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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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 |
![संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 5 svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml extension%22%20height%3D%22297%22%20width%3D%22353%22%20wrs%3Abaseline%3D%22148%22%3E%3C! 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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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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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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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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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9. निम्नलिखित में से कौन सी संख्या 11 का गुणक है ?
(a) 978626 (b) 447355 (c) 112144 (d) 869756
उत्तर – विकल्प (a) से
![संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 10 svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml extension%22%20height%3D%2264%22%20width%3D%22157%22%20wrs%3Abaseline%3D%2231%22%3E%3C! MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E978626%3C%2Fmn%3E%3Cmn%3E11%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmn%3E88966%3C%2Fmn%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3C%2Fmath%3E %3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font face%7Bfont family%3A'math17f39f8317fbdb1988ef4c628eb'%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf 8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAsmhlYWQQC2qxAAACQAAAADZoaGVhCGsXSAAAAngAAAAkaG10eE2rRkcAAAKcAAAACGxvY2EAHTwYAAACpAAAAAxtYXhwBT0FPgAAArAAAAAgbmFtZaBxlY4AAALQAAABn3Bvc3QB9wD6AAAEcAAAACBwcmVwa1uragAABJAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAAD3%2F%2FwAAAD3%2F%2F%2F%2FEAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAACAIAA6wLVAhUAAwAHAGUYAbAIELAG1LAGELAF1LAIELAB1LABELAA1LAGELAHPLAFELAEPLABELACPLAAELADPACwCBCwBtSwBhCwB9SwBxCwAdSwARCwAtSwBhCwBTywBxCwBDywARCwADywAhCwAzwxMBMhNSEdASE1gAJV%2FasCVQHAVdVVVQAAAAEAAAABAADVeM5BXw889QADBAD%2F%2F%2F%2F%2F1joTc%2F%2F%2F%2F%2F%2FWOhNzAAD%2FIASAA6sAAAAKAAIAAQAAAAAAAQAAA%2Bj%2FagAAF3AAAP%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%2F)format('truetype')%3Bfont weight%3Anormal%3Bfont style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke linecap%3D%22square%22%20stroke width%3D%221%22%20x1%3D%2226.5%22%20x2%3D%2283.5%22%20y1%3D%2220.5%22%20y2%3D%2220.5%22%2F%3E%3Ctext%20font family%3D%22Arial%22%20font size%3D%2216%22%20text anchor%3D%22middle%22%20x%3D%2254.5%22%20y%3D%2215%22%3E978626%3C%2Ftext%3E%3Ctext%20font family%3D%22Arial%22%20font size%3D%2216%22%20text anchor%3D%22middle%22%20x%3D%2255.5%22%20y%3D%2237%22%3E11%3C%2Ftext%3E%3Ctext%20font family%3D%22math17f39f8317fbdb1988ef4c628eb%22%20font size%3D%2216%22%20text anchor%3D%22middle%22%20x%3D%2298.5%22%20y%3D%2226%22%3E%3D%3C%2Ftext%3E%3Ctext%20font family%3D%22Arial%22%20font size%3D%2216%22%20text](https://www.hindinotes.org/wp-content/themes/maktub/assets/images/transparent.gif)
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
![संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 11 svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml extension%22%20height%3D%22404%22%20width%3D%22314%22%20wrs%3Abaseline%3D%22201%22%3E%3C! 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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 |
![संख्या पद्धति के ये प्रश्न ऐसे के ऐसे ही पूछे जाते हैं ! पार्ट 2 14 svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml extension%22%20height%3D%22384%22%20width%3D%22414%22%20wrs%3Abaseline%3D%22191%22%3E%3C! 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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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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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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 |
नमस्कार maim, में भी आपकी तरह ही math पर आर्टिकल पोस्ट करता हु आपने एक से बढकर एक math के टॉपिक को बड़ी अच्छी तरह से समझाने का प्रयास किया है में भी आपके लिखे आर्टिकल को पढ़ता हु
कृपया मुझे बताने का कष्ट करे कि आप math में डिवाइड (जेसे 4 बटे 5) कसे लिखते हो I am waiting your answer, Thank YOu.