 / 20

What is the value of the investment at the end of the fourth year if the value at the end of the third year is 101088 Rs. and the rate of return is 9%?

11 / 20

What is the percentage increase when the weight of cotton increases from 3 kg to 15 kg?

12 / 20

If an employee earns 5000 rupees per month and receives wage increases of 3%, 2%, and 1% in successive years, what will be the salary at the end of the third year?

13 / 20

If the value of the investment at the end of the second year is in cell C48, how would you write the formula to calculate the value at the end of the third year if the rate of return is in cell C49?

14 / 20

If the initial value is 1000 and the final value is 2500, what is the percentage increase?

15 / 20

What was the percentage change if Monday’s sales were Rs.1000 and grew to Rs.2500 on Tuesday?

16 / 20

In Excel, how would you write the formula to calculate the salary in the second year if the initial salary is in cell C35 and the percentage increase is in cell C36?

17 / 20

In Excel, how would you calculate the new weight if it increases from 3 kg to 15 kg?

18 / 20

What is the result of the Excel formula =D20 - D19 if D19 is 15 and D20 is 3?

19 / 20

What is the value of the investment at the end of the third year if the value at the end of the second year is 104000 Rs. and the rate of return is 4%?

20 / 20

What is the salary at the end of the second year if the initial salary is 5000 Rs. and the percentage increase is 3%?

Your score is

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MTH 001 Chapter 17

1 / 16

A sum of Rs. 2,000 is invested at a simple interest rate of 6% per annum. How much interest will it earn in 4 years?

2 / 16

If a partner withdraws Rs. 2,000 at the beginning of every month and the interest rate is 6% per annum, what is the total interest on drawings for the year?

3 / 16

Calculate the amount after 3 years on a principal of Rs. 2,000 at a rate of 5% compounded annually.

4 / 16

If Rs. 5,000 is borrowed at an annual simple interest rate of 9%, what is the total interest to be paid after 3 years?

5 / 16

What is the compound interest on Rs. 2,500 invested at 8% per annum for 2 years, compounded annually?

6 / 16

A store offers a 15% discount on a product with a list price of Rs. 3,000. What is the discount amount?

7 / 16

A product has a list price of Rs. 2,500. If a 10% discount is applied, what is the net cost price?

8 / 16

What is the compound interest on Rs. 1,000 invested at 10% per annum for 2 years, compounded annually?

9 / 16

If four bills of Rs. 500 each are due in 10, 20, 30, and 40 days respectively, what is the average due date?

10 / 16

Calculate the total amount to be paid after 2 years if the principal is Rs. 500 at an annual interest rate of 8%.

11 / 16

A store offers a seasonal discount of 25% on all items. If a customer buys an item with a list price of Rs. 3,200, how much do they pay after the discount?

12 / 16

A product originally priced at Rs. 5,000 is sold for Rs. 4,250 after a discount. What is the discount percentage?

13 / 16

Calculate the amount after 4 years on a principal of Rs. 1,000 at a rate of 6% compounded annually.

14 / 16

What is the simple interest on a principal amount of Rs. 1,200 at an annual interest rate of 5% for 3 years?

15 / 16

Three payments of Rs. 600, Rs. 800, and Rs. 1,200 are due in 20, 40, and 60 days, respectively. What is the average due date?

16 / 16

Calculate the interest on drawings for a partner who withdraws Rs. 3,000 at the middle of each quarter at an interest rate of 8% per annum.

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MTH 001 Chapter 18

1 / 15

If you invest $1,000 every year at an interest rate of 5% for 5 years, what will be the accumulated value?

2 / 15

What happens to the present value of an annuity if the interest rate increases?

3 / 15

What is the primary purpose of an annuity?

4 / 15

Which of the following is the correct accumulation factor formula?

5 / 15

What formula is used to calculate the present value of an annuity?

6 / 15

In the context of annuities, what is the discount factor?

7 / 15

What is an annuity?

8 / 15

What does algebraic operation on annuities typically involve?

9 / 15

If you want to receive $2,000 at the end of each half-year for 10 years with an interest rate of 11% compounded semi-annually, how much should you deposit now?

10 / 15

What is the relationship between the interest rate and the discount factor?

11 / 15

How is the discounted value of an annuity calculated?

12 / 15

How does compounding frequency affect the future value of an annuity?

13 / 15

What does the accumulation factor for n periods represent in the context of annuities?

14 / 15

What is the present value of an annuity?

15 / 15

What is the formula for calculating the accumulated value of an annuity?

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MTH 001 Chapter 19

1 / 15

Why are matrices important in business and industry?

2 / 15

What is the result of multiplying a matrix by a zero matrix?

3 / 15

Which property does the identity matrix share with the number 1 in multiplication?

4 / 15

How are matrices usually represented?

5 / 15

What does 'r' stand for in the notation r1c1 used in matrix multiplication?

6 / 15

What is a square matrix?

7 / 15

What are the elements of the identity matrix I3x3?

8 / 15

What is a matrix?

9 / 15

What is an identity matrix?

10 / 15

If matrix A is a 2x3 matrix and matrix B is a 3x2 matrix, what are the dimensions of the resulting matrix when A is multiplied by B?

11 / 15

What does the dimension or order of a matrix refer to?

12 / 15

How is the product of a matrix and the identity matrix similar to multiplying a real number by 1?

13 / 15

What is a column matrix?

14 / 15

Given a 2x2 identity matrix I and a 2x2 matrix A, what is the result of A×I?

15 / 15

What is a row matrix?

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MTH 001 Chapter 20

1 / 15

Which condition must be met for two matrices to be added or subtracted?

2 / 15

What happens if you try to multiply two matrices where the number of columns of the first matrix is not equal to the number of rows of the second matrix?

3 / 15

What is the inverse of a matrix?

4 / 15

What does it mean if two matrices are overproduced in a company setting?

5 / 15

Given a matrix A and a scalar c = 2, what is the result of cA if A = [1 2] [3 4]?

6 / 15

What is the condition for two 2x2 matrices to be inverses of each other?

7 / 15

How is the product of a row and a column obtained in matrix multiplication?

8 / 15

If A is a 2x3 matrix and B is a 3x2 matrix, what are the dimensions of AB?

9 / 15

What is the necessary condition for multiplying two matrices A and B?

10 / 15

What is the sum or difference of two matrices calculated by?

11 / 15

Given two matrices A = [1 2] [3 4] and B = [2 0] [1 2], what is AB?

