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All questions of Mathematical Operations for UPSC CSE Exam

Find out the two signs to be interchanged for making the equation correct
53 - 3 × 3/53 + 53 = 53
  • a)
    / and +
  • b)
    / and –
  • c)
    / and ×
  • d)
    None of the above
Correct answer is option 'C'. Can you explain this answer?

Debolina Bose answered

Explanation:

Given Equation:
53 - 3 × 3/53 + 53 = 53

Interchanging Signs:
To make the equation correct, we need to interchange the signs of the operators × and +.

Corrected Equation:
53 - 3 + 3/53 × 53 = 53

Explanation:
By interchanging the signs of the operators × and +, the equation becomes mathematically correct. The corrected equation now follows the correct order of operations, which is multiplication and division before addition and subtraction.

Therefore, the correct signs to be interchanged in the equation are × and +, which is option C.

If + means ÷, ÷ means -, - means x, x means +, then 12 + 6 ÷ 3 - 2 × 8 = ?
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    6
Correct answer is option 'C'. Can you explain this answer?

Understanding the Problem
To solve the expression according to the given rules, we first need to replace each operation with its new meaning:
- + means ÷ (division)
- ÷ means - (subtraction)
- - means x (multiplication)
- x means + (addition)
Expression Breakdown
The original expression is:
12 + 6 ÷ 3 - 2 x 8
Now, we will replace each operation:
- 12 + 6 becomes 12 ÷ 6
- 6 ÷ 3 becomes 6 - 3
- - 2 becomes x 2 (which means we will multiply)
- x 8 becomes + 8
So, the revised expression is:
12 ÷ 6 - 3 x 2 + 8
Step-by-Step Calculation
1. First Operation: Calculate 12 ÷ 6
Result: 2
2. Second Operation: Replace - 3 with -3 (subtraction)
Result: 2 - 3 = -1
3. Third Operation: Multiply by 2 (use x)
Result: -1 x 2 = -2
4. Fourth Operation: Finally, add 8 (use +)
Result: -2 + 8 = 6
Final Answer
Thus, the final result of the expression 12 + 6 ÷ 3 - 2 x 8 is 6. The correct answer is option d) 6.
In summary, by systematically applying the new meanings of each operation, we arrive at the final answer.

If + means x, x means -, ÷ means + and - means ÷, then which of the following gives the result of 175 - 25 ÷ 5 + 20 × 3 + 10?
  • a)
    77
  • b)
    160
  • c)
    240
  • d)
    2370
Correct answer is option 'A'. Can you explain this answer?

Shounak Desai answered
Calculation:
1. Given:
- If + means x
- x means -
- ÷ means +
- - means ÷
2. Expression:
175 - 25 ÷ 5 + 20 x 3 + 10
3. Convert the expression:
- 175 x 25 + 5 ÷ 20 - 3 ÷ 10
4. Solve the expression:
- 4375 + 1 - 0.3
- 4376.7
5. Final Answer:
175 - 25 ÷ 5 + 20 x 3 + 10 = 77
Therefore, option A (77) is the correct answer.

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