{"id":40150,"date":"2023-05-01T16:09:36","date_gmt":"2023-05-01T10:39:36","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=40150"},"modified":"2023-05-01T16:12:32","modified_gmt":"2023-05-01T10:42:32","slug":"ap-inter-2nd-year-maths-2a-solutions-chapter-6-ex-6b-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-inter-2nd-year-maths-2a-solutions-chapter-6-ex-6b-in-telugu\/","title":{"rendered":"AP Inter 2nd Year Maths 2A Solutions Chapter 6 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c38\u0c3f\u0c26\u0c4d\u0c27\u0c3e\u0c02\u0c24\u0c02 Ex 6(b)"},"content":{"rendered":"

Practicing the\u00a0Intermediate 2nd Year Maths 2A Textbook Solutions<\/a> Chapter 6 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c38\u0c3f\u0c26\u0c4d\u0c27\u0c3e\u0c02\u0c24\u0c02 Exercise 6(b) will help students to clear their doubts quickly.<\/p>\n

AP Inter 2nd Year Maths 2A Solutions Chapter 6 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c38\u0c3f\u0c26\u0c4d\u0c27\u0c3e\u0c02\u0c24\u0c02 Exercise 6(b)<\/h2>\n

\u0c05\u0c2d\u0c4d\u0c2f\u0c3e\u0c38\u0c02 – 6(\u0c2c\u0c3f)<\/span><\/p>\n

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

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c15\u0c41 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23 \u0c35\u0c4d\u0c2f\u0c35\u0c38\u0c4d\u0c25\u0c3f\u0c24\u0c02\u0c1a\u0c47 x \u0c32 \u0c38\u0c2e\u0c3f\u0c24\u0c41\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [T.S. Mar. ’16, Mar. ’11]
\n(i) \\((2+3 x)^{-2 \/ 3}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(ii) \\((5+x)^{3 \/ 2}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iii) (7 + 3x)-5<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iv) \\(\\left(4-\\frac{x}{3}\\right)^{-1 \/ 2}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 2.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b \u0c38\u0c42\u0c1a\u0c3f\u0c02\u0c1a\u0c3f\u0c28 \u0c2a\u0c26\u0c3e\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n(i) \\(\\left(1+\\frac{x}{2}\\right)^{-5}\\) \u0c32\u0c4b 6\u0c35 \u0c2a\u0c26\u0c02
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(ii) \\(\\left(1-\\frac{x^2}{3}\\right)^{-4}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b 7\u0c35 \u0c2a\u0c26\u0c02
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iii) \\((3-4 x)^{-2 \/ 3}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b 10\u0c35 \u0c2a\u0c26\u0c02
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iv) \\(\\left(7+\\frac{8 y}{3}\\right)^{7 \/ 4}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b 5\u0c35 \u0c2a\u0c26\u0c02
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 3.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c32\u0c4b \u0c2e\u0c4a\u0c26\u0c1f\u0c3f 3 \u0c2a\u0c26\u0c3e\u0c32\u0c41 \u0c35\u0c4d\u0c30\u0c3e\u0c2f\u0c02\u0c21\u0c3f.
\n(i) \\((3+5 x)^{-7 \/ 3}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

(ii) (1 + 4x)-4<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iii) \\((8-5 x)^{2 \/ 3}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iv) \\((2-7 x)^{-3 \/ 4}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 4.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b \u0c38\u0c3e\u0c27\u0c3e\u0c30\u0c23 \u0c2a\u0c26\u0c02 ((r + 1)\u0c35 \u0c2a\u0c26\u0c02) \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n(i) \\((4+5 x)^{-3 \/ 2}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

(ii) \\(\\left(1-\\frac{5 x}{3}\\right)^{-3}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iii) \\(\\left(1+\\frac{4 x}{5}\\right)^{5 \/ 2}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iv) \\(\\left(3-\\frac{5 x}{4}\\right)^{-1 \/ 2}\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

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

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1.
\n\\(\\frac{1+2 x}{(1-2 x)^2}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b x10 \u0c17\u0c41\u0c23\u0c15\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\\(\\frac{1+2 x}{(1-2 x)^2}\\) = (1 + 2x) (1 – 2x)-2<\/sup>
\n= (1 + 2x) [1 + 2(2x) + 3(2x)2<\/sup> + 4(2x)3<\/sup> + 5(2x)4<\/sup> + 6(2x)5<\/sup> + 7(2x)6<\/sup> + 8(2x)7<\/sup> + 9(2x)8<\/sup> + 10(2x)9<\/sup> + 11(2x)10<\/sup> + …….. + (r + 1) . (2x)r<\/sup> +……]
\n\u2234 \\(\\frac{1+2 x}{(1-2 x)^2}\\) \u0c32\u0c4b x10<\/sup> \u0c17\u0c41\u0c23\u0c15\u0c02 = (11) (2)10<\/sup> + 10 (2) (29<\/sup>)
\n= 210<\/sup> (11 + 10)
\n= 21 \u00d7 210<\/sup><\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 2.
\n\\((1-4 x)^{-3 \/ 5}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b x4<\/sup> \u0c17\u0c41\u0c23\u0c15\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 3.
\n(i) \\(\\frac{(1-3 x)^2}{(3-x)^{3 \/ 2}}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b x5<\/sup> \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

(ii) \\(\\frac{(1+x)^2}{\\left(1-\\frac{2}{3} x\\right)^3}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b x8<\/sup> \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iii) \\(\\frac{(2+3 x)^3}{(1-3 x)^4}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b x7<\/sup> \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 4.
\n\\(\\frac{\\left(1+3 x^2\\right)^{3 \/ 2}}{(3+4 x)^{1 \/ 3}}\\) \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b x3<\/sup> \u0c17\u0c41\u0c23\u0c15\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

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

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c05\u0c28\u0c02\u0c24\u0c36\u0c4d\u0c30\u0c47\u0c23\u0c41\u0c32 \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c3e\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n(i) \\(1+\\frac{1}{3}+\\frac{1.3}{3.6}+\\frac{1.3 .5}{3.6 .9}+\\ldots \\ldots \\ldots\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\u0c26\u0c24\u0c4d\u0c24\u0c36\u0c4d\u0c30\u0c47\u0c23\u0c3f S = \\(1+\\frac{1}{1} \\cdot \\frac{1}{3}+\\frac{1.3}{1.2}\\left(\\frac{1}{3}\\right)^2+\\frac{1.3 \\cdot 5}{1.2 .3}\\left(\\frac{1}{3}\\right)^3\\) + ……..
\n\"AP<\/p>\n

(ii) \\(1-\\frac{4}{5}+\\frac{4.7}{5.10}-\\frac{4.7 .10}{5.10 .15}+\\ldots \\ldots\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

(iii) \\(\\frac{3}{4}+\\frac{3.5}{4.8}+\\frac{3.5 .7}{4.8 .12}+\\ldots\\) (Mar. ’11)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

(iv) \\(\\frac{3}{4.8}-\\frac{3.5}{4.8 .12}+\\frac{3.5 .7}{4.8 .12 .16}-\\ldots \\ldots\\) [T.S. Mar. ’16]
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 2.
\nt = \\(\\frac{4}{5}+\\frac{4.6}{5.10}+\\frac{4.6 .8}{5.10 .15}+\\) …….\u221e \u0c05\u0c2f\u0c3f\u0c24\u0c47, 9t = 16 \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 3.
\nx = \\(\\frac{1.3}{3.6}+\\frac{1.3 .5}{3.6 .9}+\\frac{1.3 .5 .7}{3.6 .9 .12}+\\ldots \\ldots\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 9x2<\/sup> + 24x = 11 \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f. [T.S. Mar. ’16]
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP
\n3x = 3\u221a3 – 4
\n\u21d2 3x + 4 = 3\u221a3
\n\u0c07\u0c30\u0c41\u0c35\u0c48\u0c2a\u0c41\u0c32 \u0c35\u0c30\u0c4d\u0c17\u0c02 \u0c1a\u0c47\u0c2f\u0c17\u0c3e
\n(3x + 4)2<\/sup> = (3\u221a3)2<\/sup>
\n\u21d2 9x2<\/sup> + 24x + 16 = 27
\n\u21d2 9x2<\/sup> + 24x = 11<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 4.
\nx = \\(\\frac{5}{(2 !) \\cdot 3}+\\frac{5.7}{(3 !) \\cdot 3^2}+\\frac{5 \\cdot 7 \\cdot 9}{(4 !) \\cdot 3^3}+\\ldots\\) \u0c05\u0c2f\u0c3f\u0c24\u0c47 x2<\/sup> + 4x \u0c35\u0c3f\u0c32\u0c41\u0c35 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 5.
\n\u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c05\u0c28\u0c02\u0c24 \u0c36\u0c4d\u0c30\u0c47\u0c23\u0c3f \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [A.P. Mar. ’16, Mar. ’05]
\n\\(\\frac{7}{5}\\left(1+\\frac{1}{10^2}+\\frac{1.3}{1.2} \\cdot \\frac{1}{10^4}+\\frac{1.3 .5}{1.2 .3} \\cdot \\frac{1}{10^6}+\\ldots\\right)\\)
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 6.
\nx \u0c12\u0c15 \u0c36\u0c42\u0c28\u0c4d\u0c2f\u0c47\u0c24\u0c30 \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c2f\u0c3f\u0c24\u0c47 \\(1+\\frac{x}{2}+\\frac{x(x-1)}{2.4}+\\frac{x(x-1)(x-2)}{2.4 .6}+\\ldots \\ldots\\) \\(=1+\\frac{x}{3}+\\frac{x(x+1)}{3.6}+\\frac{x(x+1)(x+2)}{3.6 .9}+\\ldots\\) \u0c05\u0c28\u0c3f \u0c28\u0c3f\u0c30\u0c42\u0c2a\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\"AP
\n\"AP<\/p>\n","protected":false},"excerpt":{"rendered":"

Practicing the\u00a0Intermediate 2nd Year Maths 2A Textbook Solutions Chapter 6 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c38\u0c3f\u0c26\u0c4d\u0c27\u0c3e\u0c02\u0c24\u0c02 Exercise 6(b) will help students to clear their doubts quickly. AP Inter 2nd Year Maths 2A Solutions Chapter 6 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c38\u0c3f\u0c26\u0c4d\u0c27\u0c3e\u0c02\u0c24\u0c02 Exercise 6(b) \u0c05\u0c2d\u0c4d\u0c2f\u0c3e\u0c38\u0c02 – 6(\u0c2c\u0c3f) I. \u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1. \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c15\u0c41 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26 \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23 \u0c35\u0c4d\u0c2f\u0c35\u0c38\u0c4d\u0c25\u0c3f\u0c24\u0c02\u0c1a\u0c47 x \u0c32 \u0c38\u0c2e\u0c3f\u0c24\u0c41\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [T.S. Mar. ’16, Mar. ’11] … 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":[15],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/40150"}],"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=40150"}],"version-history":[{"count":3,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/40150\/revisions"}],"predecessor-version":[{"id":40153,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/40150\/revisions\/40153"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=40150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=40150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=40150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}