FIA Test Preparation Lecture #10

Set Theory, Logic, Combinations, Series, Matrices, Differentiation, Integration & Conic Sections

Top MCQs with Proper Lecture Notes

1. Set Theory

A set is a collection of well-defined objects.

Example:
A = {1, 2, 3, 4}

Important Symbols

MCQs: Set Theory

1. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B is:

A) {3}
B) {1, 2, 3, 4, 5}
C) {1, 2}
D) {4, 5}

Answer: B) {1, 2, 3, 4, 5}

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

A) {1, 2}
B) {4, 5}
C) {3}
D) {1, 2, 3, 4, 5}

Answer: C) {3}

3. The empty set is represented by:

A) U
B) ∅
C) ∈
D) ∩

Answer: B) ∅

4. If A = {2, 4, 6}, then 4 ____ A.

A) ∈
B) ∉
C) ∩
D) ∪

Answer: A) ∈

2. Propositional Logic

A proposition is a statement that is either true or false.

Example:
Pakistan is in Asia.
This is a proposition because it is true.

Important Logical Symbols

MCQs: Propositional Logic

5. A proposition is a statement that is:

A) Only question
B) Either true or false
C) Always false
D) Always command

Answer: B) Either true or false

6. Symbol for “and” is:

A) ∨
B) ∧
C) →
D) ↔

Answer: B) ∧

7. Symbol for “or” is:

A) ∨
B) ∧
C) ~
D) ∈

Answer: A) ∨

8. If p is true, then ~p is:

A) True
B) False
C) Both
D) Cannot say

Answer: B) False

3. Basic Combinations

Combination means selection of objects where order does not matter.

Formula

nCr = n! / r!(n − r)!

Example:
5C2 = 5! / 2!3! = 10

MCQs: Combinations

9. In combination, order:

A) Matters
B) Does not matter
C) Is always ascending
D) Is always descending

Answer: B) Does not matter

10. Value of 5C2 is:

A) 5
B) 10
C) 15
D) 20

Answer: B) 10

11. Value of 4C1 is:

A) 1
B) 2
C) 3
D) 4

Answer: D) 4

12. Value of 6C0 is:

A) 0
B) 1
C) 6
D) 12

Answer: B) 1

4. Sequence and Series

A sequence is an ordered list of numbers.
A series is the sum of terms of a sequence.

Example sequence:
2, 4, 6, 8

Series:
2 + 4 + 6 + 8

Arithmetic Sequence

Difference is same.

Example:
2, 5, 8, 11
Common difference = 3

Formula:
an = a + (n − 1)d

Geometric Sequence

Ratio is same.

Example:
2, 4, 8, 16
Common ratio = 2

Formula:
an = arⁿ⁻¹

MCQs: Sequence and Series

13. In 3, 6, 9, 12, common difference is:

A) 2
B) 3
C) 4
D) 6

Answer: B) 3

14. Next term of 2, 4, 8, 16 is:

A) 20
B) 24
C) 32
D) 36

Answer: C) 32

15. Sequence 5, 10, 15, 20 is:

A) Arithmetic sequence
B) Geometric sequence
C) Random sequence
D) Matrix

Answer: A) Arithmetic sequence

16. Sequence 3, 6, 12, 24 is:

A) Arithmetic sequence
B) Geometric sequence
C) Empty set
D) Proposition

Answer: B) Geometric sequence

17. Sum of 2 + 4 + 6 is:

A) 8
B) 10
C) 12
D) 14

Answer: C) 12

5. Matrices

A matrix is a rectangular arrangement of numbers in rows and columns.

Example:$$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$[13​24​]

This is a 2 × 2 matrix.

