Question 1

The value of Tan 45° is:

Accepted Answer

Correct Answer: 1

Explanation: Tan 45° = Sin 45° / Cos 45°. Since Sin 45° = 1/√2 and Cos 45° = 1/√2, dividing them gives 1. Alternatively, in a 45-45-90 triangle, the opposite and adjacent sides are equal length, so Opposite/Adjacent = 1. This is a very common value in height and distance problems.

Question 2

If 3x = 12, then 5x = ?

Accepted Answer

Correct Answer: 20

Explanation: First, solve for x. 3x = 12, so x = 12/3 = 4. Now substitute x=4 into the expression 5x. 5(4) = 20. This is a two-step algebraic substitution problem. Always find the value of the variable first before finding the value of the new expression.

Question 3

A polygon with 8 sides is called:

Accepted Answer

Correct Answer: Octagon

Explanation: An Octagon is a polygon with 8 sides and 8 angles. A Hexagon has 6 sides, a Heptagon has 7 sides, and a Decagon has 10 sides. The sum of interior angles of an octagon is 1080 degrees. Stop signs are the most common real-world example of a regular octagon.

Question 4

What is 10⁻² equivalent to?

Accepted Answer

Correct Answer: 0.01

Explanation: A negative exponent indicates the reciprocal of the base. 10⁻² = 1 / 10². Since 10² = 100, this becomes 1 / 100. In decimal form, 1/100 is 0.01. It moves the decimal point two places to the left. This notation is standard in scientific calculations.

Question 5

The reciprocal of 2/3 is:

Accepted Answer

Correct Answer: 3/2

Explanation: The reciprocal of a fraction is found by flipping the numerator and the denominator. So, the reciprocal of 2/3 is 3/2. In decimals, 2/3 is approx 0.66 and 3/2 is 1.5. The product of a number and its reciprocal is always 1 (Multiplicative Inverse).

Question 6

Find the volume of a cylinder with radius 2 and height 5.

Accepted Answer

Correct Answer: 20π

Explanation: The formula for the volume of a cylinder is V = πr²h. Here, r = 2 and h = 5. Substituting the values: V = π(2)²(5) = π(4)(5) = 20π. Volume represents the capacity of the cylinder. Don't forget to square the radius first before multiplying by height.

Question 7

The binary equivalent of decimal number 5 is:

Accepted Answer

Correct Answer: 101

Explanation: To convert 5 to binary: 4s place + 1s place = 5. In binary (Base 2), places are 4, 2, 1. We need one 4, zero 2s, and one 1. So, 101. Alternatively, divide 5 by 2: Quotient 2, Remainder 1. Divide 2 by 2: Quotient 1, Remainder 0. Final 1. Read remainders bottom-up: 101.

Question 8

Which of these fractions is equivalent to 3/5?

Accepted Answer

Correct Answer: 6/10

Explanation: To find an equivalent fraction, multiply the numerator and denominator by the same number. If we multiply 3/5 by 2/2, we get (3×2)/(5×2) = 6/10. Equivalent fractions represent the same value (0.6 in this case) but use different numbers. 6/10 simplifies back to 3/5.

Question 9

If a circle has diameter 10, what is its radius?

Accepted Answer

Correct Answer: 5

Explanation: The diameter is the longest chord of a circle, passing through the center. The radius is the distance from the center to the edge. Radius is exactly half of the diameter. Radius = Diameter / 2. So, Radius = 10 / 2 = 5. This is a basic definition in circle geometry.

Question 10

Calculate: 2 + 2 × 2 - 2

Accepted Answer

Correct Answer: 4

Explanation: Using BODMAS rule (Order of Operations), Multiplication comes before Addition and Subtraction. First, multiply 2 × 2 = 4. The expression becomes 2 + 4 - 2. Next, add: 2 + 4 = 6. Finally, subtract: 6 - 2 = 4. If you just calculated left to right without rules, you would get the wrong answer.

Question 11

The sum of two complementary angles is:

Accepted Answer

Correct Answer: 90°

Explanation: Complementary angles are defined as two angles that add up to exactly 90 degrees (a right angle). For example, 30° and 60° are complementary. Supplementary angles are those that add up to 180 degrees. Confusing these two is a common error in geometry exams.

Question 12

What is the slope of the line y = 3x + 5?

Accepted Answer

Correct Answer: 3

Explanation: The equation is in the Slope-Intercept form: y = mx + c, where 'm' is the slope and 'c' is the y-intercept. Comparing y = 3x + 5 with the standard formula, we see that m = 3. Therefore, the slope (gradient) of the line is 3. It represents the steepness of the line.

Question 13

Find the LCM of 2, 3, and 5.

Accepted Answer

Correct Answer: 30

Explanation: Since 2, 3, and 5 are all prime numbers, their Least Common Multiple (LCM) is simply their product. LCM = 2 × 3 × 5 = 6 × 5 = 30. There is no smaller number that is divisible by all three. This is a quick rule for finding LCM of distinct prime numbers.

Question 14

The diagonal of a square is 4√2 cm. What is its side?

Accepted Answer

Correct Answer: 4 cm

Explanation: The formula for the diagonal of a square is d = side × √2. Here, we are given d = 4√2. Comparing 4√2 = side × √2, we can clearly see that side = 4 cm. This relationship comes from the Pythagorean theorem applied to the triangle formed by two sides and the diagonal.

Question 15

Convert 18 km/h to m/s.

Accepted Answer

Correct Answer: 5 m/s

Explanation: To convert km/h to m/s, multiply the value by 5/18. So, 18 × (5/18). The 18 cancels out, leaving 5. So, 18 km/h is equal to 5 m/s. Conversely, to convert m/s to km/h, multiply by 18/5. This shortcut saves time in physics and math problems.

Question 16

Which number is neither prime nor composite?

Accepted Answer

Correct Answer: 1

Explanation: The number 1 is a unique number in mathematics. It is not prime because it does not have two distinct factors (1 and itself are the same). It is not composite because it cannot be formed by multiplying two smaller natural numbers. Therefore, 1 is neither prime nor composite.

Question 17

If A = {1, 2, 3} and B = {3, 4, 5}, find A ∩ B.

Accepted Answer

Correct Answer: {3}

Explanation: The symbol ∩ represents 'Intersection', which means finding the elements common to both sets. Set A has {1, 2, 3} and Set B has {3, 4, 5}. The only number present in both sets is 3. Therefore, A ∩ B = {3}. The union (∪) would be all elements combined.

Question 18

What is the value of 5! (5 factorial)?

Accepted Answer

Correct Answer: 120

Explanation: The factorial of a number n (denoted as n!) is the product of all positive integers less than or equal to n. 5! = 5 × 4 × 3 × 2 × 1. Calculating step-by-step: 5×4=20, 20×3=60, 60×2=120, 120×1=120. Factorials are used in permutations and combinations.

Question 19

A cyclic quadrilateral is one whose vertices lie on a:

Accepted Answer

Correct Answer: Circle

Explanation: A cyclic quadrilateral is a four-sided polygon whose vertices all touch a single circle. A key property of cyclic quadrilaterals is that their opposite angles sum to 180 degrees (they are supplementary). This property is frequently used to solve advanced geometry problems involving circles.

Question 20

Find the average of the first 5 multiples of 3.

Accepted Answer

Correct Answer: 9

Explanation: The first 5 multiples of 3 are: 3, 6, 9, 12, 15. Since this is an arithmetic progression (equally spaced numbers), the average is simply the middle number. The middle number is 9. Alternatively, (3+15)/2 = 18/2 = 9. Or sum them (45) and divide by 5 to get 9.

Mathematics MCQs