यदि x का अर्थ - है, ÷ का अर्थ + है, + का अर्थ ÷ है और - का अर्थ x है, तो निम्नलिखित को बढ़ते हुए क्रम में व्यवस्थित कीजिए :
1. 15 - 5 ÷ 5 x 20 + 10
2. 8 ÷ 10 - 3 + 5 x 6
3. 6 x 2 + 3 ÷ 12 - 3
4. 3 ÷ 7 - 5 x 10 + 3
नीचे दिए गए कूट से सही उत्तर चुनिए :
व्याख्या एवं हल
सही उत्तर (B) 2, 4, 3, 1 है।
गणितीय संक्रियाओं का चरणबद्ध मान:
- चिन्ह परिवर्तन: ।
- समीकरण 1:
।15 × 5 + 5 − 20 ÷ 10 = 75 + 5 − 2 = 78 15 5 + 5 - 20× \times 10 = 75 + 5 - 2 = 78÷ \div - समीकरण 2:
।8 + 10 × 3 ÷ 5 − 6 = 8 + 6 − 6 = 8 8 + 10 3× \times 5 - 6 = 8 + 6 - 6 = 8÷ \div - समीकरण 3:
।6 − 2 ÷ 3 + 12 × 3 = 6 − 0.67 + 36 = 41.33 6 - 2 3 + 12÷ \div 3 = 6 - 0.67 + 36 = 41.33× \times - समीकरण 4:
।3 + 7 × 5 − 10 ÷ 3 = 3 + 35 − 3.33 = 34.67 3 + 7 5 - 10× \times 3 = 3 + 35 - 3.33 = 34.67÷ \div - बढ़ते क्रम (आरोही क्रम) में व्यवस्थित करने पर:
।2 ( 8 ) < 4 ( 34.67 ) < 3 ( 41.33 ) < 1 ( 78 ) ⟹ < s t r o n g > 2 , 4 , 3 , 1 < / s t r o n g > 2 (8) < 4 (34.67) < 3 (41.33) < 1 (78) <strong>2, 4, 3, 1</strong>⟹ \implies
In English (Question & Model Answer)
If x stand for -, ÷ stands for +, + stands for ÷ and - stands for x, then arrange the following in increasing order :
1. 15 - 5 ÷ 5 x 20 + 10
2. 8 ÷ 10 - 3 + 5 x 6
3. 6 x 2 + 3 ÷ 12 - 3
4. 3 ÷ 7 - 5 x 10 + 3
Choose the correct answer from the code given below :
The correct answer is (B) 2, 4, 3, 1.
Step-by-step operator replacement & evaluation:
- Operator replacement rules:
.× → − , ÷ → + , + → ÷ , − → × \to -, \;× \times \to +, \; + \to÷ \div , \; - \to÷ \div × \times - Expression 1:
.15 × 5 + 5 − 20 ÷ 10 = ( 15 × 5 ) + 5 − ( 20 ÷ 10 ) = 75 + 5 − 2 = 78 15 5 + 5 - 20× \times 10 = (15÷ \div 5) + 5 - (20× \times 10) = 75 + 5 - 2 = 78÷ \div - Expression 2:
.8 + 10 × 3 ÷ 5 − 6 = 8 + ( 10 × 3 ÷ 5 ) − 6 = 8 + 6 − 6 = 8 8 + 10 3× \times 5 - 6 = 8 + (10÷ \div 3× \times 5) - 6 = 8 + 6 - 6 = 8÷ \div - Expression 3:
.6 − 2 ÷ 3 + 12 × 3 = 6 − ( 2 ÷ 3 ) + ( 12 × 3 ) = 6 − 0.67 + 36 = 41.33 6 - 2 3 + 12÷ \div 3 = 6 - (2× \times 3) + (12÷ \div 3) = 6 - 0.67 + 36 = 41.33× \times - Expression 4:
.3 + 7 × 5 − 10 ÷ 3 = 3 + ( 7 × 5 ) − ( 10 ÷ 3 ) = 3 + 35 − 3.33 = 34.67 3 + 7 5 - 10× \times 3 = 3 + (7÷ \div 5) - (10× \times 3) = 3 + 35 - 3.33 = 34.67÷ \div - Arranging in increasing numerical order:
.Expression 2 ( 8 ) < Expression 4 ( 34.67 ) < Expression 3 ( 41.33 ) < Expression 1 ( 78 ) ⟹ < s t r o n g > 2 , 4 , 3 , 1 < / s t r o n g > (8) <Expression 2 \text{Expression 2 } (34.67) <Expression 4 \text{Expression 4 } (41.33) <Expression 3 \text{Expression 3 } (78)Expression 1 \text{Expression 1 } <strong>2, 4, 3, 1</strong>⟹ \implies