12 / 15

What is the result of multiplying a matrix by a scalar?

13 / 15

What is the total revenue for a company if the sales matrix S = [20000 5500 10600] [18250 7000 11000] and the price matrix P = [1.60] [2.30] [3.10]?

14 / 15

What is the result of the product of matrix A = 3x3 and matrix B = 3x2?

15 / 15

How can matrices help in business applications?

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LESSON 21

1 / 20

In a punch recipe, the ratio of mango juice, apple juice, and orange juice is 3:2:1. If you have 2 liters of orange juice, how much punch can you make?

2 / 20

If the ratio of mango juice, apple juice, and orange juice in a punch recipe is 3:2:1.5 and you have 250 milliliters of orange juice, how much mango juice is needed?

3 / 20

The ratio of the ages of two brothers is 5:3. If the elder brother is 15 years old, how old is the younger brother?

4 / 20

A mixture contains milk and water in the ratio 5:3. If there is 10 liters of water, what is the total volume of the mixture?

5 / 20

The ratio of the lengths of two rectangles is 4:5. If the length of the first rectangle is 20 cm, what is the length of the second rectangle?

6 / 20

Find the unknown value in the proportion: 6/x = 9/27.

7 / 20

Find the unknown value in the proportion: 4x + 5/3 = x + 7/2.

8 / 20

In a mixture of 8 liters, the ratio of acid to water is 3:5. How much acid is in the mixture?

9 / 20

In a certain class, the ratio of passing grades to failing grades is 7:5. How many students out of 48 failed the course?

10 / 20

In a punch recipe, the ratio of mango juice, apple juice, and orange juice is 3:2:1. If you have 3 liters of mango juice, how much apple juice do you need?

11 / 20

In a punch recipe, the ratio of grape juice, lemon juice, and orange juice is 2:3:5. If you have 2 liters of grape juice, how much punch can you make?

12 / 20

If the ratio of red balls to blue balls in a bag is 7:3 and there are 21 red balls, how many blue balls are there?

13 / 20

If the ratio of the circumference of two circles is 2:3, what is the ratio of their radii?

14 / 20

If the ratio of sugar to water in a solution is 1:4, how much sugar is there in 5 liters of solution?

15 / 20

In a classroom, the ratio of boys to girls is 3:2. If there are 15 boys, how many girls are there?

16 / 20

Find the unknown value in the proportion: 5/x = 10/15.

17 / 20

A punch recipe has a ratio of mango juice, apple juice, and orange juice as 4:3:2. If you have 1 liter of orange juice, how much punch can you make?

18 / 20

If the ratio of cats to dogs in a pet shop is 3:4 and there are 24 dogs, how many cats are there?

19 / 20

Find the unknown value in the proportion: 4/x = 8/24.

20 / 20

A punch recipe has a ratio of mango juice, apple juice, and orange juice as 2:1:3. If you have 6 liters of apple juice, how much punch can you make?

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LESSON 22

1 / 20

What does the science of statistics enable us to do?

2 / 20

In its second meaning, statistics is defined as:

3 / 20

Which scale of measurement classifies observations into mutually exclusive qualitative categories?

4 / 20

A variable that varies with an individual or object is called:

5 / 20

Statistics deals with variability that:

6 / 20

Data obtained from scientific inquiry include:

7 / 20

Which scale of measurement has a true zero point and allows for meaningful ratios?

8 / 20

Which of the following describes the first meaning of the word "statistics"?

9 / 20

What does the term "statistic" refer to in the third sense?

10 / 20

Statistics is crucial for handling:

11 / 20

Which statement is true about the use of statistics in decision making?

12 / 20

A continuous variable is one that:

13 / 20

Which of the following is also known as Quantitative Analysis?

14 / 20

Which characteristic of statistics deals with aggregates rather than individual observations?

15 / 20

Which of the following is a quantitative variable?

16 / 20

Which scale of measurement includes ordering or ranking of measurements?

17 / 20

Statistics has applications in which of the following fields?

18 / 20

Which of the following is a function of statistics?

19 / 20

In statistics, what does an observation often mean?

20 / 20

What is a discrete variable?

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LESSON 23

1 / 20

If you have data for a company's turnover for five years, which chart is most suitable for visual representation?

2 / 20

If you want to represent the total number of male and female students in different schools, which type of chart would you use?

3 / 20

In a simple bar chart, what does the width of each bar represent?

4 / 20

What information does the height of a bar in a simple bar chart convey?

5 / 20

Which chart would best show the proportion of students from different schooling mediums in a college?

6 / 20

When should a component bar chart be used instead of a multiple bar chart?

7 / 20

When constructing a component bar chart, what is depicted by the different sections of each bar?

8 / 20

For which type of data would a histogram be an appropriate representation?

9 / 20

What does a multiple bar chart consist of?

10 / 20

How is a component bar chart different from a simple bar chart?

11 / 20

In which situation would you use a bivariate frequency table?

12 / 20

How do you determine the angle at which to cut a pie chart for a category?

13 / 20

What type of chart is useful for comparing two different kinds of information?

14 / 20

What type of data is best represented by a pie chart?

15 / 20

Which chart would be most appropriate to compare the import and export values of a country over multiple years?

16 / 20

In a component bar chart, what does the upper part of each bar represent?

17 / 20

In the context of data representation, what does "univariate" mean?

18 / 20

What is the first step in creating a frequency table for qualitative data?

19 / 20

How is the percentage calculated in a frequency table?

20 / 20

What does the term "frequency" refer to in a frequency table?

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LESSON 24

1 / 20

Given the following frequency distribution, calculate the mode:

Class Interval   Frequency
0-10   5
10-20   7
20-30   10
30-40   8
40-50   6

2 / 20

The median is defined as:

3 / 20

Which of the following is a desirable property of the mode?

4 / 20

What is the relationship between mean, median, and mode in a perfectly symmetrical distribution?

5 / 20

Calculate the arithmetic mean for the following data set: 5, 10, 15, 20, 25. Provide steps.

6 / 20

The arithmetic mean of a data set is calculated as:

7 / 20

What is the median of the following data set: 5, 8, 12, 15, 18?

8 / 20

In a frequency distribution, the arithmetic mean is represented as:

9 / 20

Why is the median sometimes preferred over the mean?

10 / 20

If a car travels distances of 30 miles at 60 mph and 30 miles at 40 mph, what is the harmonic mean of the speeds?

