Question 1

The sum of two numbers is 25 and their difference is 5. What are the numbers?

Accepted Answer

Correct Answer: 10, 15

Explanation: Let the numbers be x and y. x + y = 25 and x - y = 5. Adding both equations: 2x = 30, so x = 15. Substituting x into the first equation: 15 + y = 25, so y = 10. The numbers are 15 and 10. Option D is the same set, but A is usually the standard order representation.

Question 2

What is 10 cubed (10³)?

Accepted Answer

Correct Answer: 1000

Explanation: 10 cubed means 10 raised to the power of 3, or 10 multiplied by itself three times. 10 × 10 × 10 = 1000. It essentially means a 1 followed by three zeros. Understanding powers and exponents is fundamental for scientific notation and algebra.

Question 3

Find the median of 3, 5, 1, 9, 7.

Accepted Answer

Correct Answer: 5

Explanation: To find the median, first arrange the numbers in ascending order: 1, 3, 5, 7, 9. The median is the middle number. In this list of 5 numbers, the 3rd number is the middle one. So, the median is 5. If there were an even number of items, you would average the two middle numbers.

Question 4

If radius of a circle is 7 cm, its circumference is (use π=22/7):

Accepted Answer

Correct Answer: 44 cm

Explanation: The formula for circumference is C = 2πr. Substituting values: C = 2 × (22/7) × 7. The 7 in the numerator and denominator cancels out. C = 2 × 22 = 44 cm. Be careful not to confuse this with the Area formula (πr²).

Question 5

Convert 0.75 to a fraction.

Accepted Answer

Correct Answer: 3/4

Explanation: 0.75 can be written as 75/100. To simplify, divide both the numerator and denominator by their greatest common divisor, which is 25. 75 ÷ 25 = 3 and 100 ÷ 25 = 4. Thus, the fraction is 3/4. Converting decimals to fractions helps in easy calculation.

Question 6

What is the HCF of 12 and 18?

Accepted Answer

Correct Answer: 6

Explanation: HCF (Highest Common Factor) is the largest number that divides both numbers exactly. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3, 6. The highest among them is 6. HCF is helpful in simplifying fractions.

Question 7

A triangle with all sides equal is called:

Accepted Answer

Correct Answer: Equilateral

Explanation: An Equilateral triangle has all three sides of equal length. Consequently, all three internal angles are also equal, each measuring 60 degrees. An Isosceles triangle has two equal sides, and a Scalene triangle has no equal sides. This classification is based on side lengths.

Question 8

What is the value of Pi (π) approx?

Accepted Answer

Correct Answer: 3.14

Explanation: Pi (π) is the ratio of a circle's circumference to its diameter. Its approximate value is 3.14159..., commonly approximated as 3.14 or the fraction 22/7. It is an irrational number, meaning its decimal representation never ends or repeats. It is used in calculating the area and circumference of circles.

Question 9

Solve: 1/2 + 1/4

Accepted Answer

Correct Answer: 3/4

Explanation: To add fractions, you need a common denominator. The LCM of 2 and 4 is 4. Convert 1/2 to 2/4. Now add: 2/4 + 1/4 = 3/4. Always simplify the fraction if possible (though 3/4 is already in simplest form). Understanding LCM is vital for fraction operations.

Question 10

What is the square root of 144?

Accepted Answer

Correct Answer: 12

Explanation: The square root of a number is a value that, when multiplied by itself, gives the original number. 12 × 12 = 144, so the square root of 144 is 12. Memorizing squares up to 20 is highly recommended for solving math problems quickly in competitive exams.

Question 11

If the cost price is 100 and selling price is 120, what is the profit percentage?

Accepted Answer

Correct Answer: 20%

Explanation: Profit = Selling Price - Cost Price = 120 - 100 = 20. Profit Percentage = (Profit / Cost Price) × 100. So, (20 / 100) × 100 = 20%. Profit percentage is always calculated on the Cost Price, not the Selling Price, unless specified otherwise.

Question 12

The sum of angles in a triangle is:

Accepted Answer

Correct Answer: 180°

Explanation: The sum of the interior angles of any triangle (Euclidean geometry) is always 180 degrees. This property holds true whether the triangle is equilateral, isosceles, or scalene. It is a fundamental theorem used to find missing angles. For a quadrilateral, the sum is 360 degrees.

Question 13

What is the smallest prime number?

Accepted Answer

Correct Answer: 2

Explanation: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. 0 and 1 are not prime numbers. The number 2 is the only even prime number and the smallest one. 3, 5, 7, etc., follow it. This is a common trick question in exams.

Question 14

If A:B = 2:3 and B:C = 4:5, what is A:B:C?

Accepted Answer

Correct Answer: 8:12:15

Explanation: To combine the ratios, make the common term B equal. Multiply the first ratio (2:3) by 4 to get 8:12. Multiply the second ratio (4:5) by 3 to get 12:15. Now that B is 12 in both, we can combine them directly as A:B:C = 8:12:15. This is the standard method for merging ratios.

Question 15

A car travels 120 km in 2 hours. What is its speed?

Accepted Answer

Correct Answer: 60 km/h

Explanation: Speed is defined as distance traveled per unit of time. The formula is: Speed = Distance / Time. Here, Distance = 120 km and Time = 2 hours. So, Speed = 120 / 2 = 60 km/h. This concept is the basis for all Time, Speed, and Distance problems, including relative speed.

Question 16

Complete the series: 2, 4, 8, 16, ...

Accepted Answer

Correct Answer: 32

Explanation: This is a Geometric Progression where each term is multiplied by 2 to get the next term. 2×2=4, 4×2=8, 8×2=16. Therefore, the next term will be 16×2 = 32. Recognizing the pattern (doubling) is key to solving number series questions quickly.

Question 17

What is the area of a square with side length 4 cm?

Accepted Answer

Correct Answer: 16 cm²

Explanation: The area of a square is calculated using the formula: Area = side × side (or side²). Here, the side is 4 cm. So, Area = 4 × 4 = 16 cm². Remember that area is always measured in square units. This formula is derived from the general area of a rectangle (length × width).

Question 18

Solve for x: 3x + 5 = 20

Accepted Answer

Correct Answer: 5

Explanation: To find the value of x, first subtract 5 from both sides of the equation: 3x = 20 - 5, which gives 3x = 15. Next, divide both sides by 3 to isolate x: x = 15 / 3. Therefore, x = 5. This is a basic linear equation problem involving transposition.

Question 19

What is 20% of 500?

Accepted Answer

Correct Answer: 100

Explanation: To find the percentage of a number, multiply the number by the percentage fraction. 20% means 20/100. So, 500 × (20/100) = 500 × 0.2. Canceling the zeros, 5 × 20 = 100. Percentage calculations are crucial for Profit & Loss and Discount problems.

Question 20

If the average of 5 numbers is 20, what is the sum of the numbers?

Accepted Answer

Correct Answer: 100

Explanation: The formula for average is: Average = Sum of terms / Number of terms. Here, Average = 20 and Number of terms = 5. Therefore, Sum = Average × Number of terms. Sum = 20 × 5 = 100. This is a fundamental concept in statistics often used in data interpretation questions.

Mathematics MCQs

The sum of two numbers is 25 and their difference is 5. What are the numbers?

What is 10 cubed (10³)?

Find the median of 3, 5, 1, 9, 7.

If radius of a circle is 7 cm, its circumference is (use π=22/7):

Convert 0.75 to a fraction.

What is the HCF of 12 and 18?

A triangle with all sides equal is called:

What is the value of Pi (π) approx?

Solve: 1/2 + 1/4

What is the square root of 144?

If the cost price is 100 and selling price is 120, what is the profit percentage?

The sum of angles in a triangle is:

What is the smallest prime number?

If A:B = 2:3 and B:C = 4:5, what is A:B:C?

A car travels 120 km in 2 hours. What is its speed?

Complete the series: 2, 4, 8, 16, ...

What is the area of a square with side length 4 cm?

Solve for x: 3x + 5 = 20

What is 20% of 500?

If the average of 5 numbers is 20, what is the sum of the numbers?