Number System class 9 extra questions in Hindi मे संख्या पद्धति के 30 अन्य महत्वपूर्ण सवाल जो कि ड़ा आर एस अग्रवाल मैथ से लिए गए है को हल सहित बताया गया है –
Number System class 9 extra questions – संख्या पद्धति से सम्बंधित 30 अन्य महत्वपूर्ण सवाल :-
Q1. 85793 – ? + 151 = 77477
हल –
85793 + 151 – 77477 = a
85944 – 77477 = a
8467 = a
Q2. 2011 × 21 × 11 = ?
हल –
= 20111 × 231
= 20111 × (200 + 30 + 1)
= 4022200 + 603330 + 20111
= 4645641
Q3. 72519 × 9999 = ?
हल –
= 72519 × (10000 – 1)
= 725190000 – 72519
= 725117481
Q4. 2056 × 987 = ?
हल –
= 2056 × (1000 – 13)
= 2056000 – 26728
= 2029272
Q5. 1397 × 1397 = ?
हल –
= (1397)2
= (1400 – 3)2
= (1400)2 + (3)2 – 2×1400×3
= 1960000 + 9 – 8400
= 1951609
Q6. (106 × 106 – 94 × 94) = ?
हल –
= (106)2 – (94)2
= (106 – 94)(106 + 94)
= 12 × 200
= 2400
Q7. (217 × 217 + 183 × 183) = ?
हल –
= (217)2 + (183)2
= (200 + 17)2 + (200 – 17)2
= [(200)2 + (17)2 + 2×200×17] + [(200)2 + (17)2 – 2×200×17]
= 2[(200)2 + (17)2]
= 2[40000 + 289]
= 80578
Q8. [(589 + 187)2 – (589 – 187)2] / (589 × 187) = ?
हल –
माना a = 589 तथा b = 187 तब [(a + b)2 -(a – b)2] / (a × b)
हम जानते है कि (a + b)2 = a2 + b2 + 2ab और (a – b)2 = a2 + b2 – 2ab
∴ [(a + b)2 -(a – b)2] / (a × b) = [(a2 + b2 + 2ab) – (a2 + b2 – 2ab)] / ab
= 4ab / ab
= 4
Q9. (735 × 735 × 735 – 105 × 105 × 105) / (735 × 735 + 735 × 105 + 105 × 105) = ?
हल –
माना a = 735 तथा b = 105 तब (a3 – b3) / (a2 + ab + b2)
हम जानते है कि (a3 – b3) = (a – b)(a2 + b2 + ab)
∴ (a3 – b3) / (a2 + ab + b2) = (a – b)
= 735 – 105
= 620
Q10. (963 × 963 × 963 + 137 × 137 × 137) / (963 × 963 – 963 × 137 + 137 × 137) = ?
हल –
माना a = 963 तथा b = 137 तब (a3 + b3) / (a2 – ab + b2)
हम जानते है कि (a3 + b3) = (a + b)(a2 + b2 – ab)
∴ (a3 + b3) / (a2 – ab + b2) = (a + b)
= 963 + 137
= 1100
