MCQs – Free MCQs for Students

Author: tmagriou

Class 9 Mathematics Chapter 1: Matrices and Determinants-MCQa-FBISE
Short Description

This post contains important MCQs from Class 9 Mathematics – Matrices and Determinants.
These questions are helpful for board exams, tests, and revision.

MCQs-Matrices and Determinants
1. The order of a matrix having 3 rows and 4 columns is:
  - A) $$3 \times 3$$
  - B) $$4 \times 3$$
  - C) $$3 \times 4$$
  - D) $$4 \times 4$$
2. A matrix having equal number of rows and columns is called:
  - A) Rectangular matrix
  - B) Column matrix
  - C) Square matrix
  - D) Row matrix
3. A matrix having only one row is called:
  - A) Column matrix
  - B) Square matrix
  - C) Row matrix
  - D) Zero matrix
4. A matrix having only one column is called:
  - A) Row matrix
  - B) Column matrix
  - C) Square matrix
  - D) Identity matrix
5. A matrix whose all elements are zero is called:
  - A) Identity matrix
  - B) Null matrix
  - C) Scalar matrix
  - D) Square matrix
6. The matrix $$\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$$ is called:
  - A) Null matrix
  - B) Scalar matrix
  - C) Identity matrix
  - D) Square matrix
7. If $$A=\begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}$$ then $$A_{12}$$ is:
  - A) 2
  - B) 3
  - C) 4
  - D) 5
8. Two matrices can be added only if they have:
  - A) Same elements
  - B) Same order
  - C) Same determinant
  - D) Same trace
9. If $$A$$ is of order $$2 \times 3$$ and $$B$$ is of order $$2 \times 3$$, then order of $$A+B$$ is:
  - A) $$3 \times 2$$
  - B) $$2 \times 2$$
  - C) $$3 \times 3$$
  - D) $$2 \times 3$$
10. If $$A=\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$$ then $$2A$$ is:
  - A) $$\begin{bmatrix}2 & 4 \\ 6 & 8\end{bmatrix}$$
  - B) $$\begin{bmatrix}1 & 4 \\ 3 & 8\end{bmatrix}$$
  - C) $$\begin{bmatrix}2 & 2 \\ 4 & 4\end{bmatrix}$$
  - D) $$\begin{bmatrix}3 & 4 \\ 5 & 6\end{bmatrix}$$
11. If $$A=\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$ then $$|A|$$ equals:
  - A) $$ad+bc$$
  - B) $$ab-cd$$
  - C) $$ad-bc$$
  - D) $$ac-bd$$
12. The determinant of $$\begin{bmatrix}5 & 7 \\ 5 & 7\end{bmatrix}$$ is:
  - A) 35
  - B) 0
  - C) 14
  - D) 10
13. If determinant of a matrix is zero, the matrix is:
  - A) Identity
  - B) Non-singular
  - C) Singular
  - D) Scalar
14. The determinant of identity matrix of order 2 is:
  - A) 0
  - B) 1
  - C) 2
  - D) −1
15. The determinant of $$\begin{bmatrix}1 & 2 \\ 2 & 4\end{bmatrix}$$ is:
  - A) 2
  - B) −2
  - C) 0
  - D) 6
Answers
1. C
2. C
3. C
4. B
5. B
6. C
7. B
8. B
9. D
10. A
11. C
12. B
13. C
14. B
15. C
1. If $$|A| \neq 0$$, then matrix $$A$$ is:
  - A) Singular
  - B) Identity
  - C) Non-singular
  - D) Null
2. The determinant of $$\begin{bmatrix}a & 0 \\ 0 & d\end{bmatrix}$$ is:
  - A) $$a+d$$
  - B) $$ad$$
  - C) $$a-d$$
  - D) 0
3. The determinant of a triangular matrix is equal to:
  - A) Sum of diagonal elements
  - B) Product of diagonal elements
  - C) Zero
  - D) Square of diagonal elements
4. Which of the following is always a square matrix?
  - A) Row matrix
  - B) Column matrix
  - C) Identity matrix
  - D) Rectangular matrix
5. The order of determinant is defined only for:
  - A) Rectangular matrices
  - B) Square matrices
  - C) Row matrices
  - D) Column matrices
6. If $$A$$ is a null matrix, then $$|A|$$ is:
  - A) 1
  - B) −1
  - C) 0
  - D) Undefined
7. Which matrix has determinant always equal to 1?
  - A) Null matrix
  - B) Identity matrix
  - C) Scalar matrix
  - D) Rectangular matrix
8. If $$A$$ is a square matrix, then $$|A^T|$$ is equal to:
  - A) $$-|A|$$
  - B) $$|A|$$
  - C) $$|A|^2$$
  - D) 0
9. If $$|A|=4$$ and $$A$$ is $$2\times2$$, then $$|3A|$$ is:
  - A) 12
  - B) 36
  - C) 24
  - D) 9
10. A determinant is a single:
  - A) Matrix
  - B) Row
  - C) Column
  - D) Number
11. If $$|A|=-3$$, then $$|-A|$$ for a $$2\times2$$ matrix is:
  - A) −3
  - B) 3
  - C) −6
  - D) 6
12. The determinant changes sign if:
  - A) Rows are added
  - B) Columns are multiplied
  - C) Two rows are interchanged
  - D) Two rows are equal
13. If all elements of a row are zero, the determinant is:
  - A) 1
  - B) −1
  - C) 0
  - D) Undefined
14. A determinant having non-zero value is called:
  - A) Singular
  - B) Non-singular
  - C) Null
  - D) Identity
15. The determinant of a scalar matrix of order 2 with scalar $$k$$ is:
  - A) $$k$$
  - B) $$2k$$
  - C) $$k^2$$
  - D) $$k^3$$
16. A square matrix whose determinant is zero is called:
  - A) Identity matrix
  - B) Singular matrix
  - C) Scalar matrix
  - D) Diagonal matrix
17. Which operation is not possible for matrices?
  - A) Addition
  - B) Subtraction
  - C) Multiplication
  - D) Division
18. If $$|A|=1$$, then matrix $$A$$ is:
  - A) Singular
  - B) Identity
  - C) Non-singular
  - D) Null
19. The determinant of $$\begin{bmatrix}a & b \\ b & a\end{bmatrix}$$ is:
  - A) $$a^2+b^2$$
  - B) $$a^2-b^2$$
  - C) $$2ab$$
  - D) 0
20. The determinant of a $$2\times2$$ matrix represents:
  - A) A matrix
  - B) A vector
  - C) A number
  - D) A function
January 26, 2026
Class 10 Maths MCQs – Unit 7: Introduction to Trigonometry (FBISE)
Unit 7: Introduction to Trigonometry

Chapter Overview

:
This unit introduces trigonometric ratios, their definitions in a right-angled triangle, and standard trigonometric values. Key concepts include sin, cos, tan, cosec, sec, cot, reciprocal relations, and basic identities. This unit is very important for FBISE board exams.

Multiple Choice Questions (MCQs)

Q1. Trigonometry is the branch of mathematics that deals with:

A. Circles
B. Triangles
C. Angles and sides of triangles
D. Polygons

Q2. In a right-angled triangle, sine of an acute angle is defined as:

A. Adjacent / Hypotenuse
B. Opposite / Hypotenuse
C. Opposite / Adjacent
D. Hypotenuse / Opposite

Q3. Cosine of an acute angle θ is:

A. Opposite / Hypotenuse
B. Adjacent / Hypotenuse
C. Opposite / Adjacent
D. Hypotenuse / Adjacent

Q4. Tangent of an acute angle θ is:

A. Adjacent / Opposite
B. Hypotenuse / Opposite
C. Opposite / Adjacent
D. Hypotenuse / Adjacent

Q5. Which of the following is the reciprocal of sin θ?

A. sec θ
B. cos θ
C. cosec θ
D. tan θ

Q6. The reciprocal of cos θ is:

A. tan θ
B. cot θ
C. sec θ
D. cosec θ

Q7. The reciprocal of tan θ is:

A. cot θ
B. sec θ
C. cos θ
D. sin θ

Q8. Which of the following is equal to sin θ / cos θ?

A. cot θ
B. sec θ
C. tan θ
D. cosec θ

Q9. In a right-angled triangle, the longest side is called:

A. Adjacent
B. Opposite
C. Hypotenuse
D. Base

Q10. The value of sin 0° is:

A. 1
B. 0
C. 1/2
D. √3/2

Q11. The value of cos 0° is:

A. 0
B. 1
C. √3/2
D. 1/2

Q12. The value of tan 0° is:

A. 1
B. √3
C. Undefined
D. 0

Q13. The value of sin 30° is:

A. 1
B. √3/2
C. 1/2
D. 0

Q14. The value of cos 60° is:

A. 1/2
B. √3/2
C. 1
D. 0

Q15. The value of tan 45° is:

A. 0
B. 1
C. √3
D. 1/√3

Q16. The value of sin 90° is:

A. 0
B. 1/2
C. √3/2
D. 1

Q17. The value of cos 90° is:

A. 0
B. 1
C. √3/2
D. 1/2

Q18. The value of tan 90° is:

A. 0
B. 1
C. √3
D. Not defined

Q19. Which trigonometric ratio is equal to 1/sin θ?

A. sec θ
B. cos θ
C. cosec θ
D. tan θ

Q20. Which trigonometric ratio is equal to 1/cos θ?

