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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

106 × 106 + 94 × 94 = ? 106 × 106 + 94 × 94 = ? Explanation

व्याख्या: 106 = 100+6 94 = 100−6 Using: (a+b)²+(a−b)² = 2(a²+b²) Therefore, 106² + 94² = 2(100² + 6²) = 2(10000+36) = 2×10036 = 20072

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

A

21032

B

20032

C

20072

✓

D

23032

Correct Answerसही उत्तर

C. 20072

Explanationव्याख्या

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

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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

469157 × 9999 = ? 469157 × 9999 = ? Explanationव्याख्या: 9999 = 10000 − 1 Therefore, 469157 × 9999 = 469157 × (10000−1) = 4,691,570,000 − 469,157 = 4,691,100,843 Therefore, Answer = 4691100843Same topic · Same subject · Same exam

217 × 217 + 183 × 183 = ? 217 × 217 + 183 × 183 = ? Explanationव्याख्या: 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 = 80578Same topic · Same subject · Same exam

935421 × 625 = ? 935421 × 625 = ? Explanation 16 Therefore, 935421 × 625 = 935421 × 10000 16 First: 935421 ÷ 16 = 58463.8125 Then:व्याख्या: We know: 625 = 5⁴ = 10000Same 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

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