Revision Test(XI)(complex number)
_____________&____________________
1) If x, y are real and x +iy= -i(-2+3i) then x and y are
A) 3,2 B) 2,3 C) -3,-2 D) -2, -3 E) n
2) Value of {(1+i)/(1-i)}²+ {(1-i)/(1+i)}² is
A) 0 B) 1 C) -2 D) 2 E) n
3) If z= x+ iy and | z-1| +| z +1| = 4 then 3x² + 4y² = ?
A) 10 B) 12 C) 14 D) 16 E) none
4) Modulus of √12 + 6{(1-i)/(1+i)} is
A) 4 B) √3 C) 2 √3 D)4 √3 E) n
5) If one complex cube root of unity be w then the value of w⁵ + w¹⁰ is.
A) 1 B) -1 C) w D) w² E) n
6) If x √2= 1+ √(-1) then the value of x⁶ + x⁴ + x² +2 is
A) 0 B) 1 C) -1 D) x E) none
7) Square root of -5+ 12i is
A) ±(1+2i) B) ±(2+3i) C) ±(1- 2i) D)±(2 - 3i)
8) If ³√(x+ iy)= a+ ib where x,y a, b are all real, then the value of x/a + y/b is
A) (a²-b²) B) (a²+b²) C) 4(a²+b²) D) 4(a²- b²) E) none
9) If m, n are the imaginary cube roots of unity, then m⁴+ n⁴ +1/mn is .
A) 0 B) 1 C) -1 D) 2 E) none
10) If x= 2 - i √3 then the value of 2x⁴ - 5x³ - 3x² + 41x is
A) 0 B) 2 C) 3 D) 35
1/8/21
1) For any set A, (A')' is equals to
A) A' B) A C) ∅ D) none
2) The number of subsets of a set containing n elements is..
A) n B) 2ⁿ -1 C) n² D) 2ⁿ
3) if A={1,3,5,B} and B={2,4}, then
A) 4 ∈ A B) {4}⊂A C) B⊂A D) none
** Learn:: symmetric difference is (A-B)U(B-A)
4) the symmetric difference of A={1,2,3} and B={3,4,5} is
A) {1,2} B) {1,2,4,5} C) {4,3} D){2,5,1,4,3}
5) Let A={x:x∈R, x≥4} and B={x ∈R: x< 5}. then A∩B is..
A) (4,5) B) (4,5) C) (4,5) D) (4,5)
6) If A={1,2,3,4,5}, then the number of proper subsets of A is..
A)120 B) 30 C) 31 D) 32
7) In set builder method the null set is represented by..
A) { } B) ∅ C) [x: x≠ x] D) {x:x= x}
8) In a City 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is .
A) 80% B) 40% C) 60% D)70%
9) An investigator interviewed 100 students to determine the performance of three drinks milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and a coffee; 25 students take milk and tea; 12 students take tea and coffee. five student take milk only; 5 student take coffee only and 8 students take tea only. Then the number of students who did not take any of the three drinks is..
A) 10 B) 20 C) 25 D) 45
10) Two finite sets have m and n elements. The number of elements in the power set of the first set is 48 more than the total number of elements and powers set of the second set. Then, the value of m and n are..
A) 7,6 B) 6,3 C) 6,4 D) 7,4 E) 3,7
11) In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; physics 70; chemistry 40; mathematics and physics 30; mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics,Physics and Chemistry 18. how many students have offered mathematics.
A) 35 B) 48 C) 60 D) 22 E) 30
12) At the quarterly birthday party Sherry a baby boy, 40 persons choose to kiss him and 25 choose shake hands with him. 10 persons choose to both kiss him and shake hands with him. How many persons turned out at the party ? 55
13) In an examination 43% passed in maths. 48% passed in Physics and 52% passed in chemistry. only 8% students passed in all three. 14% in math and physics and 21% passed in math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200.
