Noun TMA Solution for MTH101 10 of 10

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Question and answer for MTH 101 TMA 1 sure you with 10 of 10

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Q1 If\[ Z_{1} = 2 +3i , and Z_{2} = 3 + 4i\], find \[ \frac {Z_{1}} {Z_{2}}\]
 
 
 
 

Q2 Suppose A = ( 1, 4), B = (4, 5), C = (5, 7), determine ( AxB) n( AxC).
 
 
 
 

Q3 In question 7 above, find A'n B
 
 
 
 

Q4 If U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = [1, 4, 7, 10], B =[2, 5, 8], find A'
 
 
 
 

Q5 If A' is a complement of set A, Find the equivalent of (A')'
 
 
 
 

Q6 Let A = ( 1, 4), B = (4, 5). Find AxB
 
 
 
 

Q7 Find the equation of the circle centre(-1, 2) and radius 4
 
 
 
 
Q8 Find the distance between points A(-3, 4) and B(2, 5)
 
 
 
 

Q9 What is the polar form of a complex number Z = 3 + 4i?
 
 
 
 

Q10 In solving the quadratic equation \[x^2 -4x + 3 =0\], the roots are _____________________
 
  
 

Q11 Which term of the Arithmetic Progession 49, 44, 39, . . . , is 9?
 
 
 
 

Q12 Find the equation of the circle center (2 , -3) and radius 4
 
 
 
 

Q13 Express 5 + 12i in a polar form, i.e in form of\[ Z = r( cos {\theta} + isin {\theta})\]
  
 
 

Q14 Let Z = 5 + 12i, find |Z|
 
 
 
 

Q15 As in no 5 above, find \[Z_{1} Z_{2}\].
 
 
 
 

Q16 This question is for nos 5 and 6. Let \[Z_{1} = 5 + 2i\] and \[Z_{2} = 7 + 3i \], find \[Z_{1} + Z_{2}\].
 
 
 
 

Q17 If \[ Z_{1} = 3 + 2i and Z_{2} = 4 + 3i \], find the distance between \[Z_{1} and Z_{2}\].
 
 
 
 

Q18 In the solution of a quadratic equation\[ x^2 - 4x + 5 = 0\], the roots are _____________________
 
 
 
 

Q19 Evaluate \[\frac{3n^2- 5n + 4}{4n^2 +7n +1} as n\rightarrow \infty\]
 
 
 
 

Q20 Solve for x if \[|x - 5|\leq 4\]
 
 
 
 

Q21 If \[U_{n} = 2n^2 - 4n + 5\], evaluate \[U_{1}\]
 
 
 
 

Q22 What are the values of x for which \[\frac {x^3 + 3x^2 + 2x} { x^2 + 5x +6} = 0 \]
 
 
 
 

Q23 Let x be the required Arithmetic Mean, then 8, x, 16 form three successive terms in the Aritmetic Progression. Find x.
 
 
 
 

Q24 The sum of the first and third terms of a Geometric progression is \[6\frac{1}{2}\] and the sum of the second and fourth terms is \[9\frac{3}{4}\].Find the first term.
 
 
 
 

Q25 Solve for x in \[ \frac{ | x + 2|} {4} \leq 3\]
 
 
 
 

Q26 Find the number of terms in an Arithmetic Progression whose first term is 5 common difference 3 and sum is 55
 
 
 
 

Q27 Solve the inequality \[( x -3)( x- 2) \leq 0\]
 
 
 
 

Q28 Find the values of x for which \[\frac {x^ 3 + 3x^ 2 +2x +7} {x^2 +5x +6 }\] is undefined
 
 
 
 

Q29 Find the solution set of \[\frac {x+2} {x + 1} = 1\]
 
 
 
 

Q30 The sum of an A.P. is 20, the first term being 8 and the common difference �?? 2. Find the number of terms in the series.
 
 
 
 

Q31 Evaluate\[ \frac {3n^2 -14n + 6}{n^2 + 7n + 2}\]
 
 
 
 

Q32 Find the limiting value of \[\frac { 7n + 5} { 2n - 3}\] as n \rightarrow {\infIty}
 
 
 
 

Q33 How many read Science today if and only if, they read Caravan?
 
 
 
 

Q34 How many read Caravan as their only magazine?
 
 
 
 

Q35 In a survey of 100 families, the numbers that read the most recent issues of various magazines were found to be as follows: Readers digest = 28, Readers digits and Science today = 8, Science today = 30, Readers digest and Caravan = 10, Caravan = 42, Science today and Caravan = 5, All the three magazines = 3. THE ABOVE IS FOR QUESTIONS 6 - 8. How many read none of the three magazines?
 
 
 
 

Q36 In a recent survey of 400 students in Palm Ville High College, 100 were listed as smokers and 150 as chewers of gum: 75 were listed as both smokers and chewres of gum. Find how many students are neither smokers nor gum chewers
 
 
 
 

Q37 In a geometric series, the first term is 7, the last term is 448, and the sum is 889. Find the common ratio, r
 
 
 
 

Q38 Let x be the required Geometric Mean (GM) between a and b. Then a, x, b, are the successive terms in the Geometric Progression. Find the GM
 
 
 
 

Q39 The sum of five numbers in an Arithmetic Progression is 25 and the sum of their squares is 165. Find the common difference.
 
 
 
 

Q40 The sum of the first n terms of a series is \[2n^2 - n\]. Find the nth term
 
 
 
 

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