A. tan θ
B. cosec θ
C. cot θ
D. sec θ

Q21. If sin θ = 3/5, then cos θ is:

A. 4/5
B. 5/3
C. 3/4
D. 5/4

Q22. If tan θ = 1, then θ is:

A. 30°
B. 45°
C. 60°
D. 90°

Q23. Which of the following is always true?

A. sin θ = cos θ
B. sin²θ + cos²θ = 1
C. tan θ = 1
D. sec θ = cosec θ

Q24. Which angle is considered in basic trigonometry?

A. Obtuse angle
B. Acute angle
C. Reflex angle
D. Straight angle

Q25. In ΔABC right-angled at B, hypotenuse is:

A. AB
B. BC
C. AC
D. BA

Q26. The trigonometric ratio cosec θ is defined as:

A. Hypotenuse / Opposite
B. Adjacent / Hypotenuse
C. Opposite / Adjacent
D. Hypotenuse / Adjacent

Q27. The value of cos 30° is:

A. 1/2
B. √3/2
C. 1
D. 0

Q28. The value of tan 60° is:

A. 1
B. 1/√3
C. √3
D. 0

Q29. Which of the following ratios is undefined at 0°?

A. sin 0°
B. cos 0°
C. tan 0°
D. cosec 0°

Q30. If θ is an acute angle, then sin θ is always:

A. Negative
B. Zero
C. Positive
D. Undefined

Q31. The trigonometric ratios are defined only for:

A. Any triangle
B. Right-angled triangle
C. Isosceles triangle
D. Equilateral triangle

Q32. Which ratio is also called tangent?

A. sin θ / cos θ
B. cos θ / sin θ
C. 1 / sin θ
D. 1 / cos θ

Q33. The value of sec 60° is:

A. 2
B. 1/2
C. √3
D. √3/2

Q34. The value of cosec 30° is:

A. 1/2
B. √3/2
C. 2
D. √3

Q35. Which of the following is the correct identity?

A. sin θ = 1/cos θ
B. sec θ = 1/cos θ
C. tan θ = 1/sin θ
D. cot θ = 1/sec θ

Q36. The value of cot 45° is:

A. 0
B. 1
C. √3
D. 1/√3

Q37. Which trigonometric ratio is equal to adjacent/opposite?

A. tan θ
B. sec θ
C. cot θ
D. cosec θ

Q38. The value of cot 60° is:

A. √3
B. 1
C. 1/√3
D. 0

Q39. For an acute angle θ, which ratio is the largest?

A. sin θ
B. cos θ
C. tan θ
D. cosec θ

Q40. If sin θ = cos θ, then θ equals:

A. 30°
B. 45°
C. 60°
D. 90°

Answers Key (Unit 7)
1. C
2. B
3. B
4. C
5. C
6. C
7. A
8. C
9. C
10. B
11. B
12. D
13. C
14. A
15. B
16. D
17. A
18. D
19. C
20. D
21. A
22. B
23. B
24. B
25. C
26. A
27. B
28. C
29. D
30. C
31. B
32. A
33. A
34. C
35. B
36. B
37. C
38. C
39. C
40. B
January 25, 2026
Class 10 Maths MCQs – Unit 6: Basic Statistics (FBISE)
Unit 6: Basic Statistics

Chapter Overview:
This unit deals with the collection, organization, presentation, and analysis of data. Important concepts include mean, median, mode, frequency distribution, cumulative frequency, class intervals, and graphical representation of data. MCQs from this chapter are regularly asked in FBISE board exams.

Multiple Choice Questions (MCQs)

Q1. The arithmetic mean of the first 10 natural numbers is:

A. 5
B. 5.5
C. 6
D. 4.5

Q2. Which measure of central tendency is affected most by extreme values?

A. Median
B. Mode
C. Mean
D. Range

Q3. If the mean of 5 observations is 8, then their sum is:

A. 13
B. 40
C. 8
D. 5

Q4. The value which occurs most frequently in a data set is called:

A. Mean
B. Median
C. Mode
D. Range

Q5. If the median of a data is 15, then:

A. All values are 15
B. Half of the values are less than 15
C. All values are greater than 15
D. Mean is also 15

Q6. The difference between the highest and lowest observation is called:

A. Mean
B. Median
C. Range
D. Mode

Q7. Which of the following is a positional average?

A. Mean
B. Mode
C. Median
D. Range

Q8. In a frequency table, the total number of observations is obtained by:

A. Adding class intervals
B. Adding frequencies
C. Multiplying frequencies
D. Subtracting frequencies

Q9. The class mark of the class 10–20 is:

A. 15
B. 10
C. 20
D. 30

Q10. Mean is represented by the symbol:

A. μ
B. Σ
C. x̄
D. f

Q11. The formula for mean of ungrouped data is:

A. Σf / n
B. Σx / n
C. Σfx
D. Σx

Q12. Median is the value that:

A. Occurs most frequently
B. Divides the data into two equal parts
C. Is the average of all values
D. Is the difference of extremes

Q13. If all observations in a data set are equal, then:

A. Mean ≠ Median
B. Mean = Median = Mode
C. Mode does not exist
D. Range is maximum

Q14. Which graph is used to represent cumulative frequency?

A. Bar graph
B. Histogram
C. Ogive
D. Pie chart

Q15. The total of frequencies in a frequency distribution represents:

A. Class interval
B. Range
C. Number of observations
D. Mean

Q16. Which measure is not affected by extreme values?

A. Mean
B. Mode
C. Median
D. Range

Q17. The midpoint of a class interval is called:

A. Class size
B. Class limit
C. Class mark
D. Frequency

Q18. The number of times a value occurs is called:

A. Mean
B. Frequency
C. Range
D. Median

Q19. If the sum of observations is zero, the mean is:

A. 1
B. Undefined
C. Zero
D. Negative

Q20. Which of the following can have more than one value?

A. Mean
B. Median
C. Mode
D. Range

Q21. The lower limit of the class 20–30 is:

A. 30
B. 25
C. 20
D. 10

Q22. Mean of grouped data is calculated using:

A. Σx / n
B. Σf / n
C. Σfx / Σf
D. Σf²

Q23. Which average is best for qualitative data?

A. Mean
B. Median
C. Mode
D. Range

Q24. The median of an even number of observations is:

A. The middle value
B. The average of two middle values
C. The smallest value
D. The largest value

Q25. If one value in a data set increases, then the mean:

A. Always decreases
B. Remains same
C. Always increases
D. May increase

Q26. The horizontal axis in graphs usually represents:

A. Frequency
B. Data values
C. Mean
D. Median

Q27. The vertical axis in a frequency graph represents:

A. Class interval
B. Data
C. Frequency
D. Range

Q28. The sum of deviations of observations from their mean is always:

A. Maximum
B. Minimum
C. Zero
D. Positive

Q29. If mode does not exist, then:

A. Data is uniform
B. All values occur equally
C. No value repeats
D. Data is incorrect

Q30. Which one is a graphical representation of data?

A. Table
B. Mean
C. Bar chart
D. Median

Q31. The width of a class interval is obtained by:

A. Upper limit – Lower limit
B. Lower limit – Upper limit
C. Frequency – Class mark
D. Mean – Median

Q32. Mean, median, and mode are measures of:

A. Dispersion
B. Central tendency
C. Frequency
D. Probability

Q33. The range of data 5, 10, 15, 20 is:

A. 25
B. 15
C. 20
D. 10

Q34. Which of the following is least affected by extreme values?

A. Mean
B. Mode
C. Median
D. Range

Q35. The class size of 10–20 is:

A. 5
B. 10
C. 20
D. 30

Q36. A data arranged in ascending or descending order is called:

A. Raw data
B. Grouped data
C. Array
D. Frequency table

Q37. The median of 3, 5, 7, 9, 11 is:

A. 5
B. 7
C. 9
D. 11

Q38. Which average is suitable for open-ended classes?

A. Mean
B. Median
C. Mode
D. Range

Q39. The sum of frequencies in a grouped frequency table is denoted by:

A. Σx
B. Σf
C. Σfx
D. n²

Q40. If all frequencies are doubled, the mean:

A. Doubles
B. Becomes half
C. Remains same
D. Becomes zero

Answers Key (Unit 6)
1. B
2. C
3. B
4. C
5. B
6. C
7. C
8. B
9. A
10. C
11. B
12. B
13. B
14. C
15. C
16. C
17. C
18. B
19. C
20. C
21. C
22. C
23. C
24. B
25. D
26. B
27. C
28. C
29. C
30. C
31. A
32. B
33. B
34. C
35. B
36. C
37. B
38. B
39. B
40. C
January 25, 2026
Class 10 Mathematics Chapter 5: Sets and Functions – MCQs -(FBISE)
Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers the concepts of sets, types of sets, set operations, relations, functions, domain, codomain, range, and function composition. Ideal for exam revision and self-assessment before Class 10 exams.