Important Terms

MCQs: Matrices

18. A matrix has 2 rows and 3 columns. Its order is:

A) 3 × 2
B) 2 × 3
C) 2 × 2
D) 3 × 3

Answer: B) 2 × 3

19. A matrix with equal rows and columns is called:

A) Row matrix
B) Column matrix
C) Square matrix
D) Zero matrix

Answer: C) Square matrix

20. Matrix with all zero elements is called:

A) Identity matrix
B) Zero matrix
C) Square matrix
D) Diagonal matrix

Answer: B) Zero matrix

21. In a matrix, horizontal lines are called:

A) Columns
B) Rows
C) Sets
D) Terms

Answer: B) Rows

6. Differentiation / Derivation

Differentiation finds the rate of change of a function.

If y = x², then dy/dx = 2x.

Basic Rules

MCQs: Differentiation

22. Derivative of x is:

A) 0
B) 1
C) x
D) 2x

Answer: B) 1

23. Derivative of constant 5 is:

A) 0
B) 1
C) 5
D) x

Answer: A) 0

24. Derivative of x² is:

A) x
B) 2x
C) x²
D) 2

Answer: B) 2x

25. Derivative of x³ is:

A) 3x
B) x²
C) 3x²
D) x³

Answer: C) 3x²

7. Integration

Integration is the reverse process of differentiation. It is used to find area under a curve.

Basic Rules

MCQs: Integration

26. Integration is the reverse of:

A) Addition
B) Subtraction
C) Differentiation
D) Multiplication

Answer: C) Differentiation

27. Integral of 1 dx is:

A) 1
B) x + C
C) 0
D) x²

Answer: B) x + C

28. Integral of x dx is:

A) x + C
B) x² + C
C) x²/2 + C
D) 2x + C

Answer: C) x²/2 + C

29. Integral of x² dx is:

A) x³/3 + C
B) 2x + C
C) x² + C
D) 3x² + C

Answer: A) x³/3 + C

8. Conic Sections

Conic sections are curves formed by cutting a cone with a plane.

Main Conic Sections

Basic Equations

MCQs: Conic Sections

30. A circle is the set of points at equal distance from:

A) Focus
B) Center
C) Vertex
D) Axis

Answer: B) Center

31. U-shaped conic section is called:

A) Circle
B) Ellipse
C) Parabola
D) Hyperbola

Answer: C) Parabola

32. Oval-shaped conic section is:

A) Ellipse
B) Circle
C) Line
D) Point

Answer: A) Ellipse

33. Hyperbola has:

A) One branch
B) Two separate branches
C) No branch
D) Only circle shape

Answer: B) Two separate branches

34. Standard equation of circle with center at origin is:

A) x² + y² = r²
B) y = mx + c
C) y² = 4ax
D) x + y = 0

Answer: A) x² + y² = r²

9. Mixed Important MCQs

35. A ∩ B means:

A) Union
B) Intersection
C) Complement
D) Subset

Answer: B) Intersection

36. A ∪ B means:

A) Union
B) Intersection
C) Empty set
D) Matrix

Answer: A) Union

37. In logic, ~p means:

A) p and q
B) p or q
C) not p
D) if p then q

Answer: C) not p

38. In arithmetic sequence, common difference is:

A) Same
B) Different
C) Zero always
D) Negative always

Answer: A) Same

39. In geometric sequence, common ratio is:

A) Same
B) Always zero
C) Always one
D) Not used

Answer: A) Same

40. Derivative of 7x is:

A) 7
B) x
C) 0
D) 14x

Answer: A) 7

Quick Revision Table

Homework MCQs

1. If A = {1, 2} and B = {2, 3}, A ∩ B is:

A) {1}
B) {2}
C) {3}
D) {1, 2, 3}

Answer: B) {2}

2. Value of 5C1 is:

A) 1
B) 2
C) 5
D) 10

Answer: C) 5

3. Derivative of x² is:

A) x
B) 2x
C) x²
D) 0

Answer: B) 2x

4. Integral of x dx is:

A) x²/2 + C
B) 2x + C
C) x + C
D) 0

Answer: A) x²/2 + C

5. U-shaped curve is called:

A) Circle
B) Parabola
C) Ellipse
D) Hyperbola

Answer: B) Parabola

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