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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

Which one of the following will divide (4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) completely? Explanation Therefore, the complete expression contains both 2 and 5. 2 × 5 = 10 Hence it is divisible by 10.

निम्नलिखित में से कौन (4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) को पूर्णतः विभाजित करेगा? व्याख्या: Take 4⁶¹ common: 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹(1 + 4 + 4² + 4³) = 4⁶¹(1 + 4 + 16 + 64) = 4⁶¹ × 85 Now, 85 = 5 × 17 Also, 4⁶¹ contains factor 2.

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

A

3

B

10

✓

C

11

D

13

Correct Answerसही उत्तर

B. 10

Explanationव्याख्या

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

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Which of the following fractions is less than 7 8 and greater than 1 3? Explanation 3 < fraction < 7 8 Check A: 1 4 < 1 3, so incorrect. Check B: 23 24 > 7 8, so incorrect. Check C: 11 12 > 7 8, so incorrect. Check D: Compare 17 24 with 1 3: 17 × 3 = 51 24 × 1 = 24 51 > 24 Therefore, 17 24 > 1 3 Now compare 17 24 with 7 8: 17 × 8 = 136 24 × 7 = 168 136 < 168 Therefore, 17 24 < 7 8 Hence, 1 3 < 17 24 < 7 8 Answer = D Basic Arithmeticनिम्नलिखित में से कौन-सी भिन्न 7 8 से कम और 1 3 से अधिक है? व्याख्या: We need: 1Same topic · Same subject · Same exam

Which one of the following will divide (3²⁵ + 3²⁶ + 3²⁷ + 3²⁸) completely? Explanation Therefore, the expression contains: 2 × 3 × 5 = 30 Hence it is divisible by 30.निम्नलिखित में से कौन (3²⁵ + 3²⁶ + 3²⁷ + 3²⁸) को पूर्णतः विभाजित करेगा? व्याख्या: Take 3²⁵ common: 3²⁵ + 3²⁶ + 3²⁷ + 3²⁸ = 3²⁵(1 + 3 + 9 + 27) = 3²⁵ × 40 Now, 40 = 2³ × 5 And 3²⁵ contains factor 3.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

√? = (88 × 42) ÷ 16 √? = (88 × 42) ÷ 16 Explanationव्याख्या: First calculate: 88 × 42 = 3696 Now, 3696 ÷ 16 = 231 Therefore, √? = 231 Squaring both sides: ? = 231² = (230+1)² = 230² + 460 + 1 = 52900 + 461 = 53361Same topic · Same subject · Same exam

1 2 + 1 6 + 1 12 + 1 20 + 1 30 + …… + 1 [n(n+1)] = ? 1 2 + 1 6 + 1 12 + 1 20 + 1 30 + …… + 1 [n(n+1)] = ? Explanation 2 = 1 (1×2) 1 6 = 1 (2×3) 1 12 = 1 (3×4) 1 20 = 1 (4×5) Therefore, the general term is: 1 [r(r+1)] Now, 1 [r(r+1)] = 1 r − 1 (r+1) Therefore, 1 (1×2) = 1 − 1 2 1 (2×3) = 1 2 − 1 3 1 (3×4) = 1 3 − 1 4 1 (4×5) = 1 4 − 1 5 ... 1 [n(n+1)] = 1 n − 1 (n+1) Hence, S = (1 − 1 2) (1 2 − 1 3) (1 3 − 1 4) ... (1 n − 1 (n+1)) All the middle terms cancel: −1 2 + 1 2 = 0 −1 3 + 1 3 = 0 −1 4 + 1 4 = 0 Therefore, S = 1 − 1 (n+1) Taking LCM: S = [(n+1) − 1] (n+1) = n (n+1) Hindi: [r(r+1)] = 1 r − 1 (n+1) = n (n+1)व्याख्या: Observe: 1 प्रत्येक पद को इस प्रकार लिख सकते हैं: 1 (r+1) अतः सभी बीच के पद कट जाते हैं और बचता है: 1 − 1Same topic · Same subject · Same exam

5 6 × 2 9 ÷ 4 9 × 6 7 = ? 5 6 × 2 9 ÷ 4 9 × 6 7 = ? Explanation Therefore, 5 6 × 2 9 ÷ 4 9 × 6 7 = 5 6 × 2 9 × 9 4 × 6 7 Cancel 9: = 5 6 × 2 4 × 6 7 Cancel 6: = 5 × 2 (4×7) = 10 28 = 5 14 Now, 5 ÷ 14 = 0.357142... Approximately, = 0.36 Therefore, answer = Dव्याख्या: Division by a fraction means multiplication by its reciprocal.Same topic · Same subject · Same exam

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