MCQs – Sets and Functions
1. The set $\{x : x \text{ is a prime number less than 10}\}$ {x:x is a prime number less than 10} is:
  A. $\{2,3,5,7\}$ {2,3,5,7}
  B. $\{1,2,3,5\}$ {1,2,3,5}
  C. $\{2,3,5,7,9\}$ {2,3,5,7,9}
  D. $\{1,3,5,7\}$ {1,3,5,7}
2. If $A = \{1,2,3\}$ A={1,2,3} and $B = \{3,4,5\}$ B={3,4,5}, then $A \cup B$ A∪B is:
  A. $\{1,2,3,4,5\}$ {1,2,3,4,5}
  B. $\{3\}$ {3}
  C. $\{1,2,4,5\}$ {1,2,4,5}
  D. $\{1,2,3\}$ {1,2,3}
3. For the same sets, $A \cap B$ A∩B is:
  A. $\{1,2,3,4,5\}$ {1,2,3,4,5}
  B. $\{3\}$ {3}
  C. $\{1,2,4,5\}$ {1,2,4,5}
  D. $\{1,2\}$ {1,2}
4. If $U = \{1,2,3,4,5,6\}$ U={1,2,3,4,5,6} and $A = \{2,4,6\}$ A={2,4,6}, then $A’$ A′ (complement of A) is:
  A. $\{1,3,5\}$ {1,3,5}
  B. $\{2,4,6\}$ {2,4,6}
  C. $\{1,2,3,4\}$ {1,2,3,4}
  D. $\{3,4,5\}$ {3,4,5}
5. Which of the following is a finite set?
  A. $\{1,2,3,4,5\}$ {1,2,3,4,5}
  B. $\mathbb{N}$ N
  C. $\mathbb{Z}$ Z
  D. $\mathbb{R}$ R
6. Which of the following is an infinite set?
  A. $\{2,4,6,8,10\}$ {2,4,6,8,10}
  B. $\mathbb{N}$ N
  C. $\{1,3,5,7\}$ {1,3,5,7}
  D. $\{a,b,c\}$ {a,b,c}
7. If $A = \{1,2\}$ A={1,2} and $B = \{a,b\}$ B={a,b}, the Cartesian product $A \times B$ A×B is:
  A. $\{(1,a),(1,b),(2,a),(2,b)\}$ {(1,a),(1,b),(2,a),(2,b)}
  B. $\{(a,1),(b,1),(a,2),(b,2)\}$ {(a,1),(b,1),(a,2),(b,2)}
  C. $\{(1,2),(a,b)\}$ {(1,2),(a,b)}
  D. $\{(1,a),(2,b)\}$ {(1,a),(2,b)}
8. A function is defined as:
  A. A relation where each element of the domain has exactly one image in the codomain
  B. A relation where each element of the domain may have multiple images
  C. A set of ordered pairs with repeated first elements
  D. None of these
9. If $f(x) = 2x+3$ f(x)=2x+3, then $f(2)$ f(2) is:
  A. 4
  B. 5
  C. 7
  D. 8
10. For $f(x) = x^2-1$ f(x)=x2−1, the domain is:
  A. All real numbers
  B. Positive real numbers
  C. Integers only
  D. Natural numbers only
11. The range of $f(x) = x^2$ f(x)=x2 is:
  A. All real numbers
  B. Non-negative real numbers
  C. Negative real numbers
  D. Integers
12. Which of the following is a one-to-one function?
  A. $f(x) = 2x+1$ f(x)=2x+1
  B. $f(x) = x^2$ f(x)=x2
  C. $f(x) = |x|$ f(x)=∣x∣
  D. $f(x) = x^2-4$ f(x)=x2−4
13. The function $f(x) = x^3$ f(x)=x3 is:
  A. One-to-one
  B. Not one-to-one
  C. Constant
  D. None of these
14. The function $f: \mathbb{R} \to \mathbb{R}$ f:R→R, $f(x) = x^2$ f(x)=x2, is:
  A. Many-to-one
  B. One-to-one
  C. Onto
  D. Constant
15. The composition of $f(x) = 2x$ f(x)=2x and $g(x) = x+3$ g(x)=x+3 is:
  A. $f(g(x)) = 2x+3$ f(g(x))=2x+3
  B. $f(g(x)) = 2x+6$ f(g(x))=2x+6
  C. $g(f(x)) = 2x+3$ g(f(x))=2x+3
  D. $g(f(x)) = 2x+6$ g(f(x))=2x+6
16. The set of even natural numbers is:
  A. Infinite and countable
  B. Infinite and uncountable
  C. Finite
  D. Empty
17. The empty set is denoted by:
  A. $\{\}$ {}
  B. $\varnothing$ ∅
  C. Both A and B
  D. None
18. If $A = \{1,2,3\}$ A={1,2,3}, $B = \{2,3,4\}$ B={2,3,4}, then $A – B$ A−B is:
  A. $\{1\}$ {1}
  B. $\{4\}$ {4}
  C. $\{2,3\}$ {2,3}
  D. $\{1,4\}$ {1,4}
19. The union of disjoint sets $A$ A and $B$ B contains:
  A. All elements of A and B without repetition
  B. Only elements of A
  C. Only elements of B
  D. Only common elements
20. The intersection of disjoint sets $A$ A and $B$ B is:
  A. Empty set
  B. All elements of A
  C. All elements of B
  D. None
21. A bijective function is:
  A. One-to-one and onto
  B. One-to-one only
  C. Onto only
  D. Many-to-one
22. If $f(x) = 3x-2$ f(x)=3x−2, then $f^{-1}(x)$ f−1(x) is:
  A. $\frac{x+2}{3}$ 3x+2
  B. $3x+2$ 3x+2
  C. $\frac{x-2}{3}$ 3x−2
  D. $x^3-2$ x3−2
23. Which of the following is a constant function?
  A. $f(x) = 5$ f(x)=5
  B. $f(x) = x+1$ f(x)=x+1
  C. $f(x) = 2x$ f(x)=2x
  D. $f(x) = x^2$ f(x)=x2
24. The domain of $f(x) = \frac{1}{x-2}$ f(x)=x−21 is:
  A. All real numbers except 2
  B. All real numbers
  C. All positive numbers
  D. All integers
25. If $f(x) = x+1$ f(x)=x+1 and $g(x) = x^2$ g(x)=x2, then $f(g(x))$ f(g(x)) is:
  A. $x^2+1$ x2+1
  B. $(x+1)^2$ (x+1)2
  C. $x^2-1$ x2−1
  D. $x^2+2$ x2+2
26. If $A = \{1,2,3,4\}$ A={1,2,3,4}, then the number of subsets of A is:
  A. 16
  B. 8
  C. 4
  D. 2
27. For set $A = \{a,b\}$ A={a,b}, Cartesian product $A \times A$ A×A has:
  A. 4 elements
  B. 2 elements
  C. 3 elements
  D. 1 element
28. A function $f(x) = |x|$ f(x)=∣x∣ is:
  A. Many-to-one
  B. One-to-one
  C. Constant
  D. None
29. The set of integers divisible by 5 is:
  A. Infinite and countable
  B. Infinite and uncountable
  C. Finite
  D. Empty
30. If $A = \{1,2,3\}$ A={1,2,3}, $B = \{4,5\}$ B={4,5}, then $A \times B$ A×B has:
  A. 6 elements
  B. 5 elements
  C. 3 elements
  D. 2 elements
31. A function with domain $\mathbb{R}$ R and codomain $\mathbb{R}$ R defined by $f(x) = x^2+1$ f(x)=x2+1 has range:
  A. $y \ge 1$ y≥1
  B. $y \ge 0$ y≥0
  C. $y \le 0$ y≤0
  D. All real numbers
32. $f(x) = x^3$ f(x)=x3 is:
  A. One-to-one and onto
  B. Many-to-one
  C. Constant
  D. None
33. $f(x) = \sin x$ f(x)=sinx for $x \in [0, \pi]$ x∈[0,π] is:
  A. One-to-one
  B. Many-to-one
  C. Constant
  D. None
34. The union of A = {1,2} and B = {2,3} is:
  A. {1,2,3}
  B. {2}
  C. {1,3}
  D. {1,2}
35. Intersection of A = {1,2} and B = {2,3} is:
  A. {2}
  B. {1}
  C. {3}
  D. {1,3}
36. A function which is both one-to-one and onto is called:
  A. Bijective
  B. Injective only
  C. Surjective only
  D. None
37. If $f(x) = 2x+3$ f(x)=2x+3 and $g(x) = x-1$ g(x)=x−1, then $g(f(x))$ g(f(x)) is:
  A. $2x+2$ 2x+2
  B. $2x+4$ 2x+4
  C. $2x+3$ 2x+3
  D. $2x+1$ 2x+1
38. If $A = \{1,2,3\}$ A={1,2,3}, number of proper subsets of A is:
  A. 7
  B. 8
  C. 6
  D. 3
39. The set of natural numbers is:
  A. Infinite
  B. Finite
  C. Empty
  D. None
40. Domain of $f(x) = \frac{1}{x^2-4}$ f(x)=x2−41 is:
  A. All real numbers except ±2
  B. All real numbers
  C. x > 0
  D. x < 0
41. The range of $f(x) = x^2$ f(x)=x2 is:
  A. y ≥ 0
  B. y ≤ 0
  C. All real numbers
  D. None
42. The function $f(x) = x^2+2x+1$ f(x)=x2+2x+1 is:
  A. Many-to-one
  B. One-to-one
  C. Constant
  D. None
43. The inverse of $f(x) = 3x+4$ f(x)=3x+4 is:
  A. $f^{-1}(x) = \frac{x-4}{3}$ f−1(x)=3x−4
  B. $f^{-1}(x) = 3x-4$ f−1(x)=3x−4
  C. $f^{-1}(x) = \frac{x+4}{3}$ f−1(x)=3x+4
  D. $f^{-1}(x) = x-4$ f−1(x)=x−4
44. If $A = {a,b}$ A=a,b, the Cartesian product $A \times A \times A$ A×A×A has:
  A. 8 elements
  B. 6 elements
  C. 4 elements
  D. 2 elements
45. Function $f(x) = x^2$ f(x)=x2 restricted to x ≥ 0 is:
  A. One-to-one
  B. Many-to-one
  C. Constant
  D. None
Answers – List Form
1. A
2. A
3. B
4. A
5. A
6. B
7. A
8. A
9. C
10. A
11. B
12. A
13. A
14. A
15. B
16. A
17. C
18. A
19. A
20. A
21. A
22. A
23. A
24. A
25. A
26. A
27. A
28. A
29. A
30. A
31. A
32. A
33. A
34. A
35. A
36. A
37. A
38. A
39. A
40. A
41. A
42. A
43. A
44. A
45. A
January 25, 2026
Class 10 Mathematics Chapter 4: Partial Fractions – MCQs -(FBISE)
Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers the concept of partial fractions, decomposition of rational expressions, proper and improper fractions, and application-based problems. Ideal for exam revision and self-assessment before your Class 10 exams.

