Mathematics MCQs include a wide range of solved multiple-choice questions from basic arithmetic to advanced mathematics. These questions cover topics such as Algebra, Geometry, Trigonometry, Calculus, Probability, Statistics, and Arithmetic. They are especially designed for students and candidates preparing for PPSC, FPSC, CSS, PMS, NTS, KPPSC, SPSC, and other competitive exams. Practicing these MCQs helps improve problem-solving skills, numerical ability, and analytical reasoning, making them ideal for both academic learning and job test preparation.
The correct answer is Same. In geometry, the distance between two parallel lines remains same at all points along their length. Parallel lines are defined as lines in a plane that never meet and are always the same distance apart. This distance is constant and does not decrease or increase. Therefore, the correct answer is Same.
The correct answer is 17/12. To add fractions 2/3 and 3/4, we need a common denominator. The least common denominator (LCD) of 3 and 4 is 12. Convert each fraction: 2/3 = 8/12, 3/4 = 9/12. Adding them: 8/12 + 9/12 = 17/12. 5/7 is the sum of numerators only, 5/12 is incorrect, and 7/12 is also incorrect. Therefore, 17/12 is the correct answer.
The correct answer is 9cm. The area of a triangle is given by the formula: Area = (1/2) × base × height. We are given Area = 126 cm² and base = 28 cm. So: 126 = (1/2) × 28 × height = 14 × height. Therefore, height = 126 ÷ 14 = 9 cm. 7cm, 8cm, and 10cm are incorrect values that do not satisfy the formula. Therefore, 9cm is the correct answer.
The correct answer is A ∩ B = φ. This notation states that the intersection of events A and B is the empty set, which perfectly describes mutual exclusivity.
Step-by-Step Explanation
Step 1 – Define mutually exclusive events:
Two events are mutually exclusive if they cannot occur simultaneously. For example, when rolling a die, getting a "2" and getting a "5" on the same single roll are mutually exclusive; both outcomes cannot happen at once.
Step 2 – Understand the set notation:
In probability, events are represented as sets of outcomes.
A ∩ B (A intersection B) is the set of outcomes that belong to both A and B.
φ (the Greek letter phi) denotes the empty set, meaning there are no elements.
Step 3 – Apply the definition:
For mutually exclusive events, there is no common outcome. Therefore, the set containing outcomes common to both A and B is empty.
This is written as: A ∩ B = φ
Step 4 – Eliminate incorrect options:
A ∩ B = S: This would mean the intersection is the entire sample space, implying A and B always happen together (the exact opposite of mutual exclusivity).
A ∪ B = φ: This would mean that neither A nor B ever happens, which is impossible for valid events.
A = B: If A and B are the same event, they always occur together, again contradicting mutual exclusivity.
Step 5 – Probability consequence:
For mutually exclusive events, P(A ∩ B) = 0, and the addition rule simplifies to P(A ∪ B) = P(A) + P(B).
Therefore, the correct relation for mutually exclusive events A and B is A ∩ B = φ.
The correct answer is 720. The factorial notation (!) means multiplying all positive integers from the number down to 1. The expression 10! / 7! can be simplified by expanding the factorials and cancelling common terms.
Step-by-Step Solution
Expand the Factorials:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
Cancel the Common Factor 7!:
10! / 7! = (10 × 9 × 8 × 7!) / 7!
The 7! in the numerator and denominator cancel out completely.
The correct answer is 300. We are told that 45% of the participants are boys, and the number of boys is 135. Using this information, we can find the total number of students by setting up a simple percentage equation.
Step-by-Step Solution
Understand the Relationship:
45% of the total students = Number of boys
Let the total number of students be T.
Write the Equation:
45% × T = 135
(45/100) × T = 135
Solve for T:
Multiply both sides by 100 to eliminate the denominator:
45 × T = 135 × 100
45T = 13,500
Divide both sides by 45:
T = 13,500 ÷ 45
T = 300
Verification:
45% of 300 = (45/100) × 300 = 0.45 × 300 = 135. The answer matches the given number of boys perfectly.
Hence, the total number of students participating is 300.
The correct answer is 25%. Percentage increase is calculated by finding the absolute increase (new value minus original value), dividing it by the original value, and then multiplying by 100.
Step-by-Step Solution
Identify Original and New Lengths:
Original length = 72 cm
New length = 90 cm
Calculate the Absolute Increase:
Increase = New length - Original length
Increase = 90 - 72 = 18 cm
Compute the Percentage Increase:
Percentage Increase = (Increase ÷ Original length) × 100
= (18 ÷ 72) × 100
= 0.25 × 100
= 25%
Verification:
25% of 72 cm = (25/100) × 72 = 18 cm.
72 cm + 18 cm = 90 cm, which matches the new length exactly.