Mathematics Mcqs

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.
  
  

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.
  
  

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.
  
  

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 / 2 cancels 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.
  
  

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.
  
  

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 in 4 × 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.