MCQs – Partial Fractions
1. The partial fraction decomposition of $\frac{3x + 5}{(x+1)(x+2)}$ (x+1)(x+2)3x+5 is:
  A. $\frac{1}{x+1} + \frac{2}{x+2}$ x+11+x+22
  B. $\frac{2}{x+1} + \frac{1}{x+2}$ x+12+x+21
  C. $\frac{3}{x+1} + \frac{5}{x+2}$ x+13+x+25
  D. $\frac{5}{x+1} + \frac{3}{x+2}$ x+15+x+23
2. Decompose $\frac{7}{x(x+2)}$ x(x+2)7 into partial fractions:
  A. $\frac{3}{x} + \frac{4}{x+2}$ x3+x+24
  B. $\frac{4}{x} + \frac{3}{x+2}$ x4+x+23
  C. $\frac{2}{x} + \frac{5}{x+2}$ x2+x+25
  D. $\frac{5}{x} + \frac{2}{x+2}$ x5+x+22
3. $\frac{2x+3}{x^2+5x+6}$ x2+5x+62x+3 can be decomposed as:
  A. $\frac{1}{x+2} + \frac{1}{x+3}$ x+21+x+31
  B. $\frac{2}{x+2} + \frac{1}{x+3}$ x+22+x+31
  C. $\frac{1}{x+2} + \frac{2}{x+3}$ x+21+x+32
  D. $\frac{2}{x+2} + \frac{3}{x+3}$ x+22+x+33
4. The fraction $\frac{5x+1}{x^2-x-6}$ x2−x−65x+1 decomposes into:
  A. $\frac{2}{x-3} + \frac{3}{x+2}$ x−32+x+23
  B. $\frac{1}{x-3} + \frac{4}{x+2}$ x−31+x+24
  C. $\frac{1}{x-3} + \frac{2}{x+2}$ x−31+x+22
  D. $\frac{3}{x-3} + \frac{2}{x+2}$ x−33+x+22
5. Decompose $\frac{4x+7}{x^2+5x+6}$ x2+5x+64x+7 into partial fractions:
  A. $\frac{1}{x+2} + \frac{3}{x+3}$ x+21+x+33
  B. $\frac{4}{x+2} + \frac{3}{x+3}$ x+24+x+33
  C. $\frac{2}{x+2} + \frac{5}{x+3}$ x+22+x+35
  D. $\frac{3}{x+2} + \frac{4}{x+3}$ x+23+x+34
6. Which of the following is a proper fraction?
  A. $\frac{x+2}{x^2+3x+2}$ x2+3x+2x+2
  B. $\frac{x^3+1}{x^2+2}$ x2+2×3+1
  C. $\frac{x^2+3}{x+1}$ x+1×2+3
  D. $\frac{x^3+2}{x^2+3}$ x2+3×3+2
7. The decomposition of $\frac{3x+2}{x^2+3x+2}$ x2+3x+23x+2 is:
  A. $\frac{1}{x+1} + \frac{2}{x+2}$ x+11+x+22
  B. $\frac{2}{x+1} + \frac{1}{x+2}$ x+12+x+21
  C. $\frac{3}{x+1} + \frac{2}{x+2}$ x+13+x+22
  D. $\frac{1}{x+1} + \frac{3}{x+2}$ x+11+x+23
8. The proper fraction is defined as a fraction where:
  A. Degree of numerator < degree of denominator
  B. Degree of numerator > degree of denominator
  C. Degree of numerator = degree of denominator
  D. None of these
9. Decompose $\frac{6x+11}{x^2+5x+6}$ x2+5x+66x+11 into partial fractions:
  A. $\frac{5}{x+2} + \frac{1}{x+3}$ x+25+x+31
  B. $\frac{2}{x+2} + \frac{4}{x+3}$ x+22+x+34
  C. $\frac{5}{x+2} + \frac{1}{x+3}$ x+25+x+31
  D. $\frac{1}{x+2} + \frac{5}{x+3}$ x+21+x+35
10. $\frac{x+3}{x^2-4}$ x2−4x+3 decomposes into:
  A. $\frac{2}{x-2} + \frac{1}{x+2}$ x−22+x+21
  B. $\frac{1}{x-2} + \frac{2}{x+2}$ x−21+x+22
  C. $\frac{1}{x-2} + \frac{1}{x+2}$ x−21+x+21
  D. $\frac{3}{x-2} + \frac{0}{x+2}$ x−23+x+20
11. Decompose $\frac{2x+5}{x^2-5x+6}$ x2−5x+62x+5:
  A. $\frac{1}{x-2} + \frac{1}{x-3}$ x−21+x−31
  B. $\frac{3}{x-2} + \frac{-1}{x-3}$ x−23+x−3−1
  C. $\frac{2}{x-2} + \frac{1}{x-3}$ x−22+x−31
  D. $\frac{1}{x-2} + \frac{2}{x-3}$ x−21+x−32
12. Which of the following is an improper fraction?
  A. $\frac{x^3+2x+1}{x^2+1}$ x2+1×3+2x+1
  B. $\frac{x+2}{x^2+1}$ x2+1x+2
  C. $\frac{2x+1}{x^2+3}$ x2+32x+1
  D. $\frac{x}{x^2+2}$ x2+2x
13. The decomposition of $\frac{5x+9}{x^2+4x+3}$ x2+4x+35x+9 is:
  A. $\frac{1}{x+1} + \frac{4}{x+3}$ x+11+x+34
  B. $\frac{2}{x+1} + \frac{3}{x+3}$ x+12+x+33
  C. $\frac{1}{x+1} + \frac{5}{x+3}$ x+11+x+35
  D. $\frac{3}{x+1} + \frac{2}{x+3}$ x+13+x+32
14. The fraction $\frac{3x^2+2x+1}{x^3+3x^2+2x}$ x3+3×2+2x3x2+2x+1 is:
  A. Proper
  B. Improper
  C. Constant
  D. None of these
15. Decompose $\frac{x+5}{x^2+6x+8}$ x2+6x+8x+5:
  A. $\frac{1}{x+2} + \frac{4}{x+4}$ x+21+x+44
  B. $\frac{3}{x+2} + \frac{2}{x+4}$ x+23+x+42
  C. $\frac{2}{x+2} + \frac{3}{x+4}$ x+22+x+43
  D. $\frac{1}{x+2} + \frac{5}{x+4}$ x+21+x+45
16. The decomposition of $\frac{4x+7}{x^2+3x-10}$ x2+3x−104x+7 is:
  A. $\frac{1}{x-2} + \frac{3}{x+5}$ x−21+x+53
  B. $\frac{2}{x-2} + \frac{1}{x+5}$ x−22+x+51
  C. $\frac{3}{x-2} + \frac{1}{x+5}$ x−23+x+51
  D. $\frac{1}{x-2} + \frac{2}{x+5}$ x−21+x+52
17. If a fraction is improper, it can be written as:
  A. Polynomial + proper fraction
  B. Proper fraction only
  C. Constant only
  D. None of these
18. Decompose $\frac{6x+13}{x^2+5x+6}$ x2+5x+66x+13:
  A. $\frac{7}{x+2} + \frac{-1}{x+3}$ x+27+x+3−1
  B. $\frac{5}{x+2} + \frac{3}{x+3}$ x+25+x+33
  C. $\frac{3}{x+2} + \frac{5}{x+3}$ x+23+x+35
  D. $\frac{1}{x+2} + \frac{6}{x+3}$ x+21+x+36
19. $\frac{x^2+3x+2}{x+1}$ x+1×2+3x+2 is:
  A. Improper
  B. Proper
  C. Constant
  D. None of these
20. The decomposition of $\frac{2x+1}{x^2+3x+2}$ x2+3x+22x+1 is:
  A. $\frac{1}{x+1} + \frac{1}{x+2}$ x+11+x+21
  B. $\frac{2}{x+1} + \frac{-1}{x+2}$ x+12+x+2−1
  C. $\frac{-1}{x+1} + \frac{2}{x+2}$ x+1−1+x+22
  D. $\frac{1}{x+1} + \frac{2}{x+2}$ x+11+x+22
21. Decompose $\frac{3x+7}{x^2+5x+6}$ x2+5x+63x+7
  A. $\frac{1}{x+2} + \frac{2}{x+3}$ x+21+x+32
  B. $\frac{2}{x+2} + \frac{1}{x+3}$ x+22+x+31
  C. $\frac{3}{x+2} + \frac{1}{x+3}$ x+23+x+31
  D. $\frac{1}{x+2} + \frac{3}{x+3}$ x+21+x+33
22. Decompose $\frac{4x+9}{x^2+7x+12}$ x2+7x+124x+9
  A. $\frac{1}{x+3} + \frac{3}{x+4}$ x+31+x+43
  B. $\frac{3}{x+3} + \frac{1}{x+4}$ x+33+x+41
  C. $\frac{2}{x+3} + \frac{2}{x+4}$ x+32+x+42
  D. $\frac{4}{x+3} + \frac{1}{x+4}$ x+34+x+41
23. Proper fraction:
  A. $\frac{x+2}{x^2+5x+6}$ x2+5x+6x+2
  B. $\frac{x^3+1}{x^2+1}$ x2+1×3+1
  C. $\frac{x^2+5}{x+2}$ x+2×2+5
  D. $\frac{x^3+2}{x^2+3}$ x2+3×3+2
24. Improper fraction:
  A. $\frac{x^3+2x+1}{x^2+1}$ x2+1×3+2x+1
  B. $\frac{x+1}{x^2+2}$ x2+2x+1
  C. $\frac{2x+1}{x^2+3}$ x2+32x+1
  D. $\frac{x}{x^2+2}$ x2+2x
25. Partial fraction decomposition of $\frac{5x+11}{x^2+6x+5}$ x2+6x+55x+11
  A. $\frac{1}{x+1} + \frac{4}{x+5}$ x+11+x+54
  B. $\frac{3}{x+1} + \frac{2}{x+5}$ x+13+x+52
  C. $\frac{2}{x+1} + \frac{3}{x+5}$ x+12+x+53
  D. $\frac{4}{x+1} + \frac{1}{x+5}$ x+14+x+51
26. Decompose $\frac{6x+13}{x^2+5x+6}$ x2+5x+66x+13
  A. $\frac{5}{x+2} + \frac{3}{x+3}$ x+25+x+33
  B. $\frac{3}{x+2} + \frac{5}{x+3}$ x+23+x+35
  C. $\frac{6}{x+2} + \frac{1}{x+3}$ x+26+x+31
  D. $\frac{2}{x+2} + \frac{4}{x+3}$ x+22+x+34
27. Fraction $\frac{x^2+3x+2}{x+1}$ x+1×2+3x+2 is:
  A. Improper
  B. Proper
  C. Constant
  D. None
28. Decompose $\frac{2x+3}{x^2+3x+2}$ x2+3x+22x+3
  A. $\frac{1}{x+1} + \frac{1}{x+2}$ x+11+x+21
  B. $\frac{2}{x+1} + \frac{1}{x+2}$ x+12+x+21
  C. $\frac{1}{x+1} + \frac{2}{x+2}$ x+11+x+22
  D. $\frac{3}{x+1} + \frac{1}{x+2}$ x+13+x+21
29. Fraction $\frac{3x+5}{x^2+4x+3}$ x2+4x+33x+5 decomposes into:
  A. $\frac{1}{x+1} + \frac{2}{x+3}$ x+11+x+32
  B. $\frac{2}{x+1} + \frac{1}{x+3}$ x+12+x+31
  C. $\frac{3}{x+1} + \frac{2}{x+3}$ x+13+x+32
  D. $\frac{1}{x+1} + \frac{3}{x+3}$ x+11+x+33
30. Improper fraction example:
  A. $\frac{x^3+2}{x^2+1}$ x2+1×3+2
  B. $\frac{x+2}{x^2+1}$ x2+1x+2
  C. $\frac{2x+1}{x^2+3}$ x2+32x+1
  D. $\frac{x}{x^2+2}$ x2+2x
31. Proper fraction example:
  A. $\frac{x+1}{x^2+2}$ x2+2x+1
  B. $\frac{x^3+2}{x^2+1}$ x2+1×3+2
  C. $\frac{x^2+3}{x+1}$ x+1×2+3
  D. $\frac{x^3+1}{x^2+2}$ x2+2×3+1
32. Decompose $\frac{4x+5}{x^2+5x+6}$ x2+5x+64x+5
  A. $\frac{1}{x+2} + \frac{3}{x+3}$ x+21+x+33
  B. $\frac{2}{x+2} + \frac{2}{x+3}$ x+22+x+32
  C. $\frac{3}{x+2} + \frac{1}{x+3}$ x+23+x+31
  D. $\frac{4}{x+2} + \frac{1}{x+3}$ x+24+x+31
33. Decompose $\frac{5x+8}{x^2+6x+8}$ x2+6x+85x+8
  A. $\frac{1}{x+2} + \frac{3}{x+4}$ x+21+x+43
  B. $\frac{2}{x+2} + \frac{3}{x+4}$ x+22+x+43
  C. $\frac{3}{x+2} + \frac{2}{x+4}$ x+23+x+42
  D. $\frac{4}{x+2} + \frac{1}{x+4}$ x+24+x+41
34. Fraction $\frac{x^2+3x+1}{x+1}$ x+1×2+3x+1 is:
  A. Improper
  B. Proper
  C. Constant
  D. None
35. Decompose $\frac{2x+7}{x^2+5x+6}$ x2+5x+62x+7
  A. $\frac{1}{x+2} + \frac{1}{x+3}$ x+21+x+31
  B. $\frac{2}{x+2} + \frac{1}{x+3}$ x+22+x+31
  C. $\frac{1}{x+2} + \frac{2}{x+3}$ x+21+x+32
  D. $\frac{3}{x+2} + \frac{1}{x+3}$ x+23+x+31
36. Improper fraction example:
  A. $\frac{x^3+1}{x^2+2}$ x2+2×3+1
  B. $\frac{x+2}{x^2+1}$ x2+1x+2
  C. $\frac{2x+1}{x^2+3}$ x2+32x+1
  D. $\frac{x}{x^2+2}$ x2+2x
37. Decompose $\frac{3x+7}{x^2+4x+3}$ x2+4x+33x+7
  A. $\frac{1}{x+1} + \frac{2}{x+3}$ x+11+x+32
  B. $\frac{2}{x+1} + \frac{1}{x+3}$ x+12+x+31
  C. $\frac{3}{x+1} + \frac{2}{x+3}$ x+13+x+32
  D. $\frac{1}{x+1} + \frac{3}{x+3}$ x+11+x+33
38. Decompose $\frac{4x+11}{x^2+5x+6}$ x2+5x+64x+11
  A. $\frac{1}{x+2} + \frac{3}{x+3}$ x+21+x+33
  B. $\frac{2}{x+2} + \frac{3}{x+3}$ x+22+x+33
  C. $\frac{3}{x+2} + \frac{2}{x+3}$ x+23+x+32
  D. $\frac{4}{x+2} + \frac{1}{x+3}$ x+24+x+31
39. Fraction $\frac{x^2+5x+6}{x+2}$ x+2×2+5x+6 is:
  A. Improper
  B. Proper
  C. Constant
  D. None
40. Decompose $\frac{2x+9}{x^2+5x+6}$ x2+5x+62x+9
  A. $\frac{1}{x+2} + \frac{3}{x+3}$ x+21+x+33
  B. $\frac{2}{x+2} + \frac{1}{x+3}$ x+22+x+31
  C. $\frac{1}{x+2} + \frac{2}{x+3}$ x+21+x+32
  D. $\frac{3}{x+2} + \frac{1}{x+3}$ x+23+x+31
41. Decompose $\frac{5x+12}{x^2+6x+8}$ x2+6x+85x+12
  A. $\frac{2}{x+2} + \frac{3}{x+4}$ x+22+x+43
  B. $\frac{3}{x+2} + \frac{2}{x+4}$ x+23+x+42
  C. $\frac{1}{x+2} + \frac{4}{x+4}$ x+21+x+44
  D. $\frac{4}{x+2} + \frac{1}{x+4}$ x+24+x+41
42. Fraction $\frac{x^2+2x+1}{x+1}$ x+1×2+2x+1 is:
  A. Improper
  B. Proper
  C. Constant
  D. None
43. Decompose $\frac{2x+5}{x^2+3x+2}$ x2+3x+22x+5
  A. $\frac{1}{x+1} + \frac{1}{x+2}$ x+11+x+21
  B. $\frac{2}{x+1} + \frac{1}{x+2}$ x+12+x+21
  C. $\frac{1}{x+1} + \frac{2}{x+2}$ x+11+x+22
  D. $\frac{3}{x+1} + \frac{1}{x+2}$ x+13+x+21
44. Decompose $\frac{3x+10}{x^2+5x+6}$ x2+5x+63x+10
  A. $\frac{1}{x+2} + \frac{3}{x+3}$ x+21+x+33
  B. $\frac{2}{x+2} + \frac{3}{x+3}$ x+22+x+33
  C. $\frac{3}{x+2} + \frac{2}{x+3}$ x+23+x+32
  D. $\frac{4}{x+2} + \frac{1}{x+3}$ x+24+x+31
45. Fraction $\frac{x^2+3x+2}{x+1}$ x+1×2+3x+2 is:
  A. Improper
  B. Proper
  C. Constant
  D. None
Answers – List Form
1. A
2. A
3. C
4. C
5. B
6. A
7. A
8. A
9. C
10. C
11. B
12. A
13. B
14. B
15. B
16. C
17. A
18. A
19. A
20. B
21. A
22. B
23. A
24. A
25. B
26. A
27. A
28. C
29. B
30. A
31. A
32. B
33. B
34. A
35. C
36. A
37. B
38. B
39. A
40. C
41. B
42. A
43. B
44. B
45. A
January 25, 2026
Class 10 Mathematics Chapter 3: Variations – MCQs -(FBISE)
Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers direct variation, inverse variation, joint variation, combined variation, and application problems. These MCQs are ideal for exam revision and self-assessment before the Class 10 exams.

