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

**Latex formatted questions may not properly render****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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