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কোনক্ষেত্রে 2x - ky + 7 = 0 এবং 6x - 12y + 15 = 0 সমীকরণের কোনও সমাধান নেই?

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UP TGT Mathematics 2019 Official Paper
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  1. k = -4
  2. k = 4
  3. k = 1
  4. k = -1

Answer (Detailed Solution Below)

Option 2 : k = 4
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Detailed Solution

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ধারণা:

যদি দুটি রৈখিক সমীকরণ হল,

x + b1y = c1​ এবং x + b2y = c2, অতএব,

(a) If ​​/a2 = b1​​/b2 ​​= c1​​/c2 হলে, সিস্টেমটি সামঞ্জস্যপূর্ণ এবং অসীমভাবে অনেকগুলি সমাধান রয়েছে।

(b) যদি ​​/a2 = b1​​/b2 ≠ c1​​/c2 সিস্টেমের কোন সমাধান নেই এবং এটি অসামঞ্জস্যপূর্ণ

গণনা:

সমীকরণ 2x - ky + 7 = 0 এবং 6x - 12y + 15 = 0

2/6 = - k/-12 ≠ 7/15

ব্যবহার করে, 2/6 = - k/-12

⇒ k = 24/6 = 4

∴ k = 4 এ, 2x - ky + 7 = 0 এবং 6x - 12y + 15 = 0 সমীকরণের কোনো সমাধান নেই

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