MCQs – Variations
1. If y varies directly as x and y = 10 when x = 2, then y = ? when x = 5
  A. 25
  B. 20
  C. 15
  D. 10
2. If y varies inversely as x and y = 6 when x = 2, then y when x = 3 is:
  A. 4
  B. 6
  C. 3
  D. 2
3. If y varies directly as x and inversely as z, y = 12 when x = 2, z = 3. Find y when x = 3, z = 2:
  A. 12
  B. 18
  C. 24
  D. 9
4. y varies jointly as x and z. If y = 24 when x = 2, z = 3, find y when x = 3, z = 4:
  A. 48
  B. 54
  C. 72
  D. 36
5. If y varies directly as x² and y = 16 when x = 2, find y when x = 4:
  A. 32
  B. 64
  C. 48
  D. 16
6. If y varies inversely as the square of x and y = 8 when x = 2, find y when x = 4:
  A. 4
  B. 2
  C. 1
  D. 8
7. If y varies directly as x and inversely as z², y = 18 when x = 3, z = 2. Find y when x = 6, z = 3:
  A. 6
  B. 4
  C. 8
  D. 12
8. If y varies jointly as x² and z, and y = 24 when x = 2, z = 3, find y when x = 4, z = 2:
  A. 64
  B. 32
  C. 48
  D. 16
9. If y varies directly as x³, y = 27 when x = 3. Find y when x = 6:
  A. 54
  B. 108
  C. 216
  D. 162
10. If y varies inversely as x and directly as z, y = 12 when x = 2, z = 3. Find y when x = 4, z = 6:
  A. 18
  B. 9
  C. 12
  D. 6
11. If y varies directly as x and y = 5 when x = 10, then y = ? when x = 15
  A. 7.5
  B. 10
  C. 15
  D. 5
12. y varies inversely as x. If y = 9 when x = 3, then x = ? when y = 6:
  A. 4.5
  B. 6
  C. 3
  D. 2
13. y varies directly as x and inversely as z. If y = 10 when x = 2, z = 5, find y when x = 4, z = 10:
  A. 4
  B. 5
  C. 2
  D. 8
14. If y varies jointly as x and z², y = 18 when x = 2, z = 3, find y when x = 3, z = 4:
  A. 32
  B. 64
  C. 48
  D. 72
15. If y varies inversely as x², y = 12 when x = 2, find y when x = 4:
  A. 6
  B. 3
  C. 12
  D. 8
16. If y varies directly as x and inversely as z, y = 20 when x = 4, z = 2, find y when x = 5, z = 5:
  A. 10
  B. 8
  C. 5
  D. 4
17. y varies directly as x² and inversely as z. If y = 18 when x = 3, z = 2, find y when x = 6, z = 3:
  A. 36
  B. 54
  C. 72
  D. 48
18. If y varies directly as x³ and inversely as z, y = 24 when x = 2, z = 3. Find y when x = 4, z = 6:
  A. 32
  B. 64
  C. 48
  D. 16
19. If y varies jointly as x, z, and w, y = 36 when x = 2, z = 3, w = 2. Find y when x = 3, z = 2, w = 4:
  A. 36
  B. 48
  C. 72
  D. 54
20. If y varies inversely as x and y = 10 when x = 5, find x when y = 2:
  A. 25
  B. 20
  C. 15
  D. 10
21. y varies directly as x and inversely as z². If y = 8 when x = 2, z = 1, find y when x = 4, z = 2:
  A. 2
  B. 4
  C. 8
  D. 16
22. If y varies jointly as x² and z³, y = 16 when x = 2, z = 2. Find y when x = 4, z = 4:
  A. 128
  B. 256
  C. 512
  D. 64
23. If y varies directly as x and inversely as z, y = 12 when x = 6, z = 3. Find y when x = 4, z = 2:
  A. 12
  B. 16
  C. 8
  D. 18
24. If y varies inversely as x², y = 9 when x = 3, find y when x = 6:
  A. 9/4
  B. 3/2
  C. 12
  D. 4.5
25. y varies directly as x² and inversely as z. If y = 8 when x = 2, z = 4, find y when x = 4, z = 2:
  A. 16
  B. 32
  C. 24
  D. 8
26. If y varies jointly as x², z, and w, y = 18 when x = 1, z = 2, w = 3. Find y when x = 2, z = 3, w = 2:
  A. 24
  B. 36
  C. 48
  D. 72
27. If y varies inversely as x and directly as z², y = 8 when x = 2, z = 2. Find y when x = 4, z = 4:
  A. 16
  B. 32
  C. 8
  D. 64
28. y varies directly as x³ and inversely as z². If y = 9 when x = 1, z = 3, find y when x = 3, z = 1:
  A. 81
  B. 27
  C. 9
  D. 36
29. y varies jointly as x, z², and w³. If y = 24 when x = 2, z = 1, w = 2, find y when x = 4, z = 2, w = 1:
  A. 48
  B. 36
  C. 24
  D. 72
30. y varies inversely as x² and directly as z. If y = 16 when x = 2, z = 4, find y when x = 4, z = 8:
  A. 16
  B. 8
  C. 4
  D. 2
31. If y varies directly as x and inversely as z, y = 10 when x = 5, z = 2. Find y when x = 10, z = 4:
  A. 10
  B. 5
  C. 2.5
  D. 20
32. y varies directly as x² and inversely as z³. If y = 27 when x = 3, z = 1, find y when x = 6, z = 2:
  A. 54
  B. 27
  C. 81
  D. 12
33. y varies jointly as x, z², w³. If y = 8 when x = 1, z = 2, w = 1, find y when x = 2, z = 1, w = 2:
  A. 8
  B. 16
  C. 4
  D. 2
34. y varies inversely as x and y = 12 when x = 3. Find y when x = 6:
  A. 6
  B. 4
  C. 8
  D. 2
35. If y varies directly as x² and y = 16 when x = 2, find y when x = 4:
  A. 32
  B. 64
  C. 48
  D. 24
36. y varies inversely as x² and y = 18 when x = 3. Find y when x = 6:
  A. 4.5
  B. 9
  C. 3
  D. 2
37. y varies directly as x³ and inversely as z. If y = 8 when x = 2, z = 1, find y when x = 4, z = 2:
  A. 16
  B. 32
  C. 64
  D. 8
38. y varies jointly as x², z, and w. If y = 12 when x = 2, z = 1, w = 3, find y when x = 4, z = 2, w = 1:
  A. 16
  B. 32
  C. 48
  D. 24
39. y varies inversely as x² and directly as z². If y = 9 when x = 3, z = 2, find y when x = 6, z = 4:
  A. 9
  B. 8
  C. 4
  D. 2
40. y varies directly as x² and inversely as z. If y = 12 when x = 3, z = 2, find y when x = 6, z = 3:
  A. 24
  B. 36
  C. 48
  D. 12
41. y varies jointly as x² and z². If y = 8 when x = 1, z = 2, find y when x = 2, z = 1:
  A. 2
  B. 4
  C. 8
  D. 16
42. If y varies directly as x and inversely as z, y = 15 when x = 5, z = 3. Find y when x = 3, z = 5:
  A. 9
  B. 5
  C. 6
  D. 3
43. y varies inversely as x³. If y = 8 when x = 2, find y when x = 4:
  A. 1
  B. 2
  C. 4
  D. 1
44. y varies directly as x² and inversely as z. If y = 18 when x = 3, z = 2, find y when x = 6, z = 3:
  A. 24
  B. 36
  C. 48
  D. 12
45. y varies jointly as x and z. If y = 12 when x = 2, z = 3, find y when x = 4, z = 6:
  A. 48
  B. 24
  C. 12
  D. 36
Answers – List Form
1. B
2. A
3. C
4. C
5. B
6. B
7. B
8. C
9. C
10. B
11. A
12. A
13. C
14. D
15. B
16. B
17. B
18. D
19. C
20. A
21. B
22. B
23. B
24. A
25. B
26. B
27. B
28. A
29. B
30. B
31. B
32. B
33. B
34. A
35. B
36. A
37. B
38. C
39. C
40. B
41. B
42. A
43. D
44. B
45. B
January 25, 2026
Class 10 Mathematics Chapter 2: Theory of Quadratic Equations – MCQs
Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers the theory and properties of quadratic equations, including discriminant, nature of roots, relation between roots and coefficients, factorization, sum and product of roots, and application-based problems. It is ideal for exam revision and self-assessment.