11 / 20

What is the mode in a data set?

12 / 20

When should the mode be used in a business context?

13 / 20

Using the formula for the mode, calculate the mode for the given class boundaries: l = 35.95, h = 3, fm = 14, f1 = 10, f2 = 6.

14 / 20

Which of the following is true about the arithmetic mean?

15 / 20

Calculate the arithmetic mean of the following data: 10, 20, 30, 40, 50.

16 / 20

Given the following data set: 2, 3, 3, 3, 5, 7, 7, 8, what is the mode?

17 / 20

In a frequency distribution, how is the median calculated?

18 / 20

Given a frequency distribution, how do you identify the median class?

19 / 20

In the example of EPA mileage ratings, which value represents the mode if the highest frequency is in the 36.0-38.9 class?

20 / 20

Which measure of central tendency is not affected by skewed distributions?

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LESSON 25

1 / 20

The median is preferred over the mean in cases where:

2 / 20

In an open-ended frequency distribution, which class is often problematic for computing the median?

3 / 20

What is the formula for calculating the median in a frequency distribution?

4 / 20

What is the cumulative frequency just before the median class in the EPA mileage rating example?

5 / 20

What is the second quartile also known as?

6 / 20

Which of the following is not a quantile?

7 / 20

The first quartile (Q1) divides the dataset into which proportion?

8 / 20

What is the lower class boundary of the median class in the EPA mileage rating example?

9 / 20

What is the value of n/2 in the EPA mileage rating example?

10 / 20

In a positively skewed distribution, which of the following is true?

11 / 20

How is the first decile (D1) calculated?

12 / 20

What does the empirical relation between the mean, median, and mode indicate in a unimodal distribution?

13 / 20

Why are percentile rankings useful?

14 / 20

If the mean of a dataset is 60 and the median is 50, which statement is likely true?

15 / 20

Which of the following is a true statement about percentiles?

16 / 20

Which class interval contains the median in the EPA mileage rating example?

17 / 20

The graphical representation used to locate quantiles is called:

18 / 20

In a perfectly symmetrical distribution, how do the mean, median, and mode relate to each other?

19 / 20

Which empirical relation between the mean, median, and mode is correct?

20 / 20

What is the third quartile (Q3) if the total number of observations is 40?

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LESSON 26

1 / 20

Which measure of central tendency is most affected by extreme values?

2 / 20

What is the geometric mean of the values 2, 4, 8, and 16?

3 / 20

What is the relationship between arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM)?

4 / 20

What is the harmonic mean of the values 10 and 40?

5 / 20

Which formula correctly represents the geometric mean (G)?

6 / 20

The geometric mean (G) of a set of n positive values X1, X2, …, Xn is defined as:

7 / 20

If a car travels 120 miles at speeds of 30 mph and 60 mph for equal distances, what is the harmonic mean of the speeds?

8 / 20

When dealing with average speeds, why is the harmonic mean preferred over the arithmetic mean?

9 / 20

Which formula correctly represents the harmonic mean (HM)?

10 / 20

What is the mid-range of a data set with the smallest value x0 and the largest value xm?

11 / 20

In which scenario is the geometric mean preferred over the arithmetic mean?

12 / 20

The harmonic mean (HM) of a set of n positive values X1, X2, …, Xn is defined as:

13 / 20

If the arithmetic mean of two numbers is 8 and the harmonic mean is 6, what is the geometric mean?

14 / 20

Which of the following measures of central tendency is also known as the mid-hinge?

15 / 20

What is the logarithm of the geometric mean (G) of values X1, X2, …, Xn?

16 / 20

How is the mid-quartile range calculated?

17 / 20

Given the values 3, 9, and 27, what is the geometric mean?

18 / 20

For which type of data is the geometric mean most suitable?

19 / 20

If the harmonic mean of two numbers is 12 and one of the numbers is 18, what is the other number?

20 / 20

When is the harmonic mean most appropriate to use?

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LESSON 27

1 / 20

What is the coefficient of quartile deviation if Q1 = 40 and Q3 = 80?

2 / 20

Which measure of dispersion is most appropriate for skewed data?

3 / 20

What is the coefficient of quartile deviation if Q1 = 25 and Q3 = 75?

4 / 20

How is the range of a dataset calculated?

5 / 20

Which of the following is NOT true about the range as a measure of dispersion?

6 / 20

Which of the following is an absolute measure of dispersion?

7 / 20

Which of the following statements about the quartile deviation is true?

8 / 20

Which measure of dispersion is defined as half the difference between the first and third quartiles?

9 / 20

What does the term "dispersion" refer to in statistics?

10 / 20

In which scenario is the quartile deviation particularly useful?

11 / 20

If the range of a dataset is 50 and the mid-range is 30, what are the smallest and largest values?

12 / 20

If Q1 = 20 and Q3 = 60, what is the quartile deviation?

13 / 20

Which measure of dispersion is calculated as the average of the absolute deviations from the mean?

14 / 20

What is the relative measure of range known as?

15 / 20

Which measure of dispersion takes into account every data point in a dataset?

16 / 20

What does a high coefficient of dispersion indicate about a dataset?

17 / 20

Which of the following is a relative measure of dispersion?

18 / 20

If the coefficient of dispersion for one dataset is 0.3 and for another dataset is 0.5, what can be inferred?

19 / 20

What is the formula for calculating the coefficient of dispersion?

20 / 20

What is the main disadvantage of using the range as a measure of dispersion?

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LESSON 28

1 / 20

What is the formula for the mean deviation of a frequency distribution?

2 / 20

What is the variance of a dataset if the standard deviation is 5?

3 / 20

What is the coefficient of variation?

4 / 20

How is the variance of a dataset calculated?

5 / 20

What is the variance of the number of fatalities in the given data set?

6 / 20

Which of the following measures of dispersion is also known as mean absolute deviation?

7 / 20

What is the mean deviation of the number of fatalities in motorway accidents for the given data set?

8 / 20

Which of the following statements about standard deviation is true?

9 / 20

For which purpose is the coefficient of variation particularly useful?

10 / 20

What does a high coefficient of variation indicate?

11 / 20

What is the coefficient of variation for a dataset with a mean of 50 and a standard deviation of 10?

12 / 20

If the mean of a dataset is 40 and the standard deviation is 8, what is the coefficient of variation?

13 / 20

Which measure of dispersion involves each and every data value in its computation?

14 / 20

Which measure of dispersion is represented in the same unit as the original data?

15 / 20

What does a high standard deviation indicate about a dataset?

16 / 20

What is the standard deviation of the number of fatalities in the given data set?

17 / 20

What is the shortcut formula for calculating the standard deviation in case of grouped data?

18 / 20

What is the primary advantage of using the standard deviation over the range?

19 / 20

Which formula is used for calculating the standard deviation in case of grouped data?

20 / 20

Which of the following is a measure of relative dispersion?

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LESSON 29

1 / 20

What is the sample space for tossing a coin twice?

2 / 20

How many permutations can be made from the word 'committee'?

3 / 20

Which of the following sets of events is exhaustive in a single toss of a fair coin?

4 / 20

What is the number of permutations of the letters in the word 'SCHOOL'?

5 / 20

What is the formula for the number of permutations of r objects selected from n distinct objects?

6 / 20

What is the probability of drawing an Ace or a King from a standard deck of 52 cards?

7 / 20

What is the complement of the event 'drawing a heart' from a deck of 52 cards?

8 / 20

Which of the following events are mutually exclusive?

9 / 20

What is the probability of drawing either a heart or a spade from a standard deck of 52 cards?

10 / 20

If two events cannot occur simultaneously, they are said to be:

11 / 20

If the outcome of a random experiment is unpredictable, the experiment is called:

12 / 20

What is the number of ways to select 3 officers (president, secretary, and treasurer) from a club of 4 members?

13 / 20

In a standard deck of 52 cards, what is the probability of drawing either a king or a diamond?

14 / 20

What is the sample space for rolling a six-sided die?

15 / 20

If events A and B are such that P(A) = 0.5 and P(B) = 0.3, and A and B are mutually exclusive, what is P(A or B)?

16 / 20

Which of the following best describes a simple event?

17 / 20

What is the number of combinations of 3 objects selected from 10 distinct objects?

18 / 20

How many ways can a committee of 4 be formed from a group of 10 people?

19 / 20

What is the number of ways to draw a hand of 5 cards from a well-shuffled ordinary deck of 52 cards?

20 / 20

What is the probability of drawing an Ace from a standard deck of 52 cards?

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LESSON 30

1 / 20

When a fair coin is tossed, what is the probability of getting either a head or a tail?

2 / 20

What does subjective probability rely on?

3 / 20

Which of the following sets of events is collectively exhaustive?

4 / 20

Which of the following probabilities is an example of subjective probability?

5 / 20

Which of the following is a characteristic of exhaustive events?

6 / 20

What is the classical definition of probability?

7 / 20

What does it mean for events to be equally likely?

8 / 20

Which of the following best defines mutually exclusive events?

9 / 20

Which definition of probability is based on the proportion of times an event occurs in a large number of trials?

10 / 20

If an event has a probability of 0.6, what is the probability of its complement?

11 / 20

What is an example of mutually exclusive events?

12 / 20

If a card is drawn from a deck of 52 cards, what is the probability that it is a red card?

13 / 20

What is the probability that a randomly drawn card from a standard deck of 52 cards is a 10?

14 / 20

Which of the following is a limitation of the classical definition of probability?

15 / 20

What is the probability of drawing a queen from a standard deck of 52 cards?

16 / 20

In a relative frequency approach, if an event occurs 30 times out of 100 trials, what is the probability of the event?

17 / 20

Which concept states that the probability of an event is the limit of its relative frequency as the number of trials approaches infinity?

18 / 20

If a fair coin is tossed three times, what is the probability of getting at least one head?

19 / 20

In the context of probability, what does the term 'sample space' refer to?

20 / 20

Which type of probability involves using prior knowledge and subjective judgment?

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LESSON 31

1 / 20

Which axiom of the axiomatic definition of probability ensures that the probability of a certain event is 1?

2 / 20

What does the axiomatic definition of probability require for any event Ei?

3 / 20

If P(A∩B)=0, what does this indicate about events A and B?

4 / 20

What is the relative frequency of male births if there are 359,881 male live births out of a total of 700,335 births?

5 / 20

Which of the following best describes the relative frequency definition of probability?

6 / 20

What does the relative frequency definition of probability rely on?

7 / 20

What is the probability of drawing either a king or a heart from a standard deck of 52 cards?

8 / 20

If A and B are any two events in a sample space S, what is P(A∪B) according to the addition law?

9 / 20

If events A and B are not mutually exclusive, how do you calculate P(A∪B)?

10 / 20

What is the probability of getting exactly one head in two flips of a fair coin?

11 / 20

In the context of probability, what does the symbol P(A∪B) represent?

12 / 20

What is the probability of getting heads in a fair coin toss experiment performed 10,000 times with 5067 heads?

13 / 20

Which of the following best describes empirical probability?

14 / 20

According to the axiomatic definition of probability, if P(A∪B)=1, what can be inferred about events A and B?

15 / 20

In the context of probability, what does the symbol P(A∩B) represent?

16 / 20

If a coin is tossed 4 times, what is the probability of getting at least one head?

17 / 20

If events A and B are mutually exclusive, what is P(A∪B) according to the axiomatic definition of probability?

18 / 20

Which of the following is true according to the law of complementation?

19 / 20

Which axiom of the axiomatic definition of probability states that the probability of the sample space S is 1?

20 / 20

What does the law of complementation state?

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LESSON 32

1 / 20

According to the axiomatic definition of probability, if P(A∪B)=1, what can be inferred about events A and B?

2 / 20

What is the relationship between joint probability, conditional probability, and marginal probability?

3 / 20

What is the probability that a randomly selected birth from the provided data is a female live birth?

4 / 20

What is the conditional probability of stillbirth given that the baby is male, based on the provided data?

5 / 20

In the example with the two bags of balls, what is the probability of transferring one white ball and one black ball from the first bag to the second bag?

6 / 20

After transferring two balls to the second bag, what is the probability of drawing a white ball from the second bag if two white balls were transferred?

7 / 20

What is the probability of event B occurring given that event A has already occurred if events A and B are independent?

8 / 20

In the context of probability, which of the following best describes the multiplication theorem for dependent events?

9 / 20

If two events A and B are dependent, which of the following is true?

10 / 20

What type of probability is represented by the total proportion of male births?

11 / 20

What does it mean if the probability of the intersection of two events A and B is zero, P(A∩B)=0?

12 / 20

What is the multiplication theorem of probability for independent events?

13 / 20

In the example with two bags of balls, what is the probability that two white balls are transferred from the first bag to the second bag?

14 / 20

Which term refers to the probability of a single event occurring, without consideration of any other events?

15 / 20

What are two events A and B called if the occurrence of one event does not affect the probability of the other?

16 / 20

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.5, and A and B are independent events, what is the probability of either event A or event B occurring?

17 / 20

If the probability of event A occurring is 0.5 and the probability of event B occurring is 0.6, and A and B are independent events, what is P(A∩B)?

18 / 20

Using the provided data, what is the marginal probability of a live birth?

19 / 20

What does the joint probability of events A and B represent?

20 / 20

What is the probability of getting exactly one head in two flips of a fair coin?

Your score is

0%

/75

PAST PAPERS FOR FINALS

1 / 75

In the context of probability, what does the symbol P(A∩B) represent?

2 / 75

What is the probability of getting an odd number on a fair die?

3 / 75

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the values.

4 / 75

The difference between the upper and the lower class boundaries of a class is known as:

5 / 75

What is the simple interest earned on Rs.3000 invested at 8% per annum for 6 months?

6 / 75

If two events A and B are dependent, which of the following is true?

7 / 75

The probability of a sure event is:

8 / 75

The probability of vowel letters from the word STATISTICS is:

9 / 75

Which of the following is a proposition?

10 / 75

Mode is the measure which always exists in any numerical data:

11 / 75

In the context of probability, which of the following best describes the multiplication theorem for dependent events?

12 / 75

Which term refers to the probability of a single event occurring, without consideration of any other events?

13 / 75

In a symmetric distribution:

14 / 75

Which of the following is a proposition?

15 / 75

The conjunction of two statements p and q is denoted by:

16 / 75

If R={(a,a),(b,b),(c,c)} is a relation on the set A={a,b,c}:

17 / 75

If P(A∩B)=0, what does this indicate about events A and B?

18 / 75

What does it mean if the probability of the intersection of two events A and B is zero, P(A∩B)=0?

19 / 75

According to De Morgan’s Law, ¬(p∧q)=

20 / 75

Using the provided data, what is the marginal probability of a live birth?

21 / 75

What is the probability of getting exactly one head in two flips of a fair coin?

22 / 75

If events A and B are not mutually exclusive, how do you calculate P(A∪B)?

23 / 75

Probability of a sure event is:

24 / 75

According to the axiomatic definition of probability, if P(A∪B)=1, what can be inferred about events A and B?

25 / 75

Smoking habits of the residents of an area are:

26 / 75

The probability of a sure event is:

27 / 75

Which one of the following is the negation of the statement "If Tanveer lives in Lahore then he does not live in Pakistan"?

28 / 75

If E and F are mutually exclusive events such that P(E) = 0.4 and P(F) = 0.5 then the probability of either event occurring is:

29 / 75

What type of probability is represented by the total proportion of male births?

30 / 75

The chart below is a ___ graph.

31 / 75

A conditional statement is logically equivalent to its:

32 / 75

In the example with the two bags of balls, what is the probability of transferring one white ball and one black ball from the first bag to the second bag?

33 / 75

If E and F are mutually exclusive events such that P(E) = 0.4 and P(F) = 0.5 then the probability of either event occurring is:

34 / 75

What are two events A and B called if the occurrence of one event does not affect the probability of the other?

35 / 75

According to the axiomatic definition of probability, if P(A∪B)=1, what can be inferred about events A and B?

36 / 75

The combination of 5 objects taken 2 at a time from a set of 5 distinct objects is:

37 / 75

A major disadvantage of the mean is that it is affected by:

38 / 75

If A = {1, 2, 3, 4} and B = {5, 6, 7}, then A∩B is:

39 / 75

What is the multiplication theorem of probability for independent events?

40 / 75

What is the relationship between joint probability, conditional probability, and marginal probability?

41 / 75

After transferring two balls to the second bag, what is the probability of drawing a white ball from the second bag if two white balls were transferred?

42 / 75

If A is a sure event, then P(A) =

43 / 75

In the example with two bags of balls, what is the probability that two white balls are transferred from the first bag to the second bag?

44 / 75

What does the joint probability of events A and B represent?

45 / 75

List price of a shirt is Rs 450. If the discount rate is 20%, calculate the discount amount of the shirt.

46 / 75

When 3 coins are tossed simultaneously, the probability of getting 3 heads is:

47 / 75

The conjunction of two statements p and q is denoted by:

48 / 75

What is the probability that a randomly selected birth from the provided data is a female live birth?

49 / 75

A 20 m long rope is cut to the length of 15m. What is the percentage decrease?

50 / 75

The component bar chart should be used when we have information regarding totals and their components:

51 / 75

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.5, and A and B are independent events, what is the probability of either event A or event B occurring?

52 / 75

What is the probability of getting exactly one head in two flips of a fair coin?

53 / 75

The probability of getting a tail when a coin is tossed is:

54 / 75

What is the probability that a randomly selected birth from the provided data is a female live birth?

55 / 75

If the probability of event A occurring is 0.5 and the probability of event B occurring is 0.6, and A and B are independent events, what is P(A∩B)?

56 / 75

Standard deviation is always measured from:

57 / 75

When two coins are tossed simultaneously, the probability of at least one head is:

58 / 75

What does it mean if the probability of the intersection of two events A and B is zero, P(A∩B)=0?

59 / 75

Which one of the following sets is finite?

60 / 75

The sample space of rolling two dice consists of how many possible outcomes?

61 / 75

Third Quartile = Q3 =

62 / 75

Which measure of central tendency is defined as the value that occurs most frequently in a data set?

63 / 75

If two events A and B are independent, then the probability of both events occurring together is given by:

64 / 75

Probability of a sure event is:

65 / 75

The order of elements in a set does not matter:

66 / 75

A conditional statement is logically equivalent to its:

67 / 75

What is the probability of getting exactly one head in two flips of a fair coin?

68 / 75

Which axiom of the axiomatic definition of probability ensures that the probability of a certain event is 1?

69 / 75

What is the probability of event B occurring given that event A has already occurred if events A and B are independent?

70 / 75

What is the conditional probability of stillbirth given that the baby is male, based on the provided data?

71 / 75

When relative changes in some variable quantity are to be averaged, which mean is the appropriate average to use?

72 / 75

If A is a sure event, then P(A) =

73 / 75

According to the axiomatic definition of probability, if P(A∪B)=1, what can be inferred about events A and B?

74 / 75

The number of permutations of 4 objects taken 3 at a time from a set of 5 distinct objects is:

75 / 75

The component bar chart should be used when we have information regarding totals and their components:

Your score is

0%

/50

MATH-001 EXAM 1

1 / 50

How is earnings per share (EPS) calculated?

2 / 50

How is the percent increase in price calculated?

3 / 50

What is a polynomial?

4 / 50

What is the multiplicative inverse of a real number x?

5 / 50

How is multiplication of polynomials typically represented?

6 / 50

In a punch recipe, the ratio of mango juice, apple juice, and orange juice is 3:2:1. If you have 1.5 liters of orange juice, how much punch can you make?

7 / 50

What is the result of multiplying a matrix by a scalar?

8 / 50

What is the formula for calculating the accumulation factor?

9 / 50

What does a 50% dividend mean if the face value of a share is Rs 10?

10 / 50

What is the first step in solving a linear equation?

11 / 50

How is the net price calculated after a trade discount?

12 / 50

How do you calculate the compound interest earned on Rs. 750 at 12% per annum for 8 years?

13 / 50

How do you calculate the simple interest for a principal of Rs. 500 at a rate of 11% for 4 years?

14 / 50

How do you add two matrices?

15 / 50

How do you simplify (48a – 32ab)/8a?

16 / 50

How is simple interest calculated?

17 / 50

What does the accumulation factor represent in the context of an annuity?

18 / 50

What is the requirement for multiplying two matrices?

19 / 50

What is the function of a middleman in merchandising?

20 / 50

What is the definition of an algebraic expression?

21 / 50

What is an identity matrix?

22 / 50

What is the discounted value or present worth of an annuity?

23 / 50

How many students failed if the ratio of passing to failing grades is 7:5 in a class of 36 students?

24 / 50

What is the compound interest formula?

25 / 50

What is the purpose of using matrices in business?

26 / 50

What is a discount factor?

27 / 50

How is the stock yield typically represented?

28 / 50

What is the meaning of 'face value' of a stock?

29 / 50

What is the term for a series of fixed payments made at regular intervals?

30 / 50

What is the formula to calculate the present value of an annuity?

31 / 50

What is a proportion in mathematics?

32 / 50

What is the purpose of a trade discount?

33 / 50

What is the formula for the price-earnings ratio?

34 / 50

If a bank increases its interest rate from 7% to 9%, what is the percent increase in the interest rate?

35 / 50

What is the face value of a share of stock?

36 / 50

What does the discounted value of an annuity represent?

37 / 50

How do you calculate return on investment (ROI)?

38 / 50

What is the definition of a stock?

39 / 50

What is the primary purpose of calculating return on investment (ROI)?

40 / 50

How do you calculate the future value of an annuity?

41 / 50

How many liters of mango juice are required if the punch ratio of mango juice, apple juice, and orange juice is 3:2:1.5 and you have 500 liters of orange juice?

42 / 50

What are current assets?

43 / 50

If a bank reduces its interest rate from 9% to 7%, what is the percent decrease in the interest rate?

44 / 50

What is the term for stock currently held by investors?

45 / 50

What is a middleman in the context of merchandising?

46 / 50

What is a dividend?

47 / 50

What does the coefficient of dispersion measure?

48 / 50

What is the formula to calculate the future value of an annuity?

49 / 50

What is an annuity?

50 / 50

How do you calculate the net price after a trade discount?

Your score is

0%

/50

MATH-001 EXAM 1

1 / 50

What does a 50% dividend mean if the face value of a share is Rs 10?

2 / 50

What is the term for stock currently held by investors?

3 / 50

What is a polynomial?

4 / 50

What is the result of multiplying a matrix by a scalar?

5 / 50

What is the definition of a stock?

6 / 50

What is the compound interest formula?

7 / 50

What is the multiplicative inverse of a real number x?

8 / 50

How do you calculate the future value of an annuity?

9 / 50

What is a proportion in mathematics?

10 / 50

What is the primary purpose of calculating return on investment (ROI)?

11 / 50

How is simple interest calculated?

12 / 50

What is the formula for the price-earnings ratio?

13 / 50

How is the net price calculated after a trade discount?

14 / 50

What does the coefficient of dispersion measure?

15 / 50

How do you add two matrices?

16 / 50

What is the face value of a share of stock?

17 / 50

What is the function of a middleman in merchandising?

18 / 50

How is earnings per share (EPS) calculated?

19 / 50

What does the discounted value of an annuity represent?

20 / 50

What is the term for a series of fixed payments made at regular intervals?

21 / 50

What is the purpose of a trade discount?

22 / 50

What is an annuity?

23 / 50

How is multiplication of polynomials typically represented?

24 / 50

How is the percent increase in price calculated?

25 / 50

What is the requirement for multiplying two matrices?

26 / 50

How do you simplify (48a – 32ab)/8a?

27 / 50

What is the formula to calculate the present value of an annuity?

28 / 50

How many students failed if the ratio of passing to failing grades is 7:5 in a class of 36 students?

29 / 50

What is the first step in solving a linear equation?

30 / 50

If a bank reduces its interest rate from 9% to 7%, what is the percent decrease in the interest rate?

31 / 50

In a punch recipe, the ratio of mango juice, apple juice, and orange juice is 3:2:1. If you have 1.5 liters of orange juice, how much punch can you make?

32 / 50

What is the formula to calculate the future value of an annuity?

33 / 50

What is the discounted value or present worth of an annuity?

34 / 50

How do you calculate return on investment (ROI)?

35 / 50

What is a middleman in the context of merchandising?

36 / 50

How do you calculate the simple interest for a principal of Rs. 500 at a rate of 11% for 4 years?

37 / 50

What is a dividend?

38 / 50

How do you calculate the compound interest earned on Rs. 750 at 12% per annum for 8 years?

39 / 50

What is the definition of an algebraic expression?

40 / 50

If a bank increases its interest rate from 7% to 9%, what is the percent increase in the interest rate?

41 / 50

What does the accumulation factor represent in the context of an annuity?

42 / 50

How is the stock yield typically represented?

43 / 50

What is the meaning of 'face value' of a stock?

44 / 50

What is a discount factor?

45 / 50

What is the purpose of using matrices in business?

46 / 50

What is the formula for calculating the accumulation factor?

47 / 50

What are current assets?

48 / 50

How do you calculate the net price after a trade discount?

49 / 50

What is an identity matrix?

50 / 50

How many liters of mango juice are required if the punch ratio of mango juice, apple juice, and orange juice is 3:2:1.5 and you have 500 liters of orange juice?

Your score is

0%

Mid Term Past Papers

MTH-PAST PAPERS

1 / 77

Percentage change =

2 / 77

If a relation is given by R = {(0, 1), (1, 2), (3, 4)}, then the range of R is:
A) {0, 1, 3}
B) {1, 2, 3}
C) {2, 3, 4}
D) {1, 2, 4}

3 / 77

If A = {1, 2, 3, 4} then A is proper subset of A.

4 / 77

Consider the Venn diagram below, where the shaded area represents a particular set operation. Which of the following options correctly identifies the shaded region?

5 / 77

Let p be the statement ‘you study’ and q be the statement ‘you pass the exams’. Express the following proposition as an English sentence: ( p → q )
A) If you study, then you pass the exams.
B) If you do not study, then you pass the exams.
C) If you study, then you do not pass the exams.
D) If you do not study, then you do not pass the exams.

6 / 77

From the truth table, for ( p leftrightarrow q ) to be true, both ( p ) and ( q ) must have the same truth values.

7 / 77

Let A= {a, b, c} and R is a relation defined on A such that R = {(a, b), (b, a), (a, a)}
Is R reflexive and symmetric? Justify your answer.

8 / 77

Union of any two sets satisfies commutative law.

9 / 77

The nth term of a Geometric Progression (G.P.) is:

10 / 77

Let f : → be defined by f (x) = 2x - 3
Show that f is an onto function.

11 / 77

Initial value = 1200
Final value = 1500
increase= 300
% Change =

12 / 77

For the two sets A and B, A ∩ B is a _______ of A:
A) Super set
B) Subset
C) Complement set

13 / 77

The percentage change is calculated as:

14 / 77

Let a1,a2,a3,…,an be an arithmetic sequence, then sum of the sequence Sn = n(a +a ) / 2

15 / 77

In Sets ordered pairs order of elements doesn’t matters.

16 / 77

If R and S are reflexive, then R ∩ S is:
A) Reflexive
B) Transitive
C) Symmetric

17 / 77

Which of them is a statement?

18 / 77

If ( p ) is a proposition, its negation is denoted by:

19 / 77

Let a1,a2,a3,…,an be an arithmetic sequence, then sum of the sequence Sn =

20 / 77

What percent of 36 is 5?

21 / 77

Let A = {1, 2, 3} and B = {{1,2}, 3} then A  B

22 / 77

For sets A and B, if A ⊂ B , then

23 / 77

If p is a proposition then its negation is denoted by

24 / 77

Given two sets ( A ) and ( B ), if ( A subseteq B ), then which of the following statements is true?

25 / 77

If ( A = {1, 2, 3, 4} ), then is ( A ) a proper subset of itself?

26 / 77

From the truth table, for p q to be true, if both p and q must have the same truth values.

27 / 77

Find the sum of first five terms of following geometric series:
1 + 4 + 16 +

28 / 77

The nth term of an A. P (Arithmetic Progression) is:

29 / 77

The above relation shows _______________.

30 / 77

The text concatenation operator is used to

31 / 77

{x}⊂ {x}

32 / 77

Is the singleton set ( {x} ) a subset of itself?

33 / 77

Which relation defines a function from X = {2, 4, 5} to Y = {1, 2, 4, 6}?
R1 = {(2, 4), (4, 1)}
R2 = {(2, 4), (4, 1), (4, 2), (5, 6)}
R3 = {(2, 4), (4, 1), (5, 6)}

34 / 77

The nth term of an Arithmetic Progression (A.P.) is:

35 / 77

The nth term of an A. P (Arithmetic Progression) is:

36 / 77

Given an initial value of 1200 and a final value of 1500, which represents an increase of 300, what is the percentage change?

37 / 77

The above relation shows _______________.

38 / 77

A relation R on the set of Natural numbers N is defined as:
For all , aRb iff is odd. Is R reflexive?

39 / 77

What is the negation of the statement ‘Today is Friday’?
A) Today is Saturday.
B) Today is not Friday.
C) Today is Thursday.

40 / 77

If no element is common in two sets A and B, then the sets are called:
A) Exhaustive sets
B) Dissimilar sets
C) Disjoint sets

41 / 77

If A and B are two sets such that A ∩ B = A ∪ B, then:
A) A and B are disjoint sets
B) A and B are super sets
C) A and B are equal sets
D) Order of elements in a set does not matter

42 / 77

Let A = {1, 2, 3, 4} and B = {5, 6, 7}, then ( A ∩ B ) =
A) {1, 2, 3, 4}
B) {5}
C) {1, 2, 3, 4, 5, 6, 7}

43 / 77

A ∩ B is a ---------of A.

44 / 77

Television sale $300.The sale price 20% less than regular price. What is regular price?

45 / 77

Let f : R R  be defined by f (x) = 4x +2 Prove that f is an onto function.

46 / 77

The conjunction of two statements ( p ) and ( q ) is denoted by:

47 / 77

The final statement is called…….

48 / 77

According to De Morgan’s law:
~ (p ∧ q) ≡
A) ~ p ∧ q
B) ~ p ∧ ~ q
C) ~ p ∨ ~ q
D) p ∧ ~ q

49 / 77

The proposition ( p ↔ q ) is called:
A) Negation
B) Conjunction
C) Disjunction
D) Biconditional

50 / 77

An argument is invalid if the conclusion is false when all the premises are:
A) 2
B) False
C) True
D) 3

51 / 77

In ordered pairs order of elements matters.

52 / 77

An argument is valid if the conclusion is true when all the premises are:
A) True
B) Not given
C) False

53 / 77

Initial value = 120
Final value = 200
Increase = 80
% Change =

54 / 77

Let A= {0,1,2,3,} and R is a relation defined on A such that R = { (0,0)) (0, 1), (1, 1) ( 1,0) (2,2) (0,3) (3,3) (3,0) } Is R reflexive and symmetric but not Transitive.

55 / 77

In ordered pairs, does the order of elements matter?

56 / 77

The sets {1, b} and {b, 1} are equal.
A) True
B) False

57 / 77

Name the quadrant in which these points is located.
1. (5, 2)
2. (-3, -1)
3. (-2, 3)
4. (6, 0)
5. (0, -2)
6. (4, -3)

58 / 77

If ( P ) and ( Q ) are propositions with ( P ) being true and ( Q ) being false, what is the truth value of ( P rightarrow Q )?

