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Number System practice question for Railways, SSC. Review the correct answer and explanation, then continue with related practice below.

Question language / प्रश्न भाषा

397 × 397 + 103 × 103 + 2 × 397 × 103 = ? 397 × 397 + 103 × 103 + 2 × 397 × 103 = ? Explanation

व्याख्या: The expression is: 397² + 103² + 2×397×103 Using: a²+b²+2ab = (a+b)² = (397+103)² = 500² = 250000

Answer and explanation are free to read — no sign-in required.उत्तर और व्याख्या पढ़ने के लिए साइन-इन आवश्यक नहीं है।

A

249996

B

250000

✓

C

86436

D

None of theseइनमें से कोई नहीं

Correct Answerसही उत्तर

B. 250000

Explanationव्याख्या

Explanation is not available for this older question yet. / इस पुराने प्रश्न की व्याख्या अभी उपलब्ध नहीं है।

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186 × 186 + 136 × 136 − 2 × 186 × 136 = ? 186 × 186 + 136 × 136 − 2 × 186 × 136 = ? Explanationव्याख्या: The expression is: 186² + 136² − 2×186×136 Using: a²+b²−2ab = (a−b)² = (186−136)² = 50² = 2500Same topic · Same subject · Same exam

1499 × 1499 = ? 1499 × 1499 = ? Explanationव्याख्या: 1499² = (1500−1)² Using: (a−b)² = a²−2ab+b² = 1500² − 2×1500×1 + 1 = 2250000 − 3000 + 1 = 2247001Same topic · Same subject · Same exam

[(946 + 157)² + (946 − 157)²] [(946 × 946) + (157 × 157)] = ? [(946 + 157)² + (946 − 157)²] [(946 × 946) + (157 × 157)] = ? Explanation Therefore, = 2a² + 2b² = 2(a²+b²) The denominator is: a²+b² Therefore, the complete fraction becomes: 2(a²+b²) (a²+b²) Cancel (a²+b²): = 2 Hence, answer = B. 2व्याख्या: Let: a = 946 b = 157 The numerator is: (a+b)² + (a−b)² Expand: (a+b)² = a² + 2ab + b² (a−b)² = a² − 2ab + b² Adding: (a+b)² + (a−b)² = a² + 2ab + b² + a² − 2ab + b² The +2ab and −2ab cancel.Same topic · Same subject · Same exam

{(476 + 424)² − 4 × 476 × 424} = ? {(476 + 424)² − 4 × 476 × 424} = ? Explanationव्याख्या: We know: (a+b)² − 4ab = a² + 2ab + b² − 4ab = a² − 2ab + b² = (a−b)² Therefore, (476+424)² − 4×476×424 = (476−424)² = 52² = 2704Same topic · Same subject · Same exam

106 × 106 − 94 × 94 = ? 106 × 106 − 94 × 94 = ? Explanationव्याख्या: 106² − 94² Using: a²−b² = (a−b)(a+b) = (106−94)(106+94) = 12 × 200 = 2400Same topic · Same subject · Same exam

1008 × 992 = ? 1008 × 992 = ? Explanationव्याख्या: 1008 = 1000+8 992 = 1000−8 Using: (a+b)(a−b)=a²−b² 1008×992 = 1000² − 8² = 1000000 − 64 = 999936Same topic · Same subject · Same exam

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