Question 1

Evaluate 4! / 2!

Accepted Answer

Correct Answer: 12

Explanation: Expand the factorials: 4! = 4 × 3 × 2 × 1 = 24. 2! = 2 × 1 = 2. Now divide: 24 / 2 = 12. Alternatively, cancel out terms: (4 × 3 × 2!) / 2!. The 2! cancels out, leaving 4 × 3 = 12. This method is faster for larger factorials.

Question 2

Which quadrilateral has diagonals that bisect each other at 90°?

Accepted Answer

Correct Answer: Rhombus

Explanation: In a Rhombus (and a Square), the diagonals bisect each other at right angles (90 degrees). While diagonals of a rectangle and parallelogram bisect each other, they do not necessarily do so at 90 degrees. This property allows us to calculate the area of a rhombus as (d1 × d2) / 2.

Question 3

If 2x + 3 = 11, what is x - 2?

Accepted Answer

Correct Answer: 2

Explanation: First, solve for x. 2x = 11 - 3, so 2x = 8. Dividing by 2 gives x = 4. The question asks for the value of x - 2. Substituting x=4, we get 4 - 2 = 2. Always read the question carefully; it asked for 'x-2', not just 'x'.

Question 4

The slope of a horizontal line is:

Accepted Answer

Correct Answer: 0

Explanation: A horizontal line runs straight left to right and does not rise or fall. Since the change in y (rise) is 0 for any change in x (run), the slope m = 0/run = 0. The equation of a horizontal line is of the form y = b. This is crucial for coordinate geometry graphs.

Question 5

What is the next prime number after 7?

Accepted Answer

Correct Answer: 11

Explanation: We check integers greater than 7. 8 is divisible by 2. 9 is divisible by 3. 10 is divisible by 2 and 5. 11 has no divisors other than 1 and itself. Therefore, 11 is the next prime number. 9 is a common wrong answer because it is odd, but it is composite (3×3).

Question 6

If A is a subset of B, then A ∪ B is equal to:

Accepted Answer

Correct Answer: B

Explanation: If A is a subset of B (A ⊆ B), it means all elements of A are already inside B. The Union operation (∪) combines all unique elements from both sets. Since A adds nothing new to B, the result is simply the larger set B. Conversely, the Intersection (A ∩ B) would be A.

Question 7

The sum of interior angles of a pentagon is:

Accepted Answer

Correct Answer: 540°

Explanation: The sum of interior angles is calculated using the formula (n-2) × 180°, where n is the number of sides. For a pentagon, n = 5. Sum = (5-2) × 180° = 3 × 180° = 540°. This formula works for any convex polygon. A hexagon (n=6) would be 720°.

Question 8

Solve for x: |x| = 5

Accepted Answer

Correct Answer: ±5

Explanation: The absolute value function |x| represents the distance of x from zero. Since both 5 and -5 are exactly 5 units away from zero, the equation |x| = 5 has two solutions: x = 5 and x = -5. In formal notation, this is written as x = ±5. Do not forget the negative solution.

Question 9

Which term describes data that appears most frequently?

Accepted Answer

Correct Answer: Mode

Explanation: The Mode is the value that appears most often in a data set. For example, in {2, 5, 5, 8}, the mode is 5. It is the only measure of central tendency that can be used for categorical data (like 'Red', 'Blue', 'Red'). A set can have no mode, one mode, or multiple modes.

Question 10

Find the volume of a sphere with radius r.

Accepted Answer

Correct Answer: 4/3 πr³

Explanation: The formula for the volume of a sphere is V = (4/3)πr³. It measures the space occupied by the sphere. Don't confuse it with the formula for Surface Area, which is 4πr². Volume is cubic (r³), while area is square (r²). This formula was first derived by Archimedes.

Question 11

What is the HCF of two prime numbers?

Accepted Answer

Correct Answer: 1

Explanation: Prime numbers have only two factors: 1 and the number itself. Since two distinct prime numbers share no factors other than 1, their Highest Common Factor (HCF) or Greatest Common Divisor (GCD) is always 1. For example, HCF of 3 and 7 is 1. Such numbers are called co-prime.

