Explanation: This requires the algebraic expansion formula (a + b)² = a² + 2ab + b². Here, a = x and b = 2. Substituting these values: x² + 2(x)(2) + 2². Simplifying this gives x² + 4x + 4. A common mistake is to just square both terms (x² + 4), missing the middle term.
142
The lines which never intersect are called:
✅ Correct Answer:Parallel lines
Explanation: Parallel lines are two lines in a plane that do not meet or intersect each other at any point, no matter how far they are extended. They are always the same distance apart (equidistant). An example is the tracks of a railway line. Perpendicular lines meet at 90 degrees.
143
If 40% of a number is 80, what is 20% of that number?
✅ Correct Answer:40
Explanation: You can solve this using unitary method or ratios. If 40% = 80, then 1% = 80/40 = 2. Therefore, 20% would be 20 × 2 = 40. Alternatively, notice that 20% is exactly half of 40%, so the value must be half of 80, which is 40. Logic often beats calculation.
144
What is the value of Sin 90°?
✅ Correct Answer:1
Explanation: In trigonometry, the sine of an angle in a right-angled triangle is the ratio of the opposite side to the hypotenuse. For 90 degrees, the opposite side becomes equal to the hypotenuse, making the ratio 1. This is a fundamental value on the unit circle. Sin 0° is 0, and Sin 90° is 1.
145
Which of the following is a Pythogorean Triplet?
✅ Correct Answer:3, 4, 5
Explanation: A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c². For the set 3, 4, 5: 3² + 4² = 9 + 16 = 25, and 5² = 25. Since 25 = 25, it forms a right-angled triangle. This is the most common and basic triplet used in geometry problems.
146
If the side of a cube is 3 cm, what is its Volume?
✅ Correct Answer:27 cm³
Explanation: The volume of a cube is calculated using the formula V = s³, where 's' is the length of the side. Here, s = 3 cm. So, Volume = 3 × 3 × 3 = 27 cm³. Volume measures the amount of space occupied by a 3D object and is always expressed in cubic units.
147
The probability of rolling a number greater than 4 on a standard die is:
✅ Correct Answer:1/3
Explanation: A standard die has 6 faces numbered 1 to 6. The numbers greater than 4 are 5 and 6. So, there are 2 favorable outcomes. Total outcomes are 6. Probability = Favorable / Total = 2/6. Simplifying the fraction gives 1/3. This measures the chance of the event occurring.
148
Solve for x: log₁₀(100) = x
✅ Correct Answer:2
Explanation: Logarithm asks the question: 'To what power must the base (10) be raised to produce the number (100)?'. Since 10² = 10 × 10 = 100, the answer is 2. Therefore, log base 10 of 100 is 2. Understanding logs is essential for advanced algebra and calculus problems.
149
What is the sum of angles in a Quadrilateral?
✅ Correct Answer:360°
Explanation: A quadrilateral is a polygon with 4 sides. The sum of interior angles of any polygon is given by (n-2) × 180°, where n is the number of sides. For a quadrilateral, n=4, so sum = (4-2) × 180° = 2 × 180° = 360°. This holds true for squares, rectangles, parallelograms, and irregular quadrilaterals.
150
If a² - b² = 20 and a + b = 10, find the value of a - b.
✅ Correct Answer:2
Explanation: This problem uses the algebraic identity: a² - b² = (a + b)(a - b). We are given a² - b² = 20 and a + b = 10. Substituting these values into the formula gives: 20 = 10 × (a - b). Dividing both sides by 10, we get a - b = 2. This identity is very frequently tested in algebraic simplification.
151
The geometric mean of 4 and 16 is:
✅ Correct Answer:8
Explanation: Geometric Mean (GM) of two numbers a and b is √(ab). Here, a=4, b=16. GM = √(4 × 16) = √64 = 8. Arithmetic mean would be (4+16)/2 = 10. GM is used in growth rates and financial compounding.
152
Solve for y: 2y - 6 = 0
✅ Correct Answer:3
Explanation: First, add 6 to both sides: 2y = 6. Then divide by 2: y = 6 / 2 = 3. Checking the answer: 2(3) - 6 = 6 - 6 = 0. The solution satisfies the equation. This is a simple linear equation.
153
Which fraction is largest?
✅ Correct Answer:1/2
Explanation: When the numerator is the same (1), the fraction with the smaller denominator is the larger value. 1/2 = 0.5, 1/3 = 0.33, 1/4 = 0.25, 1/5 = 0.2. Clearly, 0.5 is the largest. Think of dividing a pizza: fewer slices means bigger pieces.
154
Total degrees in a circle is:
✅ Correct Answer:360°
Explanation: A full circle represents a complete rotation, which corresponds to 360 degrees. A semicircle is 180 degrees, and a quadrant (quarter circle) is 90 degrees. This concept is fundamental in geometry and trigonometry.
155
Triangle with one angle greater than 90° is called:
✅ Correct Answer:Obtuse Triangle
Explanation: An Obtuse Triangle has one interior angle measuring more than 90 degrees. An Acute Triangle has all angles less than 90 degrees. A Right Triangle has exactly one 90-degree angle. The sum of angles remains 180 degrees in all cases.
156
What is the product of 0.5 and 0.2?
✅ Correct Answer:0.1
Explanation: Ignore decimals first: 5 × 2 = 10. Now count total decimal places in the original numbers. 0.5 has one place, 0.2 has one place. Total = 2 places. Place the decimal in 10 such that there are 2 decimal digits: 0.10, which is 0.1. Be careful with decimal placement.
157
Solve: -5 + (-3)
✅ Correct Answer:-8
Explanation: When adding two negative numbers, you add their absolute values and keep the negative sign. |-5| + |-3| = 5 + 3 = 8. Since both were negative, the result is -8. Think of it as debt: if you owe 5 and borrow 3 more, you now owe 8.
158
Find the mode of: 2, 4, 4, 6, 7, 4.
✅ Correct Answer:4
Explanation: Mode is the number that appears most frequently in a dataset. In the set {2, 4, 4, 6, 7, 4}, the number 4 appears three times, which is more than any other number. Thus, 4 is the mode. A set can have more than one mode (bimodal) or no mode.
159
If the radius of a circle is doubled, its area increases by:
✅ Correct Answer:4 times
Explanation: Area = πr². If new radius R = 2r, then new Area = π(2r)² = π(4r²) = 4πr². This means the new area is 4 times the original area. When dimensions are scaled by factor k, area scales by k².
160
A dozen consists of how many items?
✅ Correct Answer:12
Explanation: A dozen is a unit of quantity that equals 12 items. It is commonly used for selling eggs, bananas, etc. A 'Baker's Dozen' is 13. A 'Gross' is a dozen dozens, which is 144 items. This is a basic unit of measurement in daily life.