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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

1506 × 1506 = ? 1506 × 1506 = ? Explanation

व्याख्या: 1506² = (1500+6)² = 1500² + 2×1500×6 + 6² = 2250000 + 18000 + 36 = 2268036

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

A

2268036

✓

B

2278036

C

2178036

D

2368036

Correct Answerसही उत्तर

A. 2268036

Explanationव्याख्या

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

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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

Question 1 Arrange the fractions 5 9, 4 7, 3 5 and 2 3 in ascending order. 9, 4 7, 3 Explanation 5 9 ≈ 55.55% 4 7 ≈ 57.14% 3 5 = 60% 2 3 ≈ 66.67% Therefore:भिन्नों 5 5 और 2 3 को आरोही क्रम में व्यवस्थित कीजिए। व्याख्या Convert the fractions into percentages to compare their values easily. भिन्नों के मानों की आसानी से तुलना करने के लिए उन्हें प्रतिशत में बदलें। अतः:Same 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

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

397 × 397 + 103 × 103 + 2 × 397 × 103 = ? 397 × 397 + 103 × 103 + 2 × 397 × 103 = ? Explanationव्याख्या: The expression is: 397² + 103² + 2×397×103 Using: a²+b²+2ab = (a+b)² = (397+103)² = 500² = 250000Same topic · Same subject · Same exam

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