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.
122
If 3x = 12, then 5x = ?
✅ 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.
123
A polygon with 8 sides is called:
✅ 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.
124
What is 10⁻² equivalent to?
✅ 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.
125
The reciprocal of 2/3 is:
✅ 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).
126
Find the volume of a cylinder with radius 2 and height 5.
✅ 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.
127
The binary equivalent of decimal number 5 is:
✅ 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.
128
Which of these fractions is equivalent to 3/5?
✅ 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.
129
If a circle has diameter 10, what is its radius?
✅ 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.
130
Calculate: 2 + 2 × 2 - 2
✅ 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.
131
The sum of two complementary angles is:
✅ 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.
132
What is the slope of the line y = 3x + 5?
✅ 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.
133
Find the LCM of 2, 3, and 5.
✅ 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.
134
The diagonal of a square is 4√2 cm. What is its side?
✅ 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.
135
Convert 18 km/h to m/s.
✅ 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.
136
Which number is neither prime nor composite?
✅ 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.
137
If A = {1, 2, 3} and B = {3, 4, 5}, find A ∩ B.
✅ 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.
138
What is the value of 5! (5 factorial)?
✅ 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.
139
A cyclic quadrilateral is one whose vertices lie on a:
✅ 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.
140
Find the average of the first 5 multiples of 3.
✅ 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.