59 / 77

If A is a subset of the universal set U, then:
A) f
B) A
C) U

60 / 77

An argument is invalid if the conclusion is false when all the premises are:
A) False
B) True

61 / 77

Which of the relations defines a function from X = {2, 4, 5} to Y = {1, 2, 4, 6}?
A) R1 = {(2, 4), (4, 1)}
B) R2 = {(2, 4), (4, 1), (4, 2), (5, 6)}
C) R3 = {(2, 4), (4, 1), (5, 6)}
D) R2 and R3

62 / 77

?  {x}

63 / 77

Consider the following diagram
Then the shaded region is

64 / 77

Find the sum of first five terms of following geometric series:
1 + 4 + 16 + ……………

65 / 77

Let ( A = {1, 2, 3} ) and ( B = {{1,2}, 3} ). Is ( A cup B = {1, 2, 3} ) true?

66 / 77

The intersection of sets ( A ) and ( B ), denoted by ( A cap B ), is a _______ of ( A ).

67 / 77

If P and Q are proposition, P is true and Q is false, then P → Q is

68 / 77

Let A = {1, 2, 3} and B = {{1,2}, 3} then A  B = {1, 2, 3}

69 / 77

The nth term of an G. P (Geometric Progression) is:

70 / 77

Let T be a relation from set A to B, if T is symmetric then its inverse will be:
A) Symmetric
B) Antisymmetric
C) Transitive

71 / 77

If the initial value is 120 and the final value is 200, representing an increase of 80, what is the percentage change?

72 / 77

The above relation shows _______________.

73 / 77

How many functions are there from set A to set B?
A) M.n
B) n.m

74 / 77

Conjunction of two statements p and q is denoted by

75 / 77

If A = {1, 2, 3, 4} then A is proper subset of A.

76 / 77

Let ( a_1, a_2, a_3, ldots, a_n ) be an arithmetic sequence. Is the sum of the sequence ( S_n = frac{n}{2}(a_1 + a_n) ) true?

77 / 77

?% of 360=129.6

Your score is

0%

Quiz 1 - SPRING 2024

MTH 001 Quiz

1 / 18

(Amna is good in English grammar) denoted by S and (Amna is good in philosophy.) denoted by N. The statement that (Amna is not good in English neither in philosophy) can be translated in logical expression.

 

2 / 18

If A is a subset of B then A intersection B = ___.

 

3 / 18

Consider that q and p are statements such that q→p is false. Then the truth value of q→∼p is __________.

 

4 / 18

If there are two variables p and q in a logical statement then the truth table will have _________ rows.

 

5 / 18

The set of English alphabets is _____________.

 

6 / 18

Sets Z and N are infinite

 

7 / 18

Let p and q be two statements, then the conjunction of p and q is denoted as ____________.

 

8 / 18

Consider that q and p are statements such that q→p is false. Then the truth value of q∨p is ….

 

9 / 18

A tautology is a statement form that is ____________ regardless of the truth values of the statement variables.

 

10 / 18

How is a set defined in mathematics?

 

11 / 18

The negation of (x < 3) is:

12 / 18

An argument is invalid if all the premises are true but the …. Is false

 

13 / 18

How we can translate P or Q and not p and q in logical expression

 

14 / 18

The Set of Natural Numbers starts from:

 

15 / 18

The set of rational numbers between 5 and 9 is __________.

 

16 / 18

The truth value of ~p∧q when p is true and q is false is:

 

17 / 18

Translate the statement “If you have fever, then you will miss the final match” in logical expression.

 

18 / 18

An Argument is valid if the conclusion is true when all the premises are false.

 

Your score is

The average score is 53%

0%

Quiz 02

MTH 001 Quiz 2

1 / 20

Every relation is a function.

2 / 20

If f is a function from A={a,b,c} to B={1,2,3} such that f={(a,3),(b,1),(c,2)}, then f is called _____.

3 / 20

Given that AxA = { (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}, which of the given relations is a function?

4 / 20

How many functions are there from a set with two elements to a set with three elements?

5 / 20

Let N = {-5, -4, 0, 6, 8} and O = {-4, 0, 8, 9}. Then N intersection O = _____.

6 / 20

The graph of y=x2 is a straight line.

7 / 20

A function f:X→Y defined by f(x)=a, where a is a constant and x belongs to X, will be one-to-one if and only if ____.

8 / 20

The graph of y=x2 is a straight line.

9 / 20

Let A = {1,2,3}. Which of the following is a symmetric relation on A?

10 / 20

Let R be a relation from A to B. The set of all first elements of the ordered pairs which belong to R is called ____ of R.

11 / 20

Which of the following relations on the set A={1,2,3,4} is transitive?

12 / 20

A relation R on a set A is transitive if and only if:

13 / 20

In the directed graph of a symmetric relation, if there is an arrow going from one point to a second, there must be:

14 / 20

Which of the following relations on the set A={1,2,3,4} is symmetric?

15 / 20

A relation R on a set A is symmetric if and only if:

16 / 20

Consider the relation R on A={1,2,3} represented by the matrix:
[1 1 0
0 1 1
1 0 0]

17 / 20

Which of the following is a directed graph of a reflexive relation?

18 / 20

A relation R on a set A is not reflexive if and only if:

19 / 20

Which of the following relations on the set A={1,2,3,4} is reflexive?

20 / 20

A relation R on a set A is reflexive if and only if:

Your score is

MATH QUIZ

1 / 10

Every relation is a function.

2 / 10

The graph of y=x^2 is a straight line.

3 / 10

Let A = {1,2,3}. Which of the following is a symmetric relation on A?

4 / 10

How many functions are there from a set with two elements to a set with three elements?

5 / 10

Let N = {-5, -4, 0, 6, 8} and O = {-4, 0, 8, 9}. Then N intersection O = _______________.

6 / 10

A function f:X→Y defined by f(x)=a, where a is a constant and x belongs to X, will be one-to-one if and only if ____________.

7 / 10

If f is a function from A={a,b,c} to B={1,2,3} such that f={(a,3),(b,1),(c,2)}, then f is called _______________.

8 / 10

Given that AxA = { (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}, which of the given relations is a function?

9 / 10

Let R be a relation from A to B. The set of all first elements of the ordered pairs which belong to R is called ____________ of R.

10 / 10

The graph of y=x^2 is a straight line.

Your score is