#### MTH101 List of Questions and Answer

**Q1 What are the values of x for which \[\frac {x^3 + 3x^2 + 2x} { x^2 + 5x +6} = 0 \]**

**Q2 Let x be the required Arithmetic Mean, then 8, x, 16 form three successive terms in the Aritmetic Progression. Find x.**

**Q3 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.**

**Q4 The coordinate of the centre and the radius of the circle \[y^2 + x^2 �?? 14x -8y + 56 = 0\] is __________**

**Q5 The sum of five numbers in an Arithmetic Progression is 25 and the sum of their squares is 165. Find the common difference.**

**Q6 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**

**Q7 Let \[Z_1 = 12 + 5i,~~ Z_2 = 14 �?? 7i\] express \[Z_1 Z_2\] in standard form**

**Q8 The limiting value of \[\frac{n^{3}+5n^{2}+2}{2n^{3} + 9} \] as \[n\rightarrow \infty\]is __________**

**Q9 Suppose A = (1, 4), B = (4, 5), C = (5, 7), then\[ (A \times B) \cap (A \times C)\] is ____________**

**Q10 Let U = {1, 2, �?��?��?��?�., 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6}, then \[(A�?�B)^c\]**

**Q11 A company sets up a smoking fund and invests N10, 000 each year for 5years at 9% compound interest, the worth of the fund after 5years is __________**

**Q12 The smallest number of terms of the geometrical series, 8 + 24 + 72 + �?��?��?��?��?�.., that will give a total greater than 6, 000, 000 is _______**

**Q13 The common ratio in a geometric series having first term 7, the last term 448, and the sum 889 is _________________**

**Q14 The number of terms in an A.P. whose first term is 5, common difference 3, and sum 55 is _____**

**Q15 Suppose S = a + (a + d) + (a + 2d) + �?��?��?��?��?�.. + [a + (n �?? 1) d] �?��?�, the sum of n terms is __________________**

**Q16 ________ is the value of n given that 77 is the nth term of the A.P \[3\frac{1}{2}, ~~7,~~ 10\frac{1}{2}, �?�..\]**

**Q17 ________ is the limiting value of\[ 3x^3 + 5x^2 �?? 6\] as \[n\rightarrow -2\]**

**Q18 The 23rd term of the A.P �??7, �??3, +1, �?��?�gives_______________**

**Q19 The 383rd term of the series 5 + 8 + 11 + … is______________ ¬**

**Q20 The sum of five numbers in an A.P is 25 and the sum of their squares is 165. Find the numbers**

**Q21 The sum of the first n terms of a series is 2n^2 �?? n. Find the nth term and of the series.**

**Q22 Find the number of terms in an A.P. whose first term is 5, common difference 3, and sum 55.**

**Q23 let \[ Z_{1} = 5 + 12i, ~~ Z_{2} =3 + 4i\]. Find \[( Z_{1})^{2} – (Z_{2})^{2}\] in standard form**

**Q24 Determine the value(s) of x for which \[\frac{x^{7}+5x^{5}+6x^{3}}{x^{5}-5x^{4}+6 x^{3}}\] is undefined**

**Q25 Suppose \[Z_{1} = 5 + 12i \] and \[Z_{2} =3 + 4i\], express \[\frac{Z_{1}}{Z_{2}}\] in polar form**

**Q26 Find the equation of a circle having centre (5, -4) and radius 7**

**Q27 Express 12 + 5i in polar form (i.e in form of \[z=r\cos\theta + i\sin\theta\]**

**Q28 If \[ Z_{1 }= 7 + 12i\] and \[Z_{2} = 4 + 3i\]. Find the distance between \[Z_{1 }~~and ~~Z_{2}\]**

**Q29 Find the solution set for \[\frac{x-5}{x+10}\leq 1\]**

**Q30 Solve for x in \[ |x2 �?? 4|\leq 4\]**

**Q31 Let M = {a, b} then find the power set \[2^{M}\].**

**Q32 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 4, 7, 10}, B = {2, 5, 8}. Find \[A�?? \cap B�??\]**

**Q33 8 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7} Find \[ (A \cap B) �?? (B \cup C)\]**

**Q34 Determine the value(s) of x for which \[\frac{x^{7}+5x^{5}+6x^{3}}{x^{5}-5x^{4}+6 x^{3}}\] is undefined**

**Q35 Find the value(s) of x for which \[\frac{x^{3}-7x^{2}+6x}{x^{5}+4x^{4}-3}=0\]**

**Q36 A survey in a class shows that 15 out of the pupils play cricket, 11 play tennis and 6 play cricket and tennis. How many pupils are there in the class. (Hint: Assume that everyone plays at least one of these games)**

**Q37 In a survey of 100 students, the numbers studying various languages were found to be: Spanish 28: German 30: French 42: Spanish and French 10: Spanish and German 8: German and French 5: all the three languages 3. How many students were studying no language?**

**Q38 A market survey was conducted to determine consumer acceptance for a group of products. The survey revealed the following about three products A, B, & C. of 155 people interviewed, it was discovered that,74 like product A, 81 like product B,60 like product C,27 like product A & B, 25 like products A & C,35 like products B & C and 12 did not like any of the three products.Determine the number of people out of those interviewed that liked all three products. Determine the number of people out of those interviewed that liked all three products.**

**Q39 Determine the limiting value of \[\frac{3n^{2}+1}{4(n^{2}-2)}\] as \[n\rightarrow \infty\]**

**Q40 Sum to n terms of three AP�??s are \[S_{1}, ~~S_{2} ~~and~~S_{3}\]. The first term of each of them is 1 and common differences are 1, 2, and 3 respectively. Find the nth term to show that the above \[S_{1}, ~~S_{2} and~~S_{3}\] are AP�??s.**

**Q41 If\[ Z_{1} = 2 +3i , and Z_{2} = 3 + 4i\], find \[ \frac {Z_{1}} {Z_{2}}\]**

**Q42 Suppose A = ( 1, 4), B = (4, 5), C = (5, 7), determine ( AxB) n( AxC).**

**Q43 In question 7 above, find A’n B**

**Q44 If U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = [1, 4, 7, 10], B =[2, 5, 8], find A’**

**Q45 If A’ is a complement of set A, Find the equivalent of (A’)’**

**Q46 Let A = ( 1, 4), B = (4, 5). Find AxB**

**Q47 Find the equation of the circle centre(-1, 2) and radius 4**

**Q48 Find the distance between points A(-3, 4) and B(2, 5)**

**Q49 What is the polar form of a complex number Z = 3 + 4i?**

**Q50 In solving the quadratic equation \[x^2 -4x + 3 =0\], the roots are _____________________**

**Q51 Which term of the Arithmetic Progession 49, 44, 39, . . . , is 9?**

**Q52 Find the equation of the circle center (2 , -3) and radius 4**

**Q53 Express 5 + 12i in a polar form, i.e in form of\[ Z = r( cos {\theta} + isin {\theta})\]**

**Q54 Let Z = 5 + 12i, find |Z|**

**Q55 As in no 5 above, find \[Z_{1} Z_{2}\].**

**Q56 This question is for nos 5 and 6. Let \[Z_{1} = 5 + 2i\] and \[Z_{2} = 7 + 3i \], find \[Z_{1} + Z_{2}\].**

**Q57 If \[ Z_{1} = 3 + 2i and Z_{2} = 4 + 3i \], find the distance between \[Z_{1} and Z_{2}\].**

**Q58 In the solution of a quadratic equation\[ x^2 – 4x + 5 = 0\], the roots are _____________________**

**Q59 Evaluate \[\frac{3n^2- 5n + 4}{4n^2 +7n +1} as n\rightarrow \infty\]**

**Q60 Solve for x if \[|x – 5|\leq 4\]**

**Q61 If \[U_{n} = 2n^2 – 4n + 5\], evaluate \[U_{1}\]**

**Q62 What are the values of x for which \[\frac {x^3 + 3x^2 + 2x} { x^2 + 5x +6} = 0 \]**

**Q63 Let x be the required Arithmetic Mean, then 8, x, 16 form three successive terms in the Aritmetic Progression. Find x.**

**Q64 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.**

**Q65 Solve for x in \[ \frac{ | x + 2|} {4} \leq 3\]**

**Q66 Find the number of terms in an Arithmetic Progression whose first term is 5 common difference 3 and sum is 55**

**Q67 Solve the inequality \[( x -3)( x- 2) \leq 0\]**

**Q68 Find the values of x for which \[\frac {x^ 3 + 3x^ 2 +2x +7} {x^2 +5x +6 }\] is undefined**

**Q69 Find the solution set of \[\frac {x+2} {x + 1} = 1\]**

**Q70 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.**

**Q71 Evaluate\[ \frac {3n^2 -14n + 6}{n^2 + 7n + 2}\]**

**Q72 Find the limiting value of \[\frac { 7n + 5} { 2n – 3}\] as n \rightarrow {\infIty}**

**Q73 How many read Science today if and only if, they read Caravan?**

**Q74 How many read Caravan as their only magazine?**

**Q75 In a survey of 100 families, the numbers that read the most recent issues of various magazinees were found to be as follows: Readers digest = 28, Readers digets 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?**

**Q76 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**

**Q77 In a geometric series, the first term is 7, the last term is 448, and the sum is 889. Find the common ratio, r**

**Q78 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**

**Q79 The sum of five numbers in an Arithmetic Progression is 25 and the sum of their squares is 165. Find the common difference.**

**Q80 The sum of the first n terms of a series is \[2n^2 – n\]. Find the nth term**