1 . तीन संख्याओं में से पहली संख्या दूसरी संख्या की चौगुनी है और तीसरी की तीन गुनी यदि तीनों संख्याओं का औसत 95 हो तो तीसरी संख्या कितनी है ?

उत्तर – माना पहली संख्या = x है

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 17
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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 18

3.    यदि संख्या को 2736 से विभाजित करने पर शेष 75 रहता है| यदि उसी संख्या को 24 से विभाजित किया जाए तो शेष कितना रहेगा ?

उत्तर  –  संख्या 2736 से किसी संख्या को विभाजित करने पर शेष 75 रहता है अर्थात वह संख्या 2736 की कोई गुणज से 75 से अधिक होगी |

संख्या  = 2736 x 1 + 75 = 2811

अब संख्या 2811 को 24 से विभाजित करने पर  2811/24 = 117       ……….भागफल  3  शेष बचा 

अतः उसी संख्या को 24 से भाग देने पर 3 शेष बचेगा | 

4.     दो संख्याओं के घनों का योग 793  है |  संख्या का योग 13 है, तो दोनों संख्याओं का अंतर बताइए|

 उत्तर  –  माना दोनों संख्याएँ  क्रमशः a और b है |

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5. 11 संख्याओं का औसत 36 है, जबकि उनमें से 9 का औसत 34 है | यदि शेष दो संख्याओं का अनुपात 2:3 हो, तो लघुत्तम संख्या का (शेष दो संख्याओं के बीच) का मान बताइए |

उत्तर – 11 संख्याओं का औसत = 36

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 19

6. गणित की एक परीक्षा में 5 उम्मीदवारों द्वारा प्राप्त अंक लगातार 5 विषम पूर्णाकों में है | यदि उनके कुल अंक 185 है, तो उच्चतम अंक कितने है ?

उत्तर – माना प्रथम विषम पूर्णांक = x

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 20

7. 50 से कम 3 के सभी घनात्मक गुणकों का योग ज्ञात कीजिए |

उत्तर – 3 के घनात्मक गुणक की प्रथम संख्या =3 x 1 = 3

3 के घनात्मक गुणक जो 50 से कम हो = 3 x 16 = 48

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 21

8. दो संख्याओं का योग 20 के बराबर है और उनका अंतर 25 है | 2 संख्याओं का अनुपात क्या है ?

उत्तर – माना दो संख्याएँ x और y है |

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 22

9. निम्नलिखित में से कौन सी संख्या 11 का गुणक है ?

(a) 978626 (b) 447355 (c) 112144 (d) 869756

उत्तर – विकल्प (a) से

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 23

द्वितीय विधि से –

कोई भी संख्या 11 की गुणक तभी होगी जब सम स्थानों पर दी गई संख्याओं का योग

विषम स्थानों पर दी गई संख्याओं के योग के बराबर हो अर्थात

9 + 8 + 2 = 7 + 6 + 6

19 = 19 अतः विकल्प a सही है

10. तीन क्रमिक प्राकृतिक संख्याओं के वर्ग का जोड़ 196 है | संख्याओं का जोड़ क्या होगा ?

उत्तर – माना तीन क्रमिक संख्याएँ x, x + 1 तथा x + 2 है

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 24
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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 25

13. मेरे पास x गोलियां है मेरे बड़े भाई के पास मेरे से 3 अधिक गोलियां है जबकि मेरे छोटे भाई के पास मेरे से तीन कम गोलियां है | यदि गोलियों की कुल संख्या 15 है तो मेरे पास कितनी गोलियां है ?

उत्तर – मेरे बड़े भाई के पास गोलियों की संख्या = x + 3

मेरे छोटे भाई के पास गोलियों की संख्या = x – 3

प्रश्नानुसार

x + x + 3 + x – 3 = 15

3x = 15

x = 5

अत: मेरे पास गोलियों की संख्या = 5

14. 49237 x 3995 x 738 x 83 x 9 के गुणनफल का ईकाई के स्थान का अंक बताइए|

उत्तर – दी गई संख्या = 49237 x 3995 x 738 x 83 x 9

संख्या के ईकाई के अंक को गुणा करने पर

= 7 x 5 x 8 x 3 x 9

= 7 x 40 x 27

= 280 x 27

पुनः ईकाई के अंक को गुणा करने पर = 0 x 7 = 0

द्वितीय विधि –

यदि दी गई संख्याओं में दो संख्याओं के गुणनफल का ईकाई का अंक 0 हो तो दी गई सभी संख्याओं के गुणनफल का ईकाई का अंक शून्य होगा |

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 26

16. 80 और 90 के बीच की सभी अभाज्य संख्याओं का गुणनफल है –

उत्तर- 80 और 90 के बीच अभाज्य संख्या = 83, 89

संख्याओं का गुणनफल = 83 x 89 = 7387

17. वह सबसे बड़ी संख्या जिससे 729 और 901 को भाग देने पर शेषफल क्रमशः 9 और 5 होगा |

उत्तर – दी गई संख्या 729 तथा 901 मेन शेषफल क्रमशः 9 और 5 होगा क्रमशः घटाने पर प्राप्त संख्याओं का म. स. अभीष्ट संख्या होगी

अर्थात 729 – 9 = 720

901 – 5 = 896

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 27

18. 3957 में 5349 को जोड़ा जाता है| प्राप्त राशि में से 7062 को घटाया जाता है | परिणामी संख्या किससे विभाज्य नही होगी?

(a) 4 (b) 3 (c) 7 (d) 11

उत्तर- परिणामी संख्या = 3957 + 5349 – 7062

= 9306 – 7062 = 2244

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संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 28

19. लघुत्तम अभाज्य संख्या क्या है? (2, 0, 1, 3)

उत्तर- वह संख्या जो संख्या 1 तथा अपने अतिरिक्त किसी भी संख्या से भाज्य न हो, अभाज्य संख्या कहते है ?

तथा संख्या 2 सबसे छोटी अभाज्य संख्या है |

20. संख्या 323 के अभाज्य गुणनखंड है – (3, 5, 2, 0)

उत्तर – 323 = 19 x 17

19 व 17 दोनों अभाज्य है |

अतः संख्या 323 के अभाज्य गुणनफल 19 एवं 17 अर्थात दो होंगी |

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