{"id":29370,"date":"2024-02-27T17:29:18","date_gmt":"2024-02-27T11:59:18","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=29370"},"modified":"2024-02-28T09:40:20","modified_gmt":"2024-02-28T04:10:20","slug":"ap-inter-1st-year-maths-1a-solutions-chapter-3-ex-3b-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-inter-1st-year-maths-1a-solutions-chapter-3-ex-3b-in-telugu\/","title":{"rendered":"AP Inter 1st Year Maths 1A Solutions Chapter 3 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c41 Ex 3(b)"},"content":{"rendered":"

Practicing the Intermediate 1st Year Maths 1A Textbook Solutions<\/a> Chapter 3 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c41 Exercise 3(b) will help students to clear their doubts quickly.<\/p>\n

AP Inter 1st Year Maths 1A Solutions Chapter 3 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c41 Exercise 3(b)<\/h2>\n

I.<\/span><\/p>\n

Question 1.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c32\u0c2c\u0c4d\u0c26\u0c3e\u0c32\u0c41 \u0c38\u0c3e\u0c27\u0c4d\u0c2f\u0c2e\u0c48\u0c28\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c32\u0c4d\u0c32\u0c3e \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c42\u0c1a\u0c28: (1 \u00d7 3) by (3 \u00d7 1) = 1 \u00d7 1
\n\"AP
\nSolution:
\n\"AP
\n\"AP
\n\u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c4b \u0c28\u0c3f\u0c32\u0c41\u0c35\u0c41 \u0c35\u0c30\u0c41\u0c38\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f, \u0c30\u0c46\u0c02\u0c21\u0c35 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c4b\u0c28\u0c3f \u0c05\u0c21\u0c4d\u0c21\u0c41 \u0c35\u0c30\u0c41\u0c38\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c15\u0c41 \u0c38\u0c2e\u0c3e\u0c28\u0c02 \u0c15\u0c3e\u0c26\u0c41. \u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c3e \u0c32\u0c2c\u0c4d\u0c27\u0c2e\u0c41 \u0c28\u0c3f\u0c30\u0c4d\u0c35\u0c1a\u0c3f\u0c24\u0c2e\u0c41 \u0c15\u0c3e\u0c26\u0c41.
\n\"AP
\n\u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c4b \u0c28\u0c3f\u0c32\u0c41\u0c35\u0c41 \u0c35\u0c30\u0c41\u0c38\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f 1 \u2260 \u0c30\u0c46\u0c02\u0c21\u0c35 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c4b \u0c05\u0c21\u0c4d\u0c21\u0c41 \u0c35\u0c30\u0c41\u0c38\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f 2 \u0c15\u0c28\u0c41\u0c15 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15 \u0c32\u0c2c\u0c4d\u0c27\u0c02 \u0c28\u0c3f\u0c30\u0c4d\u0c35\u0c1a\u0c3f\u0c24\u0c02 \u0c15\u0c3e\u0c26\u0c41.
\n\"AP
\n\"AP<\/p>\n

Question 2.
\nA = \\(\\left[\\begin{array}{ccc}
\n1 & -2 & 3 \\\\
\n-4 & 2 & 5
\n\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{ll}
\n2 & 3 \\\\
\n4 & 5 \\\\
\n2 & 1
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 AB, BA \u0c32\u0c41 \u0c28\u0c3f\u0c30\u0c4d\u0c35\u0c1a\u0c3f\u0c24\u0c2e\u0c3e? \u0c05\u0c2f\u0c3f\u0c24\u0c47 \u0c32\u0c2c\u0c4d\u0c26 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. A, B \u0c32\u0c41 \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c30\u0c02 \u0c26\u0c43\u0c37\u0c4d\u0c1f\u0c4d\u0c2f\u0c3e \u0c35\u0c3f\u0c28\u0c3f\u0c2e\u0c2f\u0c2e\u0c35\u0c41\u0c24\u0c3e\u0c2f\u0c3e?
\nSolution:
\n\"AP
\nAB \u2260 BA
\n\u2234 A, B \u0c32\u0c41 \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c30\u0c02 \u0c26\u0c43\u0c37\u0c4d\u0c1f\u0c4d\u0c2f\u0c3e \u0c35\u0c3f\u0c28\u0c3f\u0c2e\u0c2f\u0c2e\u0c41 \u0c15\u0c3e\u0c35\u0c41.<\/p>\n

\"AP<\/p>\n

Question 3.
\nA = \\(\\left[\\begin{array}{cc}
\n4 & 2 \\\\
\n-1 & 1
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 A2<\/sup> \u0c28\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\nSolution:
\n\"AP<\/p>\n

Question 4.
\nA = \\(\\left[\\begin{array}{ll}
\ni & 0 \\\\
\n0 & i
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 A2<\/sup> \u0c28\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\nSolution:
\n\"AP<\/p>\n

Question 5.
\nA = \\(\\left[\\begin{array}{cc}
\n\\mathbf{i} & 0 \\\\
\n0 & -\\mathbf{i}
\n\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{cc}
\n0 & -1 \\\\
\n1 & 0
\n\\end{array}\\right]\\), C = \\(\\left[\\begin{array}{ll}
\n\\mathbf{0} & \\mathbf{i} \\\\
\n\\mathbf{i} & \\mathbf{0}
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47
\n(i) A2<\/sup> = B2<\/sup> = C2<\/sup> = -I [Mar. ’08]
\n(ii) AB = -BA = -C, (i2<\/sup> = -1) \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f.
\n(I \u0c05\u0c28\u0c47\u0c26\u0c3f \u0c30\u0c46\u0c02\u0c21\u0c4b \u0c24\u0c30\u0c17\u0c24\u0c3f \u0c2f\u0c42\u0c28\u0c3f\u0c1f\u0c4d \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15)
\nSolution:
\n\"AP
\n\"AP<\/p>\n

Question 6.
\nA = \\(\\left[\\begin{array}{ll}
\n2 & 1 \\\\
\n1 & 3
\n\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{lll}
\n3 & 2 & 0 \\\\
\n1 & 0 & 4
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47, AB \u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. BA \u0c28\u0c3f \u0c28\u0c3f\u0c30\u0c4d\u0c35\u0c1a\u0c3f\u0c24\u0c2e\u0c48\u0c24\u0c47 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\nSolution:
\n\"AP
\n\u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15 B \u0c32\u0c4b \u0c28\u0c3f\u0c32\u0c41\u0c35\u0c41 \u0c35\u0c30\u0c41\u0c38\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f A \u0c32\u0c4b \u0c05\u0c21\u0c4d\u0c21\u0c41 \u0c35\u0c30\u0c41\u0c38\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f. \u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 BA \u0c28\u0c3f\u0c30\u0c4d\u0c35\u0c1a\u0c3f\u0c24\u0c02 \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

\"AP<\/p>\n

Question 7.
\nA = \\(\\left[\\begin{array}{cc}
\n2 & 4 \\\\
\n-1 & k
\n\\end{array}\\right]\\), A2<\/sup> = O \u0c05\u0c2f\u0c3f\u0c24\u0c47 k \u0c35\u0c3f\u0c32\u0c41\u0c35 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [Mar. ’14, ’05]
\nSolution:
\nA2<\/sup> = O
\n\u21d2 \\(\\left[\\begin{array}{cc}
\n2 & 4 \\\\
\n-1 & k
\n\\end{array}\\right]\\left[\\begin{array}{cc}
\n2 & 4 \\\\
\n-1 & k
\n\\end{array}\\right]=\\left[\\begin{array}{ll}
\n0 & 0 \\\\
\n0 & 0
\n\\end{array}\\right]\\)
\n\u21d2 \\(\\left[\\begin{array}{cc}
\n4-4 & 8+4 k \\\\
\n-2-k & -4+k^2
\n\\end{array}\\right]=\\left[\\begin{array}{ll}
\n0 & 0 \\\\
\n0 & 0
\n\\end{array}\\right]\\)
\n\u21d2 8 + 4k = 0
\n\u21d2 4k = -8
\n\u21d2 k = -2<\/p>\n

II.<\/span><\/p>\n

Question 1.
\nA = \\(\\left[\\begin{array}{lll}
\n3 & 0 & 0 \\\\
\n0 & 3 & 0 \\\\
\n0 & 0 & 3
\n\\end{array}\\right]\\), \u0c05\u0c2f\u0c3f\u0c24\u0c47 A4<\/sup> \u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c42\u0c1a\u0c28 : A \u0c35\u0c3f\u0c15\u0c30\u0c4d\u0c23 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15.
\nSolution:
\n\"AP<\/p>\n

Question 2.
\nA = \\(\\left[\\begin{array}{ccc}
\n1 & 1 & 3 \\\\
\n5 & 2 & 6 \\\\
\n-2 & -1 & -3
\n\\end{array}\\right]\\), \u0c05\u0c2f\u0c3f\u0c24\u0c47 A3<\/sup> \u0c28\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\nSolution:
\n\"AP<\/p>\n

Question 3.
\nA = \\(\\left[\\begin{array}{ccc}
\n1 & -2 & 1 \\\\
\n0 & 1 & -1 \\\\
\n3 & -1 & 1
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 A3<\/sup> – 3A2<\/sup> – A – 3I \u0c35\u0c3f\u0c32\u0c41\u0c35 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [Mar. ’11]
\n(\u0c07\u0c15\u0c4d\u0c15\u0c21 I \u0c12\u0c15 3\u0c35 \u0c24\u0c30\u0c17\u0c24\u0c3f \u0c2f\u0c42\u0c28\u0c3f\u0c1f\u0c4d \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15)
\nSolution:
\n\"AP
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 4.
\nI = \\(\\left[\\begin{array}{ll}
\n1 & 0 \\\\
\n0 & 1
\n\\end{array}\\right]\\), E = \\(\\left[\\begin{array}{ll}
\n0 & 1 \\\\
\n0 & 0
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 (aI + bE)3<\/sup> = a3<\/sup>I + 3a2<\/sup>b\u0415 \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f. [(AP) Mar. ’15, May ’05]
\n(\u0c07\u0c15\u0c4d\u0c15\u0c21 I \u0c12\u0c15 3\u0c35 \u0c24\u0c30\u0c17\u0c24\u0c3f \u0c2f\u0c42\u0c28\u0c3f\u0c1f\u0c4d \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15)
\nSolution:
\n\"AP<\/p>\n

III.<\/span><\/p>\n

Question 1.
\nA = diag [a1<\/sub>, a2<\/sub>, a3<\/sub>), n \u2265 1 \u0c12\u0c15 \u0c2a\u0c42\u0c30\u0c4d\u0c23\u0c3e\u0c02\u0c15\u0c02 \u0c05\u0c2f\u0c3f\u0c24\u0c47 An<\/sup> = \\(\\left[a_1^n, a_2^n, a_3^n\\right]\\) \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f.
\nSolution:
\n\"AP
\nn = k + 1 \u0c15\u0c3f \u0c07\u0c26\u0c3f \u0c28\u0c3f\u0c1c\u0c02.
\n\u0c17\u0c23\u0c3f\u0c24\u0c3e\u0c28\u0c41\u0c17\u0c2e\u0c28 \u0c38\u0c3f\u0c26\u0c4d\u0c27\u0c3e\u0c02\u0c24\u0c02 \u0c26\u0c4d\u0c35\u0c3e\u0c30\u0c3e \u0c2a\u0c4d\u0c30\u0c24\u0c3f n \u2208 N \u0c15\u0c41 P(n) \u0c28\u0c3f\u0c1c\u0c2e\u0c35\u0c41\u0c24\u0c41\u0c02\u0c26\u0c3f.<\/p>\n

Question 2.
\n\u03b8 – \u03c6 = \\(\\frac{\\pi}{2}\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 \\(\\left[\\begin{array}{cc}
\n\\cos ^2 \\theta & \\cos \\theta \\sin \\theta \\\\
\n\\cos \\theta \\sin \\theta & \\sin ^2 \\theta
\n\\end{array}\\right]\\) \\(\\left[\\begin{array}{cc}
\n\\cos ^2 \\phi & \\cos \\phi \\sin \\phi \\\\
\n\\cos \\phi \\sin \\phi & \\sin ^2 \\phi
\n\\end{array}\\right]\\) = 0 \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f. [May ’11; Mar. ’04]
\nSolution:
\n\u03b8 – \u03c6 = \\(\\frac{\\pi}{2}\\)
\n\u21d2 \u03b8 = \\(\\frac{\\pi}{2}\\) + \u03c6
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 3.
\nn \u0c27\u0c28 \u0c2a\u0c42\u0c30\u0c4d\u0c23\u0c3e\u0c02\u0c15\u0c02, A = \\(\\left[\\begin{array}{ll}
\n3 & -4 \\\\
\n1 & -1
\n\\end{array}\\right]\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 An<\/sup> = \\(\\left[\\begin{array}{cc}
\n1+2 n & -4 n \\\\
\nn & 1-2 n
\n\\end{array}\\right]\\) \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f.
\nSolution:
\n\u0c17\u0c23\u0c3f\u0c24\u0c3e\u0c28\u0c41\u0c17\u0c2e\u0c28 \u0c28\u0c3f\u0c2f\u0c2e\u0c02 \u0c2a\u0c4d\u0c30\u0c15\u0c3e\u0c30\u0c02 \u0c0b\u0c1c\u0c41\u0c35\u0c41 \u0c1a\u0c47\u0c26\u0c4d\u0c26\u0c3e\u0c02.
\n\"AP
\n\"AP
\n\u2234 n = k + 1 \u0c15\u0c41 \u0c28\u0c3f\u0c1c\u0c02.
\n\u0c17\u0c23\u0c3f\u0c24\u0c3e\u0c28\u0c41\u0c17\u0c2e\u0c28 \u0c28\u0c3f\u0c2f\u0c2e\u0c02 \u0c2a\u0c4d\u0c30\u0c15\u0c3e\u0c30\u0c02 n \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c05\u0c28\u0c4d\u0c28\u0c3f \u0c2a\u0c42\u0c30\u0c4d\u0c23\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c15\u0c41 \u0c28\u0c3f\u0c1c\u0c02.<\/p>\n

Question 4.
\nA, B \u0c32\u0c41 \u0c12\u0c15\u0c47 \u0c24\u0c30\u0c17\u0c24\u0c3f \u0c1a\u0c24\u0c41\u0c30\u0c38\u0c4d\u0c30 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c48\u0c24\u0c47 AB = 0, BA \u2260 0 \u0c05\u0c2f\u0c4d\u0c2f\u0c47\u0c1f\u0c1f\u0c4d\u0c32\u0c41\u0c17\u0c3e A, B \u0c32\u0c15\u0c41 \u0c09\u0c26\u0c3e\u0c39\u0c30\u0c23\u0c32\u0c41 \u0c07\u0c35\u0c4d\u0c35\u0c02\u0c21\u0c3f.
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 5.
\n\u0c12\u0c15 \u0c38\u0c39\u0c3e\u0c2f\u0c28\u0c3f\u0c27\u0c3f\u0c15\u0c3f \u0c1a\u0c46\u0c02\u0c26\u0c3f\u0c28 \u0c30\u0c42.30,000 \u0c32\u0c28\u0c41 \u0c30\u0c46\u0c02\u0c21\u0c41 \u0c30\u0c15\u0c3e\u0c32 \u0c2c\u0c3e\u0c02\u0c21\u0c4d\u0c32\u0c32\u0c4b \u0c2e\u0c26\u0c41\u0c2a\u0c41 \u0c1a\u0c47\u0c2f\u0c3e\u0c32\u0c3f. \u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c30\u0c15\u0c02 \u0c2c\u0c3e\u0c02\u0c26\u0c41 \u0c38\u0c02\u0c35\u0c24\u0c4d\u0c38\u0c30\u0c3e\u0c28\u0c3f\u0c15\u0c3f 5% \u0c35\u0c21\u0c4d\u0c21\u0c40\u0c28\u0c3f, \u0c30\u0c46\u0c02\u0c21\u0c35 \u0c30\u0c15\u0c02 \u0c2c\u0c3e\u0c02\u0c21\u0c41 \u0c38\u0c02\u0c35\u0c24\u0c4d\u0c38\u0c30\u0c3e\u0c28\u0c3f\u0c15\u0c3f 7% \u0c35\u0c21\u0c4d\u0c21\u0c40\u0c28\u0c3f \u0c07\u0c38\u0c4d\u0c24\u0c3e\u0c2f\u0c3f. \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32 \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c02\u0c1a\u0c3f \u0c08 \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c0f\u0c35\u0c3f\u0c27\u0c02\u0c17\u0c3e \u0c35\u0c3f\u0c2d\u0c1c\u0c3f\u0c38\u0c4d\u0c24\u0c47 \u0c35\u0c21\u0c4d\u0c21\u0c40 (a) \u0c30\u0c42.1800 (b) \u0c30\u0c42.2000 \u0c35\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c3f.
\nSolution:
\n\u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c2c\u0c3e\u0c02\u0c21\u0c41\u0c28\u0c41 ‘x’ \u0c05\u0c28\u0c41\u0c15\u0c4a\u0c28\u0c41\u0c2e\u0c41.
\n\u0c30\u0c46\u0c02\u0c21\u0c35 \u0c2c\u0c3e\u0c02\u0c21\u0c41\u0c28\u0c41 30,000 – x \u0c05\u0c28\u0c41\u0c15\u0c4a\u0c28\u0c41\u0c2e\u0c41.
\n\u0c35\u0c21\u0c4d\u0c21\u0c40 \u0c36\u0c3e\u0c24\u0c02 0.05 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 0.07 \u0c05\u0c28\u0c41\u0c15\u0c4a\u0c28\u0c41\u0c2e\u0c41.
\n(a) [x, 30,000 – x] \\(\\left[\\begin{array}{l}
\n0.05 \\\\
\n0.07
\n\\end{array}\\right]\\) = [1800]
\n[0.05x + 0.07(30,000 – x)] = 1800
\n\\(\\frac{5}{100} x+\\frac{7}{100}\\) (30,000 – x) = 1800
\n5x + 21,0000 – 7x = 1,80,000
\n-2x = 1,80,000 – 2,10,000 = -30,000
\nx = 15,000
\n\u2234 \u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c2c\u0c3e\u0c02\u0c21\u0c4d = 15,000
\n\u0c30\u0c46\u0c02\u0c21\u0c35 \u0c2c\u0c3e\u0c02\u0c21\u0c4d = 30,000 – 15,000 = 15,000<\/p>\n

(b) [x 30,000 – x] \\(\\left[\\begin{array}{l}
\n0.05 \\\\
\n0.07
\n\\end{array}\\right]\\) = [2000]
\n[0.05x + 0.07(30,000 – x)] = [2000]
\n\\(\\frac{5}{100} x+\\frac{7}{100}\\) (30,000 – x) = 2000
\n5x + 2,10,000 – 7x = 2,00,000
\n-2x = 2,00,000 – 2,10,000
\n-2x = -10,000
\nx = 5,000
\n\u2234 \u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c2c\u0c3e\u0c02\u0c21\u0c4d = 5000
\n\u0c30\u0c46\u0c02\u0c21\u0c35 \u0c2c\u0c3e\u0c02\u0c21\u0c4d = 30,000 – 5000 = 25,000<\/p>\n","protected":false},"excerpt":{"rendered":"

Practicing the Intermediate 1st Year Maths 1A Textbook Solutions Chapter 3 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c41 Exercise 3(b) will help students to clear their doubts quickly. AP Inter 1st Year Maths 1A Solutions Chapter 3 \u0c2e\u0c3e\u0c24\u0c4d\u0c30\u0c3f\u0c15\u0c32\u0c41 Exercise 3(b) I. Question 1. \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c32\u0c2c\u0c4d\u0c26\u0c3e\u0c32\u0c41 \u0c38\u0c3e\u0c27\u0c4d\u0c2f\u0c2e\u0c48\u0c28\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c32\u0c4d\u0c32\u0c3e \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. \u0c38\u0c42\u0c1a\u0c28: (1 \u00d7 3) by (3 \u00d7 1) = 1 \u00d7 1 Solution: \u0c2e\u0c4a\u0c26\u0c1f\u0c3f … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[14],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/29370"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=29370"}],"version-history":[{"count":3,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/29370\/revisions"}],"predecessor-version":[{"id":29401,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/29370\/revisions\/29401"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=29370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=29370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=29370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}