MCQs – Theory of Quadratic Equations (Class 10)
1. If α and β are roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0, then α + β = ?
  A. 5
  B. 6
  C. −5
  D. −6
2. If the roots of $x^2 − kx + 12 = 0$ x2−kx+12=0 are equal, k = ?
  A. 6
  B. 8
  C. 4
  D. −4
3. Discriminant of $x^2 − 4x + 5 = 0$ x2−4x+5=0 is:
  A. −4
  B. 4
  C. 0
  D. −1
4. The roots of $x^2 − 7x + 12 = 0$ x2−7x+12=0 are:
  A. 3, 4
  B. 4, 3
  C. −3, −4
  D. 2, 6
5. If one root of $x^2 − 6x + 5 = 0$ x2−6x+5=0 is 1, the other root is:
  A. 5
  B. −5
  C. 6
  D. 4
6. Product of roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 6
  B. 5
  C. −6
  D. −5
7. Sum of roots of $3x^2 − 12x + 9 = 0$ 3×2−12x+9=0 is:
  A. 4
  B. 3
  C. −4
  D. 12
8. Roots of $x^2 + 4x + 4 = 0$ x2+4x+4=0 are:
  A. −2, −2
  B. 2, 2
  C. 2, −2
  D. −4, 1
9. If roots of $x^2 − 8x + 15 = 0$ x2−8x+15=0 are in the ratio 3:2, then the roots are:
  A. 3, 5
  B. 5, 3
  C. 6, 10
  D. 2, 3
10. If α and β are roots of $x^2 − 3x − 10 = 0$ x2−3x−10=0, then αβ = ?
  A. −10
  B. 10
  C. 3
  D. −3
11. If one root of $x^2 − 7x + 12 = 0$ x2−7x+12=0 is 4, the other root is:
  A. 3
  B. 2
  C. 5
  D. 6
12. Sum of squares of roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 11
  B. 10
  C. 13
  D. 12
13. If α and β are roots of $x^2 + 3x − 4 = 0$ x2+3x−4=0, then 1/α + 1/β = ?
  A. −3/4
  B. 3/4
  C. 1
  D. −1
14. Quadratic equation whose roots are 2 and 3 is:
  A. $x^2 − 5x + 6 = 0$ x2−5x+6=0
  B. $x^2 + 5x − 6 = 0$ x2+5x−6=0
  C. $x^2 − x − 6 = 0$ x2−x−6=0
  D. $x^2 − 6x + 5 = 0$ x2−6x+5=0
15. Roots of $x^2 − 4x + 3 = 0$ x2−4x+3=0 are:
  A. 1, 3
  B. 3, 1
  C. −1, −3
  D. 2, 3
16. Nature of roots of $x^2 + x + 1 = 0$ x2+x+1=0 is:
  A. Complex
  B. Real and equal
  C. Real and distinct
  D. Zero
17. If α + β = 7 and αβ = 12, the quadratic equation is:
  A. $x^2 − 7x + 12 = 0$ x2−7x+12=0
  B. $x^2 + 7x + 12 = 0$ x2+7x+12=0
  C. $x^2 − 12x + 7 = 0$ x2−12x+7=0
  D. $x^2 + 12x + 7 = 0$ x2+12x+7=0
18. If roots of $x^2 − 2x − 8 = 0$ x2−2x−8=0 are α and β, then α − β = ?
  A. 4
  B. 6
  C. 2√3
  D. √12
19. One root of $x^2 − 9x + 20 = 0$ x2−9x+20=0 is 4. The other root is:
  A. 5
  B. 4
  C. 6
  D. 3
20. Quadratic equation with roots −2 and 3 is:
  A. $x^2 − x − 6 = 0$ x2−x−6=0
  B. $x^2 + x − 6 = 0$ x2+x−6=0
  C. $x^2 + x + 6 = 0$ x2+x+6=0
  D. $x^2 − x + 6 = 0$ x2−x+6=0
21. If α and β are roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0, then α² + β² = ?
  A. 13
  B. 11
  C. 10
  D. 12
22. One root of $x^2 − 6x + 8 = 0$ x2−6x+8=0 is 2. The other root is:
  A. 4
  B. 2
  C. 6
  D. 3
23. Roots of $x^2 − x − 6 = 0$ x2−x−6=0 are:
  A. 3, −2
  B. −3, 2
  C. 2, −3
  D. −2, 3
24. If roots of $x^2 + 2x − 15 = 0$ x2+2x−15=0 are α and β, then α³ + β³ = ?
  A. 50
  B. 35
  C. 40
  D. 45
25. If roots of $x^2 − 7x + 12 = 0$ x2−7x+12=0 are equal, then discriminant is:
  A. 0
  B. 1
  C. −1
  D. 2
26. If one root of $x^2 − kx + 16 = 0$ x2−kx+16=0 is 4, the other root is:
  A. 4
  B. k − 4
  C. 2
  D. 3
27. Sum of reciprocals of roots of $x^2 − 3x − 4 = 0$ x2−3x−4=0 is:
  A. 3/−4
  B. −3/4
  C. −4/3
  D. 4/3
28. If α = 2β and α + β = 6, the roots of the quadratic are:
  A. 4, 2
  B. 2, 4
  C. 3, 1
  D. 1, 3
29. Roots of $x^2 + 5x + 6 = 0$ x2+5x+6=0 are:
  A. −2, −3
  B. 2, 3
  C. −1, −6
  D. 1, 6
30. One root of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is 3. The other root is:
  A. 2
  B. 3
  C. 1
  D. 4
31. αβ if α and β are roots of $x^2 − 8x + 12 = 0$ x2−8x+12=0 is:
  A. 12
  B. 8
  C. 10
  D. 6
32. Nature of roots of $x^2 − 4x + 4 = 0$ x2−4x+4=0 is:
  A. Equal and real
  B. Distinct and real
  C. Complex
  D. Zero
33. α + β if α and β are roots of $x^2 − 6x + 5 = 0$ x2−6x+5=0 is:
  A. 6
  B. 5
  C. 1
  D. 11
34. Roots of $x^2 − 10x + 21 = 0$ x2−10x+21=0 are:
  A. 3, 7
  B. 7, 3
  C. −3, −7
  D. 5, 6
35. Sum of squares of roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 13
  B. 11
  C. 10
  D. 12
36. One root of $x^2 − 2x − 8 = 0$ x2−2x−8=0 is 4. The other root is:
  A. −2
  B. 2
  C. −4
  D. 2
37. If α + β = 7, αβ = 12, then quadratic equation is:
  A. $x^2 − 7x + 12 = 0$ x2−7x+12=0
  B. $x^2 + 7x + 12 = 0$ x2+7x+12=0
  C. $x^2 − 12x + 7 = 0$ x2−12x+7=0
  D. $x^2 + 12x + 7 = 0$ x2+12x+7=0
38. α² − β² if α = 3, β = 1 is:
  A. 8
  B. 4
  C. 2
  D. 1
39. Quadratic equation whose roots are reciprocals of 2 and 3 is:
  A. $6x^2 − 5x + 1 = 0$ 6×2−5x+1=0
  B. $x^2 − 5x + 6 = 0$ x2−5x+6=0
  C. $2x^2 − 5x + 6 = 0$ 2×2−5x+6=0
  D. $3x^2 − 5x + 2 = 0$ 3×2−5x+2=0
40. Roots of $x^2 − 3x + 2 = 0$ x2−3x+2=0 are:
  A. 1, 2
  B. 2, 1
  C. −1, −2
  D. 3, 2
41. If one root of $x^2 − 6x + 9 = 0$ x2−6x+9=0 is 3, the other root is:
  A. 3
  B. −3
  C. 2
  D. 1
42. α/β + β/α if α and β are roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 17/6
  B. 13/6
  C. 3/2
  D. 7/3
43. Roots of $x^2 − 8x + 16 = 0$ x2−8x+16=0 are:
  A. 4, 4
  B. 8, 2
  C. 2, 8
  D. −4, 4
44. One root of $x^2 − 7x + 12 = 0$ x2−7x+12=0 is 4. The other root is:
  A. 3
  B. 2
  C. 5
  D. 6
45. If α + β = 5, αβ = 6, quadratic equation is:
  A. $x^2 − 5x + 6 = 0$ x2−5x+6=0
  B. $x^2 + 5x + 6 = 0$ x2+5x+6=0
  C. $x^2 − 6x + 5 = 0$ x2−6x+5=0
  D. $x^2 + 6x + 5 = 0$ x2+6x+5=0
Answers – List Form
1. A
2. C
3. A
4. A
5. A
6. A
7. A
8. A
9. A
10. A
11. A
12. A
13. B
14. A
15. A
16. A
17. A
18. C
19. A
20. A
21. A
22. A
23. A
24. B
25. A
26. B
27. B
28. A
29. A
30. A
31. A
32. A
33. A
34. A
35. A
36. A
37. A
38. A
39. A
40. A
41. A
42. B
43. A
44. B
45. A
January 25, 2026
Class 10 Mathematics Chapter 1: Quadratic Equations – MCQs -(FBISE)
Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers all essential topics of quadratic equations including factorization, roots, discriminant, nature of roots, relations between roots, and application-based problems. Perfect for exam practice, self-assessment, and revision before your Class 10 exams.

