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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

217 × 217 + 183 × 183 = ? 217 × 217 + 183 × 183 = ? Explanation

व्याख्या: 217² = 47089 183² = 33489 Therefore, 47089 + 33489 = 80578 A quicker method: 217 = 200+17 183 = 200−17 Therefore, (200+17)² + (200−17)² Using: (a+b)²+(a−b)² = 2(a²+b²) = 2(200² + 17²) = 2(40000+289) = 2×40289 = 80578

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

A

79698

B

80578

✓

C

80698

D

81268

Correct Answerसही उत्तर

B. 80578

Explanationव्याख्या

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

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If 17²⁰⁰ is divided by 18, the remainder is: Explanation Seriesयदि 17²⁰⁰ को 18 से विभाजित किया जाए, तो शेषफल क्या होगा? व्याख्या: 17 = 18 − 1 Therefore, 17 ≡ −1 (mod 18) So, 17²⁰⁰ ≡ (−1)²⁰⁰ Since 200 is even, (−1)²⁰⁰ = 1 Hence remainder = 1.Same topic · Same subject · Same exam

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[(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

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