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Ranjak Vaidic Ganit Preview (Marathi Research Book)

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Useful for student appearing all types of competitive exam.
Best for developing number sense.
For more detail refer http://tinyurl.com/knmrx7n

Veröffentlicht in: Karriere
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Ranjak Vaidic Ganit Preview (Marathi Research Book)

  1. 1. 109 | वभायता-ओळखा भाग जातो का ? 2) 12 435 1 003 12 * 003 − 1 * 435 = 36 − 435 = −399 −399 स 1003 ने पूणD भाग जात नाह7 :हणून 4321528 सदेखील 1003 ने पूणD भाग जात नाह7. iv) 159999200001 स 399999 ने पूणD भाग जातो का ? = भाजक = 399999 = 4 00001 मसाव (4, 00001 ) = मसाव (4, −1 ) 400001 चे गटवभाजन = 4 00001 भायाचे गटवभाजन = 1599992 00001 = 1600008 00001 1) 1600008 00001 4 00001 1600008 − 4 * 00001 = 1600004 2) 16 00004 4 00001 16 * 1 − 4 * 00004 = 16 − 16 = 0 0 स 399999 ने पूणD भाग जातो :हणून 159999200001 सदेखील 399999 ने पूणD भाग जातो . 109
  2. 2. SQUARING OF NUMBER UPTO 100 (ࢀࢁ)૛ = ൫(ࢀࢁ + ࢁ) ∗ ࢀ൯ ∗ ૚૙ + ࢁ૛ Examples ૚૚૛ = (૚૚ + ૚) ∗ ૚ / ૚૛ = ૚૛ /૚ = ૚૛૚ ૚૛૛ = (૚૛ + ૛) ∗ ૚ / ૛૛ = ૚૝ / ૝ = ૚૝૝ ૚ૠ૛ = (૚ૠ + ૠ) ∗ ૚ / ૠ૛ = ૛૝ / ૝ૢ = ૛ૡૢ ૚ૡ૛ = (૚ૡ + ૡ) ∗ ૚ / ૡ૛ = ૛૟ / ૟૝ = ૜૛૝ ૛૛૛ = (૛૛ + ૛) ∗ ૛ / ૛૛ = ૝ૡ/ ૙૝ = ૝ૡ૝ ૞૚૛ = (૞૚ + ૚) ∗ ૞ / ૚૛ = ૛૟૙ / ૙૚ = ૛૟૙૚ ૞ૡ૛ = (૞ૡ + ૡ) ∗ ૞ / ૡ૛ = ૜૜૙ / ૟૝ = ૜૜૟૝ ૞૟૛ = (૞૟ + ૟) ∗ ૞ / ૟૛ = ૜૚૙ / ૜૟ = ૜૚૜૟ ૢ૚૛ = (૚૙ૢഥ +ૢഥ ૛ = ૚ത૚തതૡത૙/ ૚ ૡ = ૡ૛ૡ૚ ) ∗ ૚૙ / ૢഥ ૢૠ૛ = (૚૙૜ഥ +૜ഥ ૛ = (ૢૠ − ૜) ∗ ૚૙/ ૢ ૙ = ૢ૝૙ૢ ) ∗ ૚૙ / ૜ഥ ૢ૜૛ = (૚૙ૠഥ + ૠ) ∗ ૚૙ / ૠഥ ૛ = (ૢ૜ − ૠ) ∗ ૚૙/ ૢ ૝ = ૡ૟૝ૢ Squaring of Number Near 25 , 50 , 75, 250 , 500 , 750 etc (૛૞ + ࢇ)૛ = ૟૛૞ + ૞૙ࢇ+ ࢇ૛ = ૟૙૙ + ૚૙૙ࢇ ૛ + (૛૞ + ࢇ૛) = ቀ૟ + ࢇ ૛ ቁ ∗ ૚૙૙ + (૛૞ + ࢇ૛) ∴ (૛૞ + ࢇ)૛ = ቀ૟+ ࢇ ૛ ቁ ࢘૛ ൫૛૞ + ࢇ૛൯ (૞૙ + ࢇ)૛ = ૛૞૙૙ + ૚૙૙ࢇ + ࢇ૛ = (૛૞ + ࢇ ) ∗ ૚૙૙ + ( ࢇ૛) ∴ (૞૙ + ࢇ)૛ = (૛૞ + ࢇ ) ࢘૛ ൫ ࢇ૛൯ Similarly, (ૠ૞ + ࢇ)૛ = ቀ૞૟ + ૜ࢇ ૛ ቁ ࢘૛ ቀ ૛૞ + ࢇ૛ቁ
  3. 3. Shortly, (૛૞ + ࢇ)૛ = ૟ ૛૞ ૛૞૛ + ࢇ ૛ ࢇ૛ = ቀ૟ + ࢇ ૛ ቁ ࢘૛ (૛૞ + ࢇ૛) (૞૙ + ࢇ)૛ = ૛૞ ૙૙ ૞૙૛ + ࢇ ࢇ૛ = (૛૞ + ࢇ )࢘૛ (૙૙ + ࢇ૛) (ૠ૞ + ࢇ)૛ = ૞૟ ૛૞ ૠ૞૛ + ૜ࢇ ૛ ࢇ૛ = ቀ૞૟ + ૜ࢇ ૛ ቁ ࢘૛ (૛૞ + ࢇ૛) (૚૙૙ + ࢇ)૛ = ૚૙૙ ૙૙ ૚૙૙૛ + ૛ࢇ ࢇ૛ = (૚૙૙ + ૛ࢇ) ࢘૛ (૙૙ + ࢇ૛) Similarly, (૛૞૙ + ࢇ)૛ = ૟૛ ૞૙૙ ૛૞૙૛ + ࢇ ૛ ࢇ૛ = ቀ૟૛ + ࢇ ૛ ቁ ࢘૜ (૞૙૙ + ࢇ૛) (૞૙૙ + ࢇ)૛ = ૛૞૙ ૙૙૙ ૞૙૙૛ + ࢇ ࢇ૛ = (૛૞૙ + ࢇ ) ࢘૜ ( ࢇ૛) (ૠ૞૙ + ࢇ)૛ = ૞૟૛ ૞૙૙ ૠ૞૙૛ + ૜ࢇ ૛ ࢇ૛ = ቀ૞૟૛ + ૜ࢇ ૛ ቁ ࢘૜ (૛૞ + ࢇ૛) (૚૙૙૙ + ࢇ)૛ = ૚૙૙૙ ૙૙૙ ૚૙૙૙૛ + ૛ࢇ ࢇ૛ = (૚૙૙૙ + ૛ࢇ) ࢘૜ (૙૙૙ + ࢇ૛)
  4. 4. ૛ૠ૛ = ቀ૟ + ૛ ૛ቁ / ൫૛૞ + ૛૛൯ = ૠ /૛ૢ = ૠ૛ૢ ૛ૡ૛ = ቀ૟ + ૜ ૛ ቁ / (૛૞ + ૜૛) = ૠ. ૞ / ૜૝ = ૠ/ ૞૙ + ૜૝ = ૠૡ૝ ૛ૢ૛ = ൬૟ + ૝ ૛ ൰ / (૛૞ + ૝૛) = ૡ / ૝૚ = ૡ૝૚ ૞૛૛ = (૛૞ + ૛) / ൫૙૙ + ૛૛൯ = ૛ૠ /૙૝ = ૛ૠ૙૝ ૞૜૛ = (૛૞ + ૜) / ൫૙૙ + ૜૛൯ = ૛ૡ /૙ૢ = ૛ૡ૙ૢ ૞૟૛ = (૛૞ + ૟) / ൫૙૙ + ૟૛൯ = ૜૚ /૜૟ = ૜૚૜૟ ૟૚૛ = (૛૞ + ૚૚) / ൫૙૙ + ૚૚૛൯ = ૜૟ / ૚૛૚ = ૜ૠ૛૚ ૟૛૛ = (૛૞ + ૚૛) / ൫૙૙ + ૚૛૛൯ = ૜ૠ / ૚૝૝ = ૜ૡ૝૝ ૠ૟૛ = ቀ૞૟ + ૜ ૛ ቁ / (૛૞ + ૚૛) = ૞ૠ. ૞ / ૛૟ = ૞ૠ/ ૞૙ + ૛૝ = ૞ૠૠ૟ ૛૞૛૛ = ቀ૟૛ + ૛ ૛ ቁ / (૞૙૙ + ૛૛) = ૟૜ / ૞૙૝ = ૟૜૞૙૝ ૛૞ૡ૛ = ቀ૟૛ + ૡ ૛ ቁ / (૞૙૙ + ૡ૛) = ૟૟ / ૞૟૝ = ૟૟૞૟૝ ૝ૢૡ૛ = ૞૙૛ഥ૛ = (૛૞૙ − ૛)/ ቀ૙૙૙ + ૛ഥ૛ቁ = ૛૝ૡ / ૙૙૝ = ૛૝ૡ૙૙૝ ૞૙૝૛ = (૛૞૙ + ૝)/ (૙૙૙ + ૝૛) = ૛૞૝ / ૙૚૟ = ૛૞૝૙૚૟ ૝૜૛૛ = ૞૟തതതૡത૛ = (૛૞૙ − ૟ૡ)/ ቀ૙૙૙ + ૟തതതૡത૛ቁ = ૚ૡ૛ / ૝૟૛૝ = ૚ૡ૟૟૛૝ ૢૢૡ૛ = ૚૙૙૛ഥ૛ = (૚૙૙૙ − ૝)/ ቀ૙૙૙ + ૛ഥ૛ቁ = ૢૢ૟ / ૙૙૝ = ૢૢ૟૙૙૝ ૢૢૢૡૢ૛ = (ૢૢૢૡૢ − ૚૚)/ ቀ૙૙૙૙૙ + ૚തതത૚ത૛ቁ = ૢૢૢૠૡ / ૙૙૚૛૚ = ૢૢૢૠૡ૙૙૚૛૚ Examples 1) (ࢇ࢞૛ + ࢈࢞ + ࢉ)૜ = ? = ۺ܍ܜ ࢖ = (ࢇ࢞૛ + ࢈࢞ + ࢉ) , ࢚ࢎࢋ࢔ ࢖૜ = ࢖૛ × ࢖ By Duplex Squaring Method ࢖૛ = (ࢇ࢞૛)૛ + ૛ × (ࢇ࢞૛) × (࢈࢞) + [૛ × (ࢇ࢞૛)(ࢉ) + (࢈࢞)૛] + ૛ × (࢈࢞) × (ࢉ) + ࢉ ∴ ࢖૛ = (ࢇ૛)࢞૝ + (૛ࢇ࢈)࢞૜ + (૛ࢇࢉ + ࢈૛)࢞૛ + (૛࢈ࢉ)࢞ + ࢉ૛ ∴ ࢖૜ = (ࢇ૛)࢞૝ + (૛ࢇ࢈)࢞૜ + (૛ࢇࢉ + ࢈૛)࢞૛ + (૛࢈ࢉ)࢞ + ࢉ૛ × (ࢇ࢞૛ + ࢈࢞ + ࢉ) (ࢇ૜)࢞૟ + (૜ࢇ૛࢈)࢞૞ + (૜ࢇ࢈૛ + ૜ࢇ૛ࢉ)࢞૝ + (࢈૜ + ૟ࢇ࢈ࢉ)࢞૜ + (૜࢈૛ࢉ + ૜ࢇࢉ૛)࢞૛ + (૜࢈ࢉ૛)࢞ + ࢉ૜

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