MCQs – Quadratic Equations
1. If the roots of $x^2 – 5x + 6 = 0$ x2−5x+6=0 are α and β, then α + β = ?
  A. 5
  B. 6
  C. −5
  D. −6
2. If one root of $x^2 – 7x + k = 0$ x2−7x+k=0 is 3, the value of k is:
  A. 10
  B. 12
  C. 15
  D. 21
3. The roots of $2x^2 – 7x + 3 = 0$ 2×2−7x+3=0 are:
  A. 1, 3/2
  B. 3, 1/2
  C. 3/2, 1
  D. −1, 3
4. For $x^2 + 4x + 5 = 0$ x2+4x+5=0, the discriminant is:
  A. 4
  B. −4
  C. −1
  D. 0
5. If the roots of $x^2 – 8x + 15 = 0$ x2−8x+15=0 are in the ratio 3:2, then the roots are:
  A. 3, 5
  B. 3, 2
  C. 6, 10
  D. 5, 3
6. Which of the following has equal roots?
  A. $x^2 – 6x + 9 = 0$ x2−6x+9=0
  B. $x^2 – 7x + 12 = 0$ x2−7x+12=0
  C. $x^2 – 5x + 6 = 0$ x2−5x+6=0
  D. $x^2 + 3x + 2 = 0$ x2+3x+2=0
7. If α and β are roots of $x^2 – 5x + 6 = 0$ x2−5x+6=0, then αβ = ?
  A. 6
  B. 5
  C. −6
  D. 1
8. Sum of roots of $3x^2 – 12x + 9 = 0$ 3×2−12x+9=0 is:
  A. 3
  B. 4
  C. 12
  D. −4
9. One root of $x^2 – 9x + 14 = 0$ x2−9x+14=0 is 7. The other root is:
  A. 2
  B. 3
  C. 4
  D. 5
10. If the roots of $x^2 + 2x – 15 = 0$ x2+2x−15=0 are α and β, then α − β = ?
  A. 8
  B. 7
  C. 6
  D. 5
11. Quadratic equation whose roots are 2 and −3 is:
  A. $x^2 + x − 6 = 0$ x2+x−6=0
  B. $x^2 − x − 6 = 0$ x2−x−6=0
  C. $x^2 + x + 6 = 0$ x2+x+6=0
  D. $x^2 − 5x + 6 = 0$ x2−5x+6=0
12. If the roots of $x^2 + kx + 12 = 0$ x2+kx+12=0 are equal, k = ?
  A. 4
  B. −4
  C. 6
  D. −6
13. If α and β are roots of $x^2 − 4x + 3 = 0$ x2−4x+3=0, then 1/α + 1/β = ?
  A. 4/3
  B. 3/4
  C. 1
  D. −1
14. If one root of $x^2 + px + 2 = 0$ x2+px+2=0 is 2, find p.
  A. −3
  B. 3
  C. −4
  D. 4
15. Roots of $x^2 + 5x + 6 = 0$ x2+5x+6=0 are:
  A. −2, −3
  B. 2, 3
  C. −1, −6
  D. 1, 6
16. If roots of $2x^2 − 7x + 3 = 0$ 2×2−7x+3=0 are α and β, then α/β + β/α = ?
  A. 7/3
  B. 17/6
  C. 13/6
  D. 3/2
17. α² + β² if α and β are roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 13
  B. 25
  C. 11
  D. 10
18. Roots of $x^2 − 3x − 10 = 0$ x2−3x−10=0 are in AP. The roots are:
  A. −2, 5
  B. 2, −5
  C. 5, −2
  D. −5, 2
19. Equation whose roots are reciprocals of roots of $x^2 − 4x + 3 = 0$ x2−4x+3=0 is:
  A. $3x^2 − 4x + 1 = 0$ 3×2−4x+1=0
  B. $x^2 − 3x + 4 = 0$ x2−3x+4=0
  C. $x^2 − 4x + 3 = 0$ x2−4x+3=0
  D. $4x^2 − 3x + 1 = 0$ 4×2−3x+1=0
20. Roots of $x^2 − x − 6 = 0$ x2−x−6=0 are:
  A. 3, −2
  B. −3, 2
  C. 2, −3
  D. −2, 3
21. If sum of roots of $x^2 − kx + 12 = 0$ x2−kx+12=0 is 7, then k = ?
  A. 7
  B. −7
  C. 12
  D. −12
22. One root of $x^2 − 8x + 12 = 0$ x2−8x+12=0 is 6. The other root is:
  A. 2
  B. 3
  C. 4
  D. 5
23. $x^2 − 2kx + k = 0$ x2−2kx+k=0 has equal roots for k = ?
  A. 1
  B. 2
  C. 4
  D. 0
24. Sum of squares of roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 25
  B. 13
  C. 11
  D. 6
25. If roots of $x^2 − 6x + 8 = 0$ x2−6x+8=0 are α and β, 1/α + 1/β = ?
  A. 3/4
  B. 4/3
  C. 1
  D. 2
26. Roots of $x^2 − x − 12 = 0$ x2−x−12=0 are:
  A. 4, −3
  B. −4, 3
  C. 3, −4
  D. −3, 4
27. One root of $2x^2 − 5x + 2 = 0$ 2×2−5x+2=0 is 2. The other root is:
  A. 1/2
  B. 1
  C. 2
  D. −1
28. Product of roots of $x^2 − 7x + 12 = 0$ x2−7x+12=0 is:
  A. 12
  B. 7
  C. −12
  D. 5
29. Roots of $x^2 − 2x − 15 = 0$ x2−2x−15=0 are:
  A. 5, −3
  B. −5, 3
  C. 3, −5
  D. −3, 5
30. One root of $x^2 − kx + 16 = 0$ x2−kx+16=0 is 4. The other root is:
  A. 4
  B. 12
  C. k − 4
  D. 16
31. Quadratic equation with roots 1/2 and 1/3 is:
  A. $6x^2 − 5x + 1 = 0$ 6×2−5x+1=0
  B. $2x^2 − 5x + 6 = 0$ 2×2−5x+6=0
  C. $x^2 − 5x + 6 = 0$ x2−5x+6=0
  D. $3x^2 − 5x + 2 = 0$ 3×2−5x+2=0
32. If α and β are roots of $x^2 − 3x + 2 = 0$ x2−3x+2=0, then 1/α² + 1/β² = ?
  A. 5/4
  B. 1/4
  C. 4/5
  D. 2/3
33. One root of $x^2 − 5x + k = 0$ x2−5x+k=0 is twice the other, k = ?
  A. 0
  B. 2
  C. 4
  D. 6
34. If roots of $x^2 − x − 6 = 0$ x2−x−6=0 are α and β, then α³ + β³ = ?
  A. 35
  B. 27
  C. 28
  D. 26
35. Quadratic equation whose roots differ by 1 and sum to 7 is:
  A. $x^2 − 7x + 12 = 0$ x2−7x+12=0
  B. $x^2 − 6x + 12 = 0$ x2−6x+12=0
  C. $x^2 − 7x + 10 = 0$ x2−7x+10=0
  D. $x^2 − 6x + 10 = 0$ x2−6x+10=0
36. α³ + β³ if α and β are roots of $x^2 − 5x + 6 = 0$ x2−5x+6=0 is:
  A. 50
  B. 35
  C. 40
  D. 30
37. If roots of $x^2 + px + q = 0$ x2+px+q=0 are equal, then p² − 4q = ?
  A. 0
  B. 1
  C. 2
  D. −1
38. One root of $x^2 − 4x + 4 = 0$ x2−4x+4=0 is:
  A. 2
  B. 4
  C. 1
  D. 0
39. α² + β² if α and β are roots of $x^2 + 3x + 2 = 0$ x2+3x+2=0 is:
  A. 1
  B. 5
  C. 13
  D. 9
40. One root of $x^2 − 7x + 12 = 0$ x2−7x+12=0 is 3. The other root is:
  A. 4
  B. 5
  C. 6
  D. 2
41. Roots of $x^2 − 6x + 5 = 0$ x2−6x+5=0 are:
  A. 1, 5
  B. −1, 5
  C. 1, −5
  D. −1, −5
42. Sum of squares of roots of $x^2 − 10x + 21 = 0$ x2−10x+21=0 is:
  A. 50
  B. 58
  C. 49
  D. 60
43. Roots of $x^2 − 2x − 3 = 0$ x2−2x−3=0 are:
  A. 3, −1
  B. −3, 1
  C. 1, −3
  D. −1, 3
44. Roots of $x^2 − 5x + 4 = 0$ x2−5x+4=0 are:
  A. 4, 1
  B. 1, 4
  C. −1, 4
  D. 2, 2
45. If one root of $x^2 − 8x + 15 = 0$ x2−8x+15=0 is 3, the other root is:
  A. 5
  B. 6
  C. 4
  D. 2
Answers – List Form
1. A
2. C
3. C
4. B
5. A
6. A
7. A
8. B
9. A
10. B
11. A
12. B
13. A
14. A
15. A
16. B
17. C
18. A
19. A
20. A
21. A
22. A
23. B
24. B
25. B
26. A
27. A
28. A
29. B
30. C
31. A
32. A
33. C
34. A
35. A
36. A
37. A
38. A
39. B
40. A
41. A
42. C
43. A
44. A
45. A
January 25, 2026

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