A) how many student passed in maths only? 32
B) find the ratio of students passing in maths only to the students passing in chemistry only. 16:19
C) what is the ratio of the number of students passing in physics only to the students passing in either physics or chemistry or both? 22:80
14) In the AMS club, all the members participate either in the Tambola or the Fete, 420 participate in Fete, 350 Participate in the Tambola and 220 participate in both. How many members does the club have ? 550
15) There are 20000 people living in Defence Colony, Gurgaon. Out of them 9000 subscribe to Star TV Network and 12000 to Zee TV Network. If 4000 subscribe to both, how many do not subscribe to any of the two? 3000
16) Last year, there were 3 sections in the catalyst, a mock test paper. Out of them, 33 students cleared the cutoff in section 1, 34 students clear the cutoff In section 2 and 32 cleared the cutoff in section 3, 10 students clear the cutoff in section 1and section 2, 9 cleared the cutoff in section 2 and section 3, 8 cleared the cutoff in section 1 and section 3. The number of people who cleared each section alone was equal and was 21 for each section.
A) How many cleared all the three sections ? 6
B) How many cleared only one of the three sections? 63
C) The ratio of the number of students clearing the cutoff in one or more of the sections to the number of students clearing the cutoff in section 1 alone is? 78/21
17) In the Indian athletic squad sent to the Sydney Olympics, 21 athletes were in the triathlon team 26 were in the pentathlon team and 29 were in the marathon team. 14 athletes can take part in triathlon and pentathlon 12 can take part in marathon and triathlon 15 can take part in Pentathlon and marathon and 8 can take part in all the three games.
A) How many players are there in all? 43
B) How many were in the marathon team only? 10
18) In a test in which 120 students appeared, 90 passed in history, 65 passed in political science. 75 passed in the political science. 30 students passed in only one subject and 55 students in only two. Five students passed in no subject.
A) how many students passed in all the three subjects? 30
B) find the number of students who passed in at least two subjects. 85
19) 5% of the passengers who boarded Gauhati New Delhi Rajdhani Express on 20 February 2020, do not like coffee, tea and ice cream and 10% like all the three. 20% like coffee and tea, 25% like ice cream and coffee and 25% like icecream and tea. 55% like coffee, 50% like tea and 50% like icecream.
A) the passengers who like only coffee is greater than the passengers who like only icecream by. 100%
B) the percentage of passengers who like both tea and ice cream but not coffee is. 15
C) the percentage of passengers who like at least 2 of the 3 product is. 50
D) if the number of passengers is 180, then the number of passengers who like ice cream only is. 18
20) In a survey survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% like the coffee and tea, 32% smoked and drink tea and 30% smoked and drink coffee . Only 6% did none of these. if the total number of student is 2000 then
A) The ratio of the number of students who like only coffee to the number who like only tea is. 2:3
B) The number of students who like coffee and smoking but not tea is. 240
C) The percentage of those who those who like coffee or tea but not smoking among those who like at least one of these is:. More than 30
D) the percentage of those who like at least one of these is. 94
E) The two items having the ratio 1:2 are....
Ans.Coffee and smoking only and tea only..
F) The number of persons who like coffee and smoking only and the number who like coffee only bear a ratio. 3:2
G) percentage of those who like tea and smoking but not coffee age is. 14
21) 30 monkeys went to a picnic.
25 monkeys chose to irritate cows while 20 choose to irritate buffaloes. how many of chose to irritate both buffaloes and cows? 15
22) In the CBSE Board exams last year 53% passed in Biology, 61% passed in English, 60% in Social Studies, 24% in Biology and English. 35% in English and Social studies, 27% in Biology and Social studies and 5% in none.
A) percentage of passes in all subject is. 7
B) if the number of student in the class is 200. how many passed in only one subject ? 46
C) if the number of students in the class is 300, what will be the % change in the number passes in only two subjects, if the original number of student is 200 ? 50%
D) what is the ratio of percentage of passes in Biology and Social Studies but not English in relation to the percentage of passes in Social Studies and English but not Biology. 5:7
23) In the AMS Quiz held last year, participants were free to choose their respective areas from which they were asked questions. Out of 880 participants, 224 chose Mythology, 240 science and 336 chose Sports, 64 choose both sports and Science, 80 chose Mythology and sports, 40 choose Mythology and Science and 24 chose all the three areas.
A) the percentage of participants who did not choose any area is. 27.27%
B) If those participating, the percentage who choose only one area is. Less than 60%
C) Number of participants who choose at least two areas is: 136
D) Which of the following areas shows a ratio of 1:8 ?
a) Mythology and Science but not Sports: Mythology only
b) Mythology and sports but not science: science only:
Ans: Mythology and Science but not Sports: Mythology only
E) the ratio of students choosin sports and Science but not Mythology to science but not Mythology and sports is 1:4
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