LAST TIME REVISION SET THEORY (4)

1) Using set operations show that the number 231 and 260 are prime to each other.

2) Applying set operations prove that, 3 + 4 = 7

3) In a class of 70 students, each student has taken either English or Hindi or both. 45 students have taken English and 30 students have taken Hindi. How many students have taken both English and Hindi.                 5

4) A market research group conducted a survey of 1000 consumers and reported that 700 consumers liked product A and 480 consumers liked product B. What is the least number that must have liked both products ?       180

5) In a town 60% read magazine A; 25% do not read magazine A but read magazine B. Calculate the percentage of those who do not read any magazine. Also find the highest and lowest possible figures of those who read magazine B.      15%,85%, 25%

6) In a statistical investigation of 1003 families of Calcutta, it was found that 63 families had neither a radio nor a TV, 794 families had a radio and 187 had a television. How many families in that group had both a radio and a TV.?      41

7) Three daily newspaper, E, B, H are published in a certain city. 62% of the citizens read E, 59% read B, 41% read H, 40% read both E and B, 28% read both B and H, 24% read both E and H. Find the percentage of citizens who read all the three papers.       Data inadequate

8) In a survey of college students, it was found that 40% use their own books, 50% use library books , 30% use borrowed books, 20% use both their own books and library books, 15% use their own books and borrowed books, 10% use library books and borrowed books, and 4% use their own books, library books and borrowed books. Calculate the percentage of students who do not use a book at all.      21%

9) In a city three daily newspapers X, Y, Z are published; 65% of the citizens read X, 54% read Y, 45% read Z; 32% read X and Y; 32% read Y and Z; 28% read X and Z; 12% do not read any one of these three papers. If the total number of people in the city be 1000000, find the number of citizens  who read all the three newspapers.     220000

10) A company studies the product preferences of 300 consumers, it was found that 226 liked product A, 51 liked product B, 54 liked product C; 21 liked product A and B, 54 liked products A and C, 39 liked products B and C and 9 liked all the three products. Prove that, the study of results are not correct. ( asume that each consumers likes at least one of the three products).        

11)  The production manager of Sen, Sarkar and Lahiri Company examined 100 items produced by the workers and furnished the following reports to his boss;
Defect measurement 50, defect in colouring 30, defect in quality 25, defect in quality and colouring 10, defect in measurement and colouring 8, defect in measurement and quality 20 and 5 are defective in all respect. The manager was penalized for the report.  Using appropriate result of set theory, explain the reason for the penal measure.     

12) In a survey of 150 students, it was found that 40 students studied Economics, 50 students studied Mathematics, 60 students studied Accountancy and 15 students studied all the three subjects. It was also found that 27 students studied Economics and Accountancy , 35 students studied Accountancy and Mathematics and 25 students studied Economics and Mathematics. Find the number who studied only Economics and the number who studied none of these subjects.         3,72

13) Out of 1000 students in a college, 540 played football, 465 played cricket and 370 played volleyball; of the total 325 played both football and cricket, 260 played football and volleyball, 235 played cricket and volleyball, 125 played all the three games. How many students 
a) did not play any game.
b) played only one game
c) played just 2 games ?    320,110,445

14) A group consists of a number of Students and each student of the group can speak at least one of the language Bengali, Hindi and English. 65 can speak Bengali, 54 Hindi and 37 English, 31 can speak both Bengali and Hindi , 17 both Hindi and English, 18 both Bengali and English. Determine the greatest and least number of students in the group.      107,90

15) An investigator interviewed 100 students to determine their preference for the three drinks; milk (M), coffee (C) and tea (T). He reported the following:
10 students had all the three drinks M, C and T; 20 had M and C; 30 had C and T, 25 had M and T, 12 had M only, 5 had C only and 8 had T only. 
How many did not take any of the three drinks.      20

Comments

Post a Comment

Popular posts from this blog

REVISION - XII

DETERMINANT  1) If two rows or two columns of a determinant are identical then the value of the determinant is a) 0 b) 2 c) -1 d) 1 2) If D= 0     a    b              -a     0    c              -b    -c    0 then D is  a) 0 b) 1 c) a d) b 3) a+b    a+2b    a+3b     a+2b  a+3b    a+4b= 0     a+4b  a+5b     a+6b 4 ) 1+ a      1        1       1       1+ b     1        1         1      1+ c = abc(1/a + 1/b + 1/c) 5) loga       p      1     logb       q       1 = 0 (a,b,c> 0)     logc       r     ...
Read more

SHORT QUESTIONS- X (All chapter)

Image
GOODS AND SERVICES TAX Multiple Choice Questions 1) IGST is charged on: a) interstate transaction b) intrastate transaction c) both a, b d) none 2) GST payable is equals to a)  ITC --output GST b) output GST + ITC c) output GST - ITC d) output GST 3) A dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000. If the rate of GST is 18% and GST, then SGST is: a) Rs1620 b) Rs3240 c) nil d) none 4) In a transaction from Delhi to Lucknow, MRP = Rs10000, discount= 10%, GST= 28%. Here IGST is: a)  Rs2520 b) Rs5040 c) nil  d) none 5) A refrigerator was sold for Rs15000 under intrastate transaction from station A to station B and the GST rate is 18%. CGST is: a) Rs1450 b) Rs 1350 c) Rs1300 d) Rs2700  6) A dealer purchased goods worth Rs 15000 and sold them for Rs21000 within the state. If the rate of GST is 12%, then the net SGST paid by the dealer is: a) Rs360 b) Rs720 c) Rs800 d) Rs850  7) A dealer in Delhi sold a water heater whose marked is Rs22000...
Read more

MULTIPLE CHOICE QUESTIONS -XII

MAXIMUM AND MINIMUM 1) The minimum value of f(x)= x²+ 250/x is a) 55  b) 25 c) 50 d) 75  2) If  f(x)=  1/(4x²+ 2x +1) , then its maximum value is  a) 2/3 b) 4/3  c) 3/4 d) 1  3) The function  f(x)=  2x³- 3x²- 12x +4 has a) no maximum and minimum b) one maximum and one minimum  c) two maximum d)  two minimum  4) The height of the cylinder of maximum volume that can be inscribed in a sphere of radius a is  a) 3a/2  b) √2a/3 c) 2 a/√3 d)  a/√3 5) Maximum value of (logx)/x in [0,∞) is a) (log2)/2 b) 0 c) 1/e d) e 6) let the function f: R--> R be defined by f(x)= 2x + cosx; then f(x).. a) has maximum value at x=0. b) has minimum value at x=π c) is a decreasing function d) is an increasing function  7) The maximum distance from the origin of a point on the curve x= a sin t - b sin(at/b), