{"id":3587,"date":"2023-12-06T05:55:53","date_gmt":"2023-12-06T00:25:53","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=3587"},"modified":"2023-12-07T14:16:09","modified_gmt":"2023-12-07T08:46:09","slug":"samacheer-kalvi-11th-maths-solutions-chapter-2-ex-2-13","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-11th-maths-solutions-chapter-2-ex-2-13\/","title":{"rendered":"Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13"},"content":{"rendered":"

You can Download Samacheer Kalvi 11th Maths Book Solutions<\/a> Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13<\/h2>\n

Choose the correct or the most suitable questions.<\/p>\n

Question 1.
\nIf |x + 2| \u2264 9, then x belongs to
\n(a) (-\u221e, -7)
\n(b) [-11, 7]
\n(c) (-\u221e, -7) \u222a [11, \u221e)
\n(d)(-11, 7)
\nSolution:
\n(b) [-11, 7]
\nHint:
\n-x – 2 \u2264 9 x + 2 \u2264 9
\n-x < 9 + 2 = 11 x \u2264 9 – 2 = 7
\n\u21d2 x \u2265 -11
\nso x \u2208 [-11, 7]<\/p>\n

Question 2.
\nGiven that x, y and b are real numbers x < y, b \u2265 0, then ……..
\n(a) xb < yb (b) xb > yb
\n(c) xb \u2264 vb
\n(d) xlb \u2265 ylb
\nSolution:
\n(a) xb < yb
\nHint:
\n\"Samacheer<\/p>\n

Question 3.
\n\"Samacheer
\n(a) [2, \u221e]
\n(b) (2, \u221e)
\n(c) (-\u221e, 2)
\n(d) (-2, \u221e)
\nSolution:
\n(b) (2, \u221e)
\nHint:
\n\"Samacheer<\/p>\n

Question 4.
\nThe solution of 5x – 1 < 24 and 5x + 1 > -24 is …….
\n(a) (4, 5)
\n(b) (-5, -4)
\n(c) (-5, 5)
\n(d) (-5, 4)
\nSolution:
\n(c) (-5, 5)
\nHint:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nThe solution set of the following inequality |x – 1| \u2265 |x – 3| is …….
\n(a) [0, 2]
\n(b) (2, \u221e)
\n(c) (0, 2)
\n(d) (-\u221e, 2)
\nSolution:
\n(b) (2, \u221e)<\/p>\n

Question 6.
\n\"Samacheer
\n(a) 16
\n(b) 18
\n(c) 9
\n(d) 12
\nSolution:
\n(b) 18
\nHint:
\n\"Samacheer<\/p>\n

Question 7.
\n\"Samacheer
\n(a) -2
\n(b) -8
\n(c) -4
\n(d) -9
\nSolution:
\n(c) -4
\nHint:
\n\"Samacheer<\/p>\n

Question 8.
\n\"Samacheer
\n(a) 0.5
\n(b) 2.5
\n(c) 1.5
\n(d) 1.25
\nSolution:
\n(a) 0.5
\nHint:
\n\"Samacheer<\/p>\n

Question 9.
\n\"Samacheer
\n(a) 2
\n(b) 1
\n(c) 3
\n(d) 4
\nSolution:
\n(b) 1
\nHint:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 10.
\nIf 3 is the logarithm of 343, then the base is ……
\n(a) 5
\n(b) 7
\n(c) 6
\n(d) 9
\nSolution:
\n(b) 7
\nHint.
\n\u21d2 logx<\/sub>343 = 3 \u21d2 343 = x3<\/sup>
\n(.i.e.,) 73<\/sup> = x3<\/sup> \u21d2 x = 7
\n\u21d2 x = 7<\/p>\n

Question 11.
\nFind a so that the sum and product of the roots of the equation 2x2<\/sup> + (a – 3)x + 3a – 5 = 0 are equal is ……..
\n(a) 1
\n(b) 2
\n(c) 0
\n(d) 4
\nSolution:
\n(b) 2
\nHint:
\n\"Samacheer<\/p>\n

Question 12.
\nIf a and b are the roots of the equation x2<\/sup> – kx + 16 = 0 and satisfy a2<\/sup> + b2<\/sup> = 32, then the value of k is ……
\n(a) 10
\n(b) -8
\n(c) (-8, 8)
\n(d) 6
\nSolution:
\n(c) -8, 8
\nHint:
\na + b = k ….(1) ab = 16 ….(2)
\na2<\/sup> + b2<\/sup> = (a + b)2<\/sup> – 2ab = 32 .
\nk2<\/sup> – 32 = 32 \u21d2 k2<\/sup> = 64 \u21d2 k = \u00b18<\/p>\n

Question 13.
\nThe number of solutions of x2<\/sup> + |x – 1| = 1 is ………
\n(a) 1
\n(b) 0
\n(c) 2
\n(d) 3
\nSolution:
\n(c) 2
\n\"Samacheer
\nWe have two solutions 0, 1<\/p>\n

Question 14.
\nThe equations whose roots are numerically equal but opposite in sign to the roots of 3x2<\/sup> – 5x – 7 = 0 is ……
\n(a) 3x2<\/sup> – 5x – 7 = 0
\n(b) 3x2<\/sup> + 5x – 7 = 0
\n(c) 3x2<\/sup> – 5x + 7 = 0
\n(d) 3x2<\/sup> + x – 7 = 0
\nSolution:
\n(b) 3x2<\/sup> + 5x – 7 = 0
\nHint:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 15.
\nIf 8 and 2 are the roots of x2<\/sup> + ax + c = 0 and 3, 3 are the roots of x2<\/sup> + ax + b = 0, then the roots of the equation x2<\/sup> + ax + b = 0 are …….
\n(a) 1, 2
\n(b) -1, 1
\n(c) 9, 1
\n(d) -1, 2
\nSolution:
\n(c) 9, 1
\nHint:
\nSum = 8 + 2 = 10 = -a \u21d2 a = -10
\nProduct = 3 \u00d7 3 = 9 = b \u21d2 b = 9
\nNow the equation x2<\/sup> + ax + b = 0
\n\u21d2 x2<\/sup> – 10x + 9 = 0
\n\u21d2 (x- 9) (x – 1) = 0
\nx = 1 or 9<\/p>\n

Question 16.
\nIf a and b are the real roots of the equation x2<\/sup> – kx + c = 0, then the distance
\nbetween the points (a, 0) and (b, 0) is ……..
\n\"Samacheer
\nSolution:
\n\"Samacheer
\nHint:
\na + b = k, ab = c
\n\"Samacheer<\/p>\n

Question 17.
\n\"Samacheer
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nSolution:
\n(c) 3
\n\"Samacheer<\/p>\n

Question 18.
\n\"Samacheer
\n(a) -1\/2
\n(b) -2\/3
\n(c) 1\/2
\n(d) 2\/3
\nSolution:
\n(a) -1\/2
\nHint:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 19.
\nThe number of real roots of (x + 3)4<\/sup> + (x + 5)4<\/sup> = 16 is ……
\n(a) 4
\n(b) 2
\n(c) 3
\n(d) 0
\nSolution:
\n(a) 4
\nHint:
\nThe equation is (x + 3)4<\/sup> + (x + 5)4<\/sup> = 16
\n(x + 3)4<\/sup> + (x + 5)4<\/sup> = 24<\/sup>
\nThis is biquadratic equation. It has 4 roots.<\/p>\n

Question 20.
\nThe value of log3<\/sub> 11 . log11<\/sub> 13 . log13<\/sub> 15 . log15<\/sub> 27 . log27<\/sub> 81 is …….
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nSolution:
\n(d) 4
\nSolution:
\n(d) 4
\nHint.
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 Choose the correct or the most suitable questions. Question 1. If |x + 2| \u2264 …<\/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":[7],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/3587"}],"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=3587"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/3587\/revisions"}],"predecessor-version":[{"id":60080,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/3587\/revisions\/60080"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=3587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=3587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=3587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}