M.L Aggarwal Solutions

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ML Aggarwal Solution Class 10 Chapter 15 Circles Exercise 15.1

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 Exercise 15.1 Question 1 Using the given information, find the value of x in each of the following figures : Sol : (i) ∠ADB and ∠ACB are in the same segment. ∠ADB = ∠ACB = 50° Now in ∆ADB, ∠DAB + X + ∠ADB = 180° (Angles of a triangles) ⇒42∘+x+50∘=180∘ ⇒x+92∘=180∘ ⇒x=180∘−92∘=88∘ (ii) ∠ABD=∠ACD (Angles in the same segment) But ∠ACD=32° ∴∠ABD=32° Now in ΔABD ∠ABD+∠ADB+∠DAB=180° ⇒32°+45°+x=180° ⇒77°+x=180° ⇒x=180°-77°=103° (iii) ∠BAD=∠BCD (Angles in the same segement) But ∠BAD=20° ∴∠BCD=20∘ ∵∠CEA=90∘ ∴∠CED=90∘ Now in Δ CED, ∠CED+∠BCD+∠CDE=180∘ ⇒90∘+20∘+x=180∘ ⇒110∘+x=180∘ ⇒x=180∘−110∘=70∘ (iv) In ΔABC ∠ABC+∠ACB+∠BAC=180° (∵Sum of angles of a triangle) $\Rightarrow 69...
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ML Aggarwal Solution Class 9 Chapter 20 Statistics Exercise 20.2

  Exercise 20.2 Question 1 Sol : (i) discrete  (ii) continuous  (iii) discrete  (iv) continuous  (v) continuous  Question 2 Sol : Given data  13, 6, 10 ,5 ,11 ,14 ,2 ,8 ,15 ,16 ,9 ,13 ,17 ,11, 19 ,5 ,7 ,12 ,20 ,21 ,18 ,1 ,8 ,12 ,18 Classes 0-4 5-9 10-14 15-9 20-24 Frequency 2 7 8 6 2 Question 3 Sol : (i)  Classes 1-10 11-20 21-30 31-40 Frequency 8 7 6 6 (ii) Range = Maximum value - Minimum value  =40-2=38 (iii) Third class of frequency table =21+302=512 =25.5 Question 4 Sol : Variate : A particular value of a variable is called variate Class size :  The difference be...
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ML Aggarwal Solution Class 9 Chapter 4 Factorisation Exercise 4.3

Exercise 4.3 Question 1 (i) 4x 2 -25y 2 ∵a 2 -b 2 =(a+b)(a-b) ⇒(2x) 2 -(5y) 2 ⇒(2x+5y)(2x-5y) (ii) 9x 2 -1 ⇒(3x) 2 -1 2 ⇒(3x+1)(3x-1) Question 2 (i) 150-6a 2 ⇒6(25-a 2 ) ⇒6(5 2 -a 2 ) ⇒6(5+a)(5-a) (ii) 32x 2 -18y 2 ⇒2(16x 2 -9y 2 ) ⇒2[(4x) 2 -(3y) 2 ] ⇒2(4x+3y)(4x-3y) Question 3 (i) (x-y) 2 -9 ⇒(x-y) 2 -3 2 ⇒(x-y+3)(x-y-3) (ii) 9(x+y) 2 -x 2 ⇒9[(x+y) 2 -x 2 ] ⇒9[(x+y+x)(x+y-x)] ⇒9(2x+y)y ⇒9y(2x+y) Question 4 (i) 20x 2 -45y 2 ⇒5(4x 2 -9y 2 ) ⇒5((2x) 2 -(3y) 2 ) ⇒5(2x+3y)(2x-3y) (ii) 9x 2 -4(y+2x) 2 ⇒(3x) 2 -(2(y+2x)) 2 ⇒(3x+2y+4x)(3x-2y-4x) ⇒(7x+2y)(-x-2y) ⇒-(7x-2y)(x+y) Question 5 (i) 2(x-2y) 2 -50y 2 ⇒2[(x-2y) 2 -25y 2 ] ⇒2[(x-2y) 2 -(5y) 2 ] ⇒2[(x-2y+5y)(x-2y-5y)] ⇒(x+3y)(x-7y) ⇒2(x+3y)(x-7y) (ii) 32-2(x-4) 2 ⇒2[16-(x-4) 2 ] ⇒2[4 2 -(x-4) 2 ] ⇒2[(4+x-4)(4-x+4)] ⇒2.x.(8-x) ⇒2x(8-x) Question 6 (i) 108a 2 -3(b-c) 2 ⇒3[36a 2 -(b-c) 2 ] ⇒3[(6a) 2 -(b-c) 2 ] ⇒3[(6a+b-c)(6a-b+c)] (ii) πa 5 -π 3 ab 2 ⇒πa[a 4 -π 2 b 2 ] ⇒πa[(a 2 ) 2 -(πb) 2 ] ⇒πa[(a 2 +πb)(a 2 -πb)] Question...
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