Question 12

If a line is vertical, its slope is:

Accepted Answer

Correct Answer: Undefined

Explanation: The slope is defined as 'rise over run' (change in y / change in x). For a vertical line, the 'run' (change in x) is zero because it doesn't move left or right. Division by zero is mathematically undefined (or infinite). Therefore, vertical lines have an undefined slope. Horizontal lines have a slope of 0.

Question 13

The sum of probabilities of all possible outcomes of an event is always:

Accepted Answer

Correct Answer: 1

Explanation: In probability theory, the sum of probabilities of all mutually exclusive and exhaustive outcomes is exactly 1 (or 100%). This implies that one of the possible outcomes must happen. For a coin toss, P(Head) + P(Tail) = 0.5 + 0.5 = 1. Probability values range from 0 to 1.

Question 14

A matrix with only one row is called:

Accepted Answer

Correct Answer: Row Matrix

Explanation: A matrix that consists of a single row is called a Row Matrix or Row Vector. Its order is 1 × n (1 row, n columns). For example, [1 2 3] is a row matrix. Conversely, a matrix with only one column is called a Column Matrix. This classification is based on dimensions.

Question 15

The roots of the equation x² - 9 = 0 are:

Accepted Answer

Correct Answer: 3, -3

Explanation: To solve x² - 9 = 0, add 9 to both sides: x² = 9. Taking the square root of both sides gives x = ±√9. Therefore, x = 3 or x = -3. Alternatively, factor it as a difference of squares: (x-3)(x+3) = 0. Both methods yield the roots 3 and -3.

Question 16

What is the value of 5⁰ + 5¹?

Accepted Answer

Correct Answer: 6

Explanation: Any non-zero number raised to the power of 0 is 1. So, 5⁰ = 1. Any number raised to the power of 1 is the number itself. So, 5¹ = 5. Adding them together: 1 + 5 = 6. A common mistake is to think 5⁰ is 0, which would lead to the wrong answer.

Question 17

Evaluate: Sin²θ + Cos²θ

Accepted Answer

Correct Answer: 1

Explanation: This is the most fundamental Pythagorean identity in trigonometry. For any angle θ, the square of the sine plus the square of the cosine always equals 1. This comes from the Pythagorean theorem (Opposite² + Adjacent² = Hypotenuse²) applied to a right triangle with a hypotenuse of 1 on the unit circle.

Question 18

The range of the data set 5, 10, 15, 20, 25 is:

Accepted Answer

Correct Answer: 20

Explanation: Range is a measure of dispersion in statistics. It is calculated as the difference between the largest value and the smallest value in a data set. Here, Largest = 25 and Smallest = 5. So, Range = 25 - 5 = 20. It gives a quick idea of the spread of the data.

Question 19

What is the determinant of a 2x2 Identity Matrix?

Accepted Answer

Correct Answer: 1

Explanation: An Identity Matrix has 1s on the main diagonal and 0s elsewhere. For a 2x2 identity matrix [[1, 0], [0, 1]], the determinant is calculated as (1×1) - (0×0) = 1. In fact, the determinant of an identity matrix of any size is always 1. It acts like the number 1 in matrix multiplication.

Question 20

The set of all possible subsets of a set is called:

Accepted Answer

Correct Answer: Power Set

Explanation: The Power Set is the set that contains all possible subsets of a given set, including the empty set and the set itself. If a set has 'n' elements, its power set will have 2ⁿ elements. For example, if A={1,2}, the Power Set is { {}, {1}, {2}, {1,2} }. It is a fundamental concept in Set Theory.

Mathematics MCQs

Evaluate 4! / 2!

Which quadrilateral has diagonals that bisect each other at 90°?

If 2x + 3 = 11, what is x - 2?

The slope of a horizontal line is:

What is the next prime number after 7?

If A is a subset of B, then A ∪ B is equal to:

The sum of interior angles of a pentagon is:

Solve for x: |x| = 5

Which term describes data that appears most frequently?

Find the volume of a sphere with radius r.

What is the HCF of two prime numbers?

If a line is vertical, its slope is:

The sum of probabilities of all possible outcomes of an event is always:

A matrix with only one row is called:

The roots of the equation x² - 9 = 0 are:

What is the value of 5⁰ + 5¹?

Evaluate: Sin²θ + Cos²θ

The range of the data set 5, 10, 15, 20, 25 is:

What is the determinant of a 2x2 Identity Matrix?

The set of all possible subsets of a set is called: