What is the domain of the set R = {0, 2, 3}?
- {0, 1, 2, 3}
- {1, 2, 3}
- {0, 2, 3}
- {0, 1, 2}
{0, 2, 3} is the domain of the set R.
The domain of a set is simply the set itself.
Mathematics Mcqs
The standard form of a quadratic equation is ____.
- ax + b = 0
- ax³ + bx² + cx + d = 0
- ax² + bx + c = 0
- ax⁴ + bx³ + cx² + dx + e = 0
A Port had provisioned food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is:
Initially, food for 150 men for 45 days. After 10 days, food for 150 men for 35 days remains. With 25 men leaving, 125 men remain. The food will last for (150 * 35) / 125 = 42 days, making option C correct.
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Which of the following fractions is greater than 3/4 and less than 5/6
To find the fraction, convert them to decimals: 3/4 = 0.75 and 5/6 ≈ 0.833. Option C, 4/5 = 0.8, is the only fraction that falls between 0.75 and 0.833. Options A and B are too small.
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3.14 X 106 is equal to:
Multiplying 3.14 by 10 to the power of 6 (1,000,000) means moving the decimal point six places to the right, resulting in 3,140,000. Therefore, options A, B, and C are incorrect.
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P is 6 times greater than Q then by what percent is Q smaller than P?
If P is 6 times greater than Q, then Q is 1/6th of P. The percentage Q is smaller than P is ((P-Q)/P) * 100 = (5/6) * 100 = 83.33%. Thus, options A, B, and C are incorrect.
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The sum of the squares of two positive integers is 100 and the difference between their square is 28. The sum of the numbers is>
Let the integers be x and y. Given x² + y² = 100 and x² - y² = 28. Adding these equations yields 2x² = 128, so x = 8. Substituting x² = 64 into the first equation gives y² = 36, so y = 6. The sum is 8 + 6 = 14.
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There are twice as many boys as there are girls If 30% of the boys and 45%of the girls failed in the exams then what percentage of the class passed the exams?
The calculation shows that 65% of the class passed the exams, which is not among the given options, making "None of these" correct.
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A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours B atone for doing in:
To find B's time, calculate individual work rates. A's rate is 1/4. (A+C)'s rate is 1/2, so C's rate is 1/2 - 1/4 = 1/4. (B+C)'s rate is 1/3, so B's rate is 1/3 - 1/4 = 1/12. Therefore, B alone takes 12 hours to complete the work. Options A, B, and D are incorrect calculations.
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If Amna is x years old then 5 times Amna’s age three years ago is:
The correct answer is 5(x – 3) because the problem requires converting English language logic into a step-by-step algebraic expression.
- Step 1 (Past Age): Amna's current age is given as x. To find her age three years ago, we subtract 3 from her current age, giving us the expression
(x - 3). - Step 2 (Multiplication): The question specifically asks for 5 times her past age. We represent this by multiplying the entire past age grouping by 5, which results in
5(x - 3). - Incorrect Options:
- 3(x – 5) is incorrect because it represents 3 times Amna's age five years ago.
- 3(x + 5) is incorrect because it represents 3 times Amna's age five years into the future.
- None of these is incorrect because option 2 is the exact mathematical representation needed.
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Evaluate the expression: 27 / 3 + 4 ÷ 2 – 1
The correct answer is 10 because following the BODMAS / PEMDAS order of operations requires performing division before moving on to addition and subtraction.
- C. 10: This is the correct choice. The equation resolves step-by-step through standard mathematical order rules:
- Step 1 (Division): Evaluate both division operators. 27 / 3 = 9 and 4 div 2 = 2. This simplifies the expression to 9 + 2 - 1$.
- Step 2 (Addition): Add the numbers from left to right. 9 + 2 = 11$. The expression becomes 11- 1$.
- Step 3 (Subtraction): Subtract the final value. 11 - 1 = 10$.
- Incorrect Options:
- A. 0: This is incorrect. It usually results from neglecting order of operations entirely or subtracting values prematurely before resolving the division terms.
- B. 12: This is incorrect. It occurs if the arithmetic steps are miscalculated or if operations are forced sequentially from left to right without giving priority to division.
- D. None of these: This is incorrect because Option C yields the precise mathematical answer derived using universally accepted algebraic protocols.
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A sequence is called Arithmetic if it has:
The correct answer is Common difference because an arithmetic sequence progresses by adding or subtracting a fixed constant value between each consecutive term.
- Step 1 (Definition): A sequence is arithmetic if the difference between any two consecutive terms remains constant. This constant value is known as the common difference.
- Incorrect Options:
- Addition is incorrect because addition is the operational process used to apply the common difference, not the defining characteristic of the sequence itself.
- Common ratio is incorrect because a common ratio defines a geometric sequence, where each term is multiplied by a constant to get the next term.
- None of these is incorrect because the second option is the precise mathematical definition.
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Arithmetic mean between x -3 and x + 3 is:
The correct answer is x because the arithmetic mean of two terms is calculated by finding their average.
- Step 1 (Set up the formula): The arithmetic mean formula for two values a and b is
(a + b) / 2. Substituting our values gives((x - 3) + (x + 3)) / 2. - Step 2 (Simplify the numerator): Combining like terms in the numerator, the -3 and +3 cancel each other out, leaving
x + x = 2x. - Step 3 (Divide by 2): Dividing
2x / 2cancels out the 2s, which leaves us with x. - Incorrect Options:
- -6 is incorrect because it represents the difference between the bounds, not the central average.
- 6 is incorrect because it is the total distance between the two expressions, not their midpoint.
- None of these is incorrect because option 3 perfectly satisfies the arithmetic mean definition.
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A single A.M between a and b is:
The correct answer is (a+b)/2 because the standard formula for finding a single arithmetic mean (A.M.) between two values is their mathematical average.
- Step 1 (Definition): For any two numbers a and b, their single arithmetic mean forms an arithmetic progression sequence. This value sits exactly halfway between them.
- Step 2 (Formula Calculation): The midpoint formula is found by adding the two terms together and dividing the total sum by 2, which gives us
(a + b) / 2. - Incorrect Options:
- =√ab is incorrect because it represents the Geometric Mean (G.M.) between two positive numbers.
- 2ab/(a+b) is incorrect because it represents the Harmonic Mean (H.M.) between two numbers.
- None of these is incorrect because the first option is the exact mathematical standard for the arithmetic mean.
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Sum of 4 A.M between 18 and 3 is:
The correct answer is 42 because the sum of n arithmetic means between two numbers is always equal to n times their single arithmetic mean.
- Step 1 (Find the single A.M.): Calculate the single arithmetic mean between 18 and 3 using the average formula:
(18 + 3) / 2 = 21 / 2 = 10.5. - Step 2 (Calculate the sum): Use the property that the sum of n arithmetic means is
n × A.M.. For 4 means, this results in4 × 10.5 = 42. - Incorrect Options:
- 15 is incorrect because it is simply the absolute difference between 18 and 3, not the sum of the means.
- 12 is incorrect because it does not satisfy the property of the sequence's arithmetic progression.
- None of these is incorrect because option 3 matches the correct mathematical solution.
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In Roman numerals, “C” represents:
In the Roman numeral system, the letter "C" is the standard representation for the numerical value of 100.
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If sales tax is 3%, how much tax would you pay for an item that costs $2000
The correct answer is $60. The sales tax is calculated by multiplying the price of the item by the tax rate. In this case, the item costs $2000 and the tax rate is 3% (which is 0.03 as a decimal).
Step‑by‑Step Calculation
- Convert the percentage to a decimal: 3% = 3 ÷ 100 = 0.03.
- Multiply the price by the decimal tax rate: $2000 × 0.03 = $60.
- Alternatively, you can compute 3% of 2000 by first finding 1% (which is $20) and then multiplying by 3 – that also gives $60.
Therefore, the total tax you would pay is $60.
Why the Other Options Are Incorrect
- $80: This would be 4% of $2000 (2000 × 0.04 = 80), not 3%.
- $100: This is 5% of $2000 (2000 × 0.05 = 100), which is a higher tax rate.
- $400: This is 20% of $2000 (2000 × 0.20 = 400), far above the given 3% rate.
Only the $60 calculation correctly applies the 3% tax rate, making it the correct answer.
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What is the LCM of 70 and 80?
The Least Common Multiple (LCM) of 70 and 80 is 560, as it is the smallest positive integer divisible by both numbers.
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The radius of a circle is 10 cm and the length of one of its chords is 12 cm then the distance of the chord from the center is:
The correct answer is 8 cm. This problem is a classic application of the perpendicular from the center to a chord theorem in circle geometry. According to this theorem, a perpendicular drawn from the center of a circle to any chord bisects that chord, meaning it divides the chord into two equal halves.
Step‑by‑Step Solution
- Step 1: Visualize the right triangle. Draw a circle with center O. Let AB be a chord of length 12 cm. Draw a perpendicular from O to AB, meeting AB at point M. Since OM ⟂ AB, M is the midpoint of AB.
- Step 2: Find the half‑chord length. AM = MB = 12 ÷ 2 = 6 cm.
- Step 3: Identify the hypotenuse. In right triangle OMA, OA is the radius of the circle, so OA = 10 cm (the hypotenuse).
- Step 4: Apply the Pythagorean theorem. OM² + AM² = OA² → OM² + 6² = 10² → OM² + 36 = 100 → OM² = 64 → OM = √64 = 8 cm.
Thus, the perpendicular distance from the center to the chord is 8 cm.
Why the Other Options Are Incorrect
- 6 cm (Option 1): This is the length of the half‑chord (AM), not the distance from the center. Many confuse the two values.
- 10 cm (Option 3): This is the radius of the circle. The radius is the hypotenuse, not the distance from the center to the chord (which must be shorter than the radius).
- 12 cm (Option 4): This is the total length of the chord itself. The distance from the center to the chord is always less than the radius for any non‑diameter chord, so 12 cm (greater than 10) is geometrically impossible.
Hence, applying the perpendicular‑bisector theorem and the Pythagorean theorem confirms that the distance is exactly 8 cm.
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