{"id":49987,"date":"2021-05-19T15:00:57","date_gmt":"2021-05-19T09:30:57","guid":{"rendered":"https:\/\/samacheerkalviguru.com\/?p=49987"},"modified":"2021-05-24T17:53:04","modified_gmt":"2021-05-24T12:23:04","slug":"samacheer-kalvi-12th-maths-guide-chapter-1-ex-1-5-in-tamil","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-guide-chapter-1-ex-1-5-in-tamil\/","title":{"rendered":"Samacheer Kalvi 12th Maths Guide Chapter 1 \u0b85\u0ba3\u0bbf\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b85\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bcb\u0bb5\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bcd Ex 1.5"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide<\/a> Pdf Chapter 1 \u0b85\u0ba3\u0bbf\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b85\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bcb\u0bb5\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bcd Ex 1.5 Textbook Questions and Answers, Notes.<\/p>\n

TN Board 12th Maths Solutions Chapter 1 \u0b85\u0ba3\u0bbf\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b85\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bcb\u0bb5\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bcd Ex 1.5<\/h2>\n

\u0b95\u0bc7\u0bb3\u0bcd\u0bb5\u0bbf 1.
\n\u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bae\u0bcd \u0ba8\u0bc7\u0bb0\u0bbf\u0baf\u0b9a\u0bcd \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0ba4\u0bca\u0b95\u0bc1\u0baa\u0bcd\u0baa\u0bc8 \u0b95\u0bbe\u0bb8\u0bcd\u0bb8\u0bbf\u0baf\u0ba9\u0bcd \u0ba8\u0bc0\u0b95\u0bcd\u0b95\u0bb2\u0bcd \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bbf\u0bb2\u0bcd \u0ba4\u0bc0\u0bb0\u0bcd\u0b95\u0bcd\u0b95\u0bb5\u0bc1\u0bae\u0bcd:
\n(i) 2x-3y+3z=2,x+2y-z=3,3x-y+2z=1.
\n(ii) 2x + 4y + 67 = 22, 3x + 8y + 53 = 27, -x+y+2z = 2
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n\u0bb5\u0bbf\u0bb0\u0bbf\u0bb5\u0bc1\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0b85\u0ba3\u0bbf\u0baf\u0bc8 \u0ba8\u0bbf\u0bb0\u0bc8 – \u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0ba4\u0bca\u0b9f\u0b95\u0bcd\u0b95 \u0ba8\u0bbf\u0bb2\u0bc8 \u0ba8\u0bbf\u0bb0\u0bc8 \u0b89\u0bb0\u0bc1\u0bae\u0bbe\u0bb1\u0bcd\u0bb1\u0b99\u0bcd\u0b95\u0bb3\u0bcd \u0b9a\u0bc6\u0baf\u0bb2\u0bcd\u0baa\u0b9f\u0bc1\u0bb5\u0ba4\u0ba9\u0bcd \u0bae\u0bc2\u0bb2\u0bae\u0bcd \u0ba8\u0bbe\u0bae\u0bcd! \u0baa\u0bc6\u0bb1\u0bc1\u0bb5\u0ba4\u0bc1
\n\"Samacheer
\n\"Samacheer
\n\u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b9a\u0bae\u0bbe\u0ba9 \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bcd,
\nx+2y – z = 3 ……. (1)
\n6y + 5z = -4 ……. (2)
\n– 5z = – 20 \u21d2 z = \\(\\frac{-20}{-5}\\)
\nz = 4 \u0b8e\u0ba9 2 \u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\n-6y + 5(4) = -4
\n\u21d2 -6y +20 = – 4 \u21d2 -4-20 = -24
\n\u21d2 y = \\(\\frac{-24}{-6}\\) = 4
\ny = z = 4 \u0b8e\u0ba9 (1) \u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1
\nx + 2(4) – 4 = 3
\n\u21d2 x + 8 – 4 = 3
\n\u21d2 x + 4 = 3
\n\u21d2 x = 3 – 4 = -1.
\n\u2234 \u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 \u0b95\u0ba3\u0bae\u0bcd {-1, 4, 4}<\/p>\n

\"Samacheer<\/p>\n

(ii) 2x+4y + 63 = 22, 3x + 8y + 5z = 27,
\n-x + y + 2z = 2
\n\u0bb5\u0bbf\u0bb0\u0bbf\u0bb5\u0bc1\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0b85\u0ba3\u0bbf\u0baf\u0bc8 \u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf\u0bb5 \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0ba4\u0bca\u0b9f\u0b95\u0bcd\u0b95\u0ba8\u0bbf\u0bb2\u0bc8 \u0b89\u0bb0\u0bc1\u0bae\u0bbe\u0bb1\u0bcd\u0bb1\u0b99\u0bcd\u0b95\u0bb3\u0bcd \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0b95\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1
\n\"Samacheer
\n\"Samacheer
\n\u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b9a\u0bae\u0bae\u0bbe\u0ba9 \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0ba4\u0bca\u0b95\u0bc1\u0baa\u0bcd\u0baa\u0bbe\u0ba9\u0ba4\u0bc1,
\n-x+y+ 2z = 2 …(1)
\ny+z = 3 …(2)
\nz = 2 ….(3)
\n(3) \u0b90 (2)\u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1 y + 2 = 3
\n\u21d2 y=3- 2 = 1
\ny= 1 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd z = 2 \u0b8e\u0ba9 (1) \u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1
\n-x + 1 + 2 (2) = 2 \u21d2 -x + 1 + 4 = 2
\n\u21d2 -x+5 = 2 \u21d2 -x = 2-5
\n\u21d2 -x = -3 \u21d2 x = 3
\n\u2234 \u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 \u0b95\u0ba3\u0bae\u0bcd {3, 1, 2}<\/p>\n

\"Samacheer<\/p>\n

\u0b95\u0bc7\u0bb3\u0bcd\u0bb5\u0bbf 2.
\nax2<\/sup> + bx + c -\u0b90 x + 3, x – 5, \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd x-1-\u0b86\u0bb2\u0bcd \u0bb5\u0b95\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0baa\u0bcb\u0ba4\u0bc1 \u0bae\u0bc0\u0ba4\u0bbf\u0baf\u0bbe\u0ba9\u0ba4\u0bc1 \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bc7 21, 61 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd 9 \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd a, b \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd c-\u0b90\u0b95\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95. (\u0b95\u0bbe\u0bb8\u0bcd\u0bb8\u0bbf\u0baf\u0ba9\u0bcd \u0ba8\u0bc0\u0b95\u0bcd\u0b95\u0bb2\u0bcd \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bc8 \u0b89\u0baa\u0baf\u0bcb\u0b95\u0bbf\u0b95\u0bcd\u0b95\u0bb5\u0bc1\u0bae\u0bcd)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\nP(x) = ax2<\/sup> + bx + c \u0b8e\u0ba9\u0bcd\u0b95.
\n\u0b95\u0bca\u0b9f\u0bc1\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f P(-3) = 21
\n[\u2235 P(x) \u00f7 x + 3, \u0bae\u0bc0\u0ba4\u0bbf 21]
\n\u21d2 a (-3)2<\/sup> + b(-3) + c = 21
\n\u21d2 9a – 3b + c = 21 ….. (1)
\n\u0bae\u0bc7\u0bb2\u0bc1\u0bae\u0bcd, P(5) = 61
\n\u21d2 a(5)2<\/sup> + b(5) + c = 61
\n[\u0bae\u0bc0\u0ba4\u0bbf \u0ba4\u0bc7\u0bb1\u0bcd\u0bb1\u0ba4\u0bcd\u0ba4\u0bc8 \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0bbf]
\n25a + 5b + c = 61 … (2)
\n\u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd P(1) = 9
\n\u21d2 a(1)2<\/sup> + b(1) + c = 9
\n\u21d2 a + b + c = 9 … (3)
\n\u0bb5\u0bbf\u0bb0\u0bbf\u0bb5\u0bc1\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0b85\u0ba3\u0bbf\u0baf\u0bc8 \u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf\u0bb5 \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0ba4\u0bca\u0b9f\u0b95\u0bcd\u0b95\u0ba8\u0bbf\u0bb2\u0bc8 \u0b89\u0bb0\u0bc1\u0bae\u0bbe\u0bb1\u0bcd\u0bb1\u0b99\u0bcd\u0b95\u0bb3\u0bcd \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0b95\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1.
\n\"Samacheer
\n\"Samacheer
\n\u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf\u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b9a\u0bae\u0bbe\u0ba9 \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0ba4\u0bca\u0b95\u0bc1\u0baa\u0bcd\u0baa\u0bbe\u0ba9\u0ba4\u0bc1,
\na+ b + c = 9 ….. (1)
\n– 56 \u2013 6c = \u2013 41 …..(2)
\n\u21d2 c = \\(\\frac{48}{8}\\)=6
\nc= 6 \u0b8e\u0ba9 (2) -\u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\n\u21d2 -56 – 6(6) = 41
\n\u21d2 -5b = 36 – 41
\n\u21d2 -5b = – 41 + 36 = -5
\n\u21d2 b = \\(\\frac{-5}{-5}\\) = 1
\nb = 1, c = 6 \u0b8e\u0ba9 (1) -\u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\na + 1 + 6 = 9
\n\u21d2 a + 7 = 9
\n\u21d2 a = 9 – 7
\n\u21d2 a = 2
\n\u2234 a= 2, b = 1, \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd c = 6<\/p>\n

\"Samacheer<\/p>\n

\u0b95\u0bc7\u0bb3\u0bcd\u0bb5\u0bbf 3.
\n\u0b92\u0bb0\u0bc1 \u0ba4\u0bca\u0b95\u0bc8 \u20b9 65,000 \u0b86\u0ba3\u0bcd\u0b9f\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bc7 6%, 8% \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd 9% \u0b8e\u0ba9\u0bcd\u0bb1 \u0bb5\u0b9f\u0bcd\u0b9f\u0bbf \u0bb5\u0bc0\u0ba4\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0bae\u0bc2\u0ba9\u0bcd\u0bb1\u0bc1 \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0b99\u0bcd\u0b95\u0bb3\u0bbf\u0bb2\u0bcd \u0bae\u0bc1\u0ba4\u0bb2\u0bc0\u0b9f\u0bc1 \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0baa\u0bcd\u0baa\u0b9f\u0bc1\u0b95\u0bbf\u0bb1\u0ba4\u0bc1. \u0bae\u0bca\u0ba4\u0bcd\u0ba4 \u0b86\u0ba3\u0bcd\u0b9f\u0bc1 \u0bb5\u0bb0\u0bc1\u0bae\u0bbe\u0ba9\u0bae\u0bcd \u20b9 4,800. \u0bae\u0bc2\u0ba9\u0bcd\u0bb1\u0bbe\u0bb5\u0ba4\u0bc1 \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0bb5\u0bb0\u0bc1\u0bae\u0bbe\u0ba9\u0bae\u0bbe\u0ba9\u0ba4\u0bc1 \u0b87\u0bb0\u0ba3\u0bcd\u0b9f\u0bbe\u0bb5\u0ba4\u0bc1 \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0bb5\u0bb0\u0bc1\u0bae\u0bbe\u0ba9\u0ba4\u0bcd\u0ba4\u0bc8 \u0bb5\u0bbf\u0b9f 1600 \u0b85\u0ba4\u0bbf\u0b95\u0bae\u0bcd \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd \u0b92\u0bb5\u0bcd\u0bb5\u0bca\u0bb0\u0bc1 \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bc1\u0bae\u0bcd \u0bae\u0bc1\u0ba4\u0bb2\u0bc0\u0b9f\u0bc1 \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0ba4\u0bca\u0b95\u0bc8\u0baf\u0bc8\u0b95\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95.(\u0b95\u0bbe\u0bb8\u0bcd \u0ba8\u0bc0\u0b95\u0bcd\u0b95\u0bb2\u0bcd \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bc8 \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0bc1\u0b95)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n6%, 8% \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd 9% \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0bae\u0bc1\u0ba4\u0bb2\u0bc0\u0b9f\u0bc1 \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0baa\u0bcd\u0baa\u0b9f\u0bc1\u0bae\u0bcd \u0ba4\u0bca\u0b95\u0bc8 \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bc7 \u20b9x, \u20b9y \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u20b9z \u0b8e\u0ba9\u0bcd\u0b95.
\n\u2234 \u0b95\u0bca\u0b9f\u0bc1\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0ba4\u0bb0\u0bb5\u0bbf\u0ba9\u0bcd\u0baa\u0b9f\u0bbf, x + y + z = 65000… (1)
\n\"Samacheer
\n\u21d2 -8y + 9z = 60000…… (3)
\n\u0bb5\u0bbf\u0bb0\u0bbf\u0bb5\u0bc1\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0b85\u0ba3\u0bbf\u0baf\u0bc8 \u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf\u0bb5 \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0ba4\u0bca\u0b9f\u0b95\u0bcd\u0b95\u0ba8\u0bbf\u0bb2\u0bc8 \u0b89\u0bb0\u0bc1\u0bae\u0bbe\u0bb1\u0bcd\u0bb1\u0b99\u0bcd\u0b95\u0bb3\u0bcd \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0b95\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1
\n\"Samacheer
\n\u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf\u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b9a\u0bae\u0bbe\u0ba9 \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0ba4\u0bca\u0b95\u0bc1\u0baa\u0bcd\u0baa\u0bbe\u0ba9\u0ba4\u0bc1,
\nx + y + z = 65000 … (1)
\n2y + 3z = 90000 ….(2)
\n21z = 42000
\n\u21d2 z = \\(\\frac{420000}{21}\\) = 20000
\nZ = 20,000 \u0b8e\u0ba9 (2)\u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\n2y + 3(20,000) = 90000
\n\u21d22y + 60,000 = 90,000
\n2y = 90,000 – 60,000
\n= 30,000
\n\u21d2 y = \\(\\frac{30,000}{2}\\) = 15,000
\ny=15,000 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd z = 20,000 \u0b8e\u0ba9 (1) \u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\nx+ 15,000 + 20,000 = 65000
\n\u21d2 x + 35,000 = 65000
\n\u21d2 x = 65,000-35,000
\n\u21d2 x = 30,000
\n6% \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0ba9\u0bcd \u0bb5\u0bbf\u0bb2\u0bc8 \u20b930,000, 8% \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u20b915,000 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd 9% \u0baa\u0ba4\u0bcd\u0ba4\u0bbf\u0bb0\u0ba4\u0bcd\u0ba4\u0bbf\u0ba9\u0bcd \u0bb5\u0bbf\u0bb2\u0bc8 \u20b920,000.<\/p>\n

\"Samacheer<\/p>\n

\u0b95\u0bc7\u0bb3\u0bcd\u0bb5\u0bbf 4.
\n\u0b92\u0bb0\u0bc1 \u0b9a\u0bbf\u0bb1\u0bc1\u0bb5\u0ba9\u0bcd y = ax’ + bx + c \u0b8e\u0ba9\u0bcd\u0bb1 \u0baa\u0bbe\u0ba4\u0bc8\u0baf\u0bbf\u0bb2\u0bcd (-6, 8), (-2 – 12) \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd (3,8). \u0b8e\u0ba9\u0bc1\u0bae\u0bcd \u0baa\u0bc1\u0bb3\u0bcd\u0bb3\u0bbf\u0b95\u0bb3\u0bcd \u0bb5\u0bb4\u0bbf\u0baf\u0bbe\u0b95 \u0b9a\u0bc6\u0bb2\u0bcd\u0b95\u0bbf\u0bb1\u0bbe\u0ba9\u0bcd. P(7,60) \u0b8e\u0ba9\u0bcd\u0bb1 \u0baa\u0bc1\u0bb3\u0bcd\u0bb3\u0bbf\u0baf\u0bbf\u0bb2\u0bcd \u0b89\u0bb3\u0bcd\u0bb3 \u0b85\u0bb5\u0ba9\u0bc1\u0b9f\u0bc8\u0baf \u0ba8\u0ba3\u0bcd\u0baa\u0ba9\u0bc8 \u0b9a\u0ba8\u0bcd\u0ba4\u0bbf\u0b95\u0bcd\u0b95 \u0bb5\u0bbf\u0bb0\u0bc1\u0bae\u0bcd\u0baa\u0bc1\u0b95\u0bbf\u0bb1\u0bbe\u0ba9\u0bcd. \u0b85\u0bb5\u0ba9\u0bcd \u0b85\u0bb5\u0ba9\u0bc1\u0b9f\u0bc8\u0baf \u0ba8\u0ba3\u0bcd\u0baa\u0ba9\u0bc8 \u0b9a\u0ba8\u0bcd\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bbe\u0ba9\u0bbe? (\u0b95\u0bbe\u0bb8\u0bcd \u0ba8\u0bc0\u0b95\u0bcd\u0b95\u0bb2\u0bcd \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bc8 \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0bc1\u0b95).
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n\u0b95\u0bca\u0b9f\u0bc1\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f y = ax2<\/sup> + bx + c ….(1)
\n(-6, 8), (1) -\u0ba9\u0bcd \u0bae\u0bc0\u0ba4\u0bc1 \u0b85\u0bae\u0bc8\u0ba8\u0bcd\u0ba4\u0bc1\u0bb3\u0bcd\u0bb3\u0ba4\u0bc1
\n\u21d2 8 = a(-6)2<\/sup> + b(-6) + c
\n\u21d2 8 = 36a – 6b + c ….(2)
\n(-2,-12), (1)-\u0ba9\u0bcd \u0bae\u0bc0\u0ba4\u0bc1 \u0b85\u0bae\u0bc8\u0ba8\u0bcd\u0ba4\u0bc1\u0bb3\u0bcd\u0bb3\u0ba4\u0bc1
\n\u21d2 -12 = a(-2)2<\/sup> + b(-2) + c
\n\u21d2 -12 = 4a – 2b + c ….(3)
\n\u0bae\u0bc7\u0bb2\u0bc1\u0bae\u0bcd (3, 8), (1)-\u0ba9\u0bcd \u0bae\u0bc0\u0ba4\u0bc1 \u0b85\u0bae\u0bc8\u0ba8\u0bcd\u0ba4\u0bc1\u0bb3\u0bcd\u0bb3\u0ba4\u0bc1
\n\u21d2 8 = a(3) 2 + b(3) +c
\n\u21d2 8 = 9a + 3b + c ….(4)
\n\u0bb5\u0bbf\u0bb0\u0bbf\u0bb5\u0bc1\u0baa\u0bcd\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f \u0b85\u0ba3\u0bbf\u0baf\u0bc8 \u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf\u0bb5 \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0ba4\u0bca\u0b9f\u0b95\u0bcd\u0b95\u0ba8\u0bbf\u0bb2\u0bc8 \u0b89\u0bb0\u0bc1\u0bae\u0bbe\u0bb1\u0bcd\u0bb1\u0b99\u0bcd\u0b95\u0bb3\u0bcd \u0b9a\u0bc6\u0baf\u0bcd\u0baf\u0b95\u0bcd \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\n\"Samacheer
\n\u0b8f\u0bb1\u0bc1\u0baa\u0b9f\u0bbf \u0bb5\u0b9f\u0bbf\u0bb5\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 \u0b95\u0bbf\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0b9a\u0bae\u0bae\u0bbe\u0ba9 \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0ba4\u0bca\u0b95\u0bc1\u0baa\u0bcd\u0baa\u0bbe\u0b95 \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1
\n36a-6b + c = 8 ….. (1)
\n-3b + 2c = -29 … (2)
\n5c = -50
\nc = \\(\\frac{-50}{5}\\) = -10
\nc=-10 \u0b8e\u0ba9 (2) -\u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\n-3b + 2(-10) = -29
\n\u21d2 -3b – 20 = -29
\n\u21d2 -3b = -29 + 20
\n\u21d2 -3b = -9
\n\u21d2 b = \\(\\frac{-9}{-3}\\) =3
\nb = 3 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd c = -10 \u0b8e\u0ba9 (1)\u0bb2\u0bcd \u0baa\u0bbf\u0bb0\u0ba4\u0bbf\u0baf\u0bbf\u0b9f \u0b95\u0bbf\u0b9f\u0bc8\u0baa\u0bcd\u0baa\u0ba4\u0bc1,
\n36a – 6(3) – 10 = 8
\n\u21d2 36a – 18 – 10 = 8
\n\u21d2 36a – 28 = 8
\n\u21d2 36a = 8 + 28 = 36
\n\u21d2 a = \\(\\frac{36}{36}\\) = 1
\n\u2234 a= 1, b = 3, c = -10
\n\u0b8e\u0ba9\u0bb5\u0bc7 \u0b9a\u0bbf\u0bb1\u0bc1\u0bb5\u0ba9\u0bbf\u0ba9\u0bcd \u0baa\u0bbe\u0ba4\u0bc8
\ny = 1(x2<\/sup>) + 3(x) – 10
\ny = x2<\/sup> + 3x – 10
\n\u0b85\u0bb5\u0ba9\u0bc1\u0b9f\u0bc8\u0baf \u0ba8\u0ba3\u0bcd\u0baa\u0ba9\u0bcd P(7, 60) \u0b8e\u0ba9\u0bcd\u0bb1 \u0baa\u0bc1\u0bb3\u0bcd\u0bb3\u0bbf\u0baf\u0bbf\u0bb2\u0bcd \u0b89\u0bb3\u0bcd\u0bb3\u0ba4\u0bbe\u0bb2\u0bcd,
\n60 = (7)2<\/sup> + 3(7) -10
\n\u21d2 60 = 49 + 21 – 10
\n\u21d2 60 = 70 – 10 = 60
\n\u21d2 60 = 60
\n(7, 60) \u0baa\u0bbe\u0ba4\u0bc8\u0baf\u0bc8 \u0ba8\u0bbf\u0bb1\u0bc8\u0bb5\u0bc1 \u0b9a\u0bc6\u0baf\u0bcd\u0b95\u0bbf\u0bb1\u0ba4\u0bc1, \u0b85\u0bb5\u0ba9\u0bcd
\nP(7, 60)\u0bb2\u0bcd \u0b89\u0bb3\u0bcd\u0bb3 \u0b85\u0bb5\u0ba9\u0bcd \u0ba8\u0ba3\u0bcd\u0baa\u0ba9\u0bc8 \u0b9a\u0ba8\u0bcd\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bbe\u0ba9\u0bcd.<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide Pdf Chapter 1 \u0b85\u0ba3\u0bbf\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b85\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bcb\u0bb5\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bcd Ex 1.5 Textbook Questions and Answers, Notes. TN Board 12th Maths Solutions Chapter 1 \u0b85\u0ba3\u0bbf\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b85\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bcb\u0bb5\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bcd Ex 1.5 \u0b95\u0bc7\u0bb3\u0bcd\u0bb5\u0bbf 1. \u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bae\u0bcd \u0ba8\u0bc7\u0bb0\u0bbf\u0baf\u0b9a\u0bcd \u0b9a\u0bae\u0ba9\u0bcd\u0baa\u0bbe\u0b9f\u0bc1\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0ba4\u0bca\u0b95\u0bc1\u0baa\u0bcd\u0baa\u0bc8 \u0b95\u0bbe\u0bb8\u0bcd\u0bb8\u0bbf\u0baf\u0ba9\u0bcd \u0ba8\u0bc0\u0b95\u0bcd\u0b95\u0bb2\u0bcd \u0bae\u0bc1\u0bb1\u0bc8\u0baf\u0bbf\u0bb2\u0bcd \u0ba4\u0bc0\u0bb0\u0bcd\u0b95\u0bcd\u0b95\u0bb5\u0bc1\u0bae\u0bcd: (i) 2x-3y+3z=2,x+2y-z=3,3x-y+2z=1. (ii) 2x + 4y + 67 = …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[8],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/49987"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=49987"}],"version-history":[{"count":0,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/49987\/revisions"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=49987"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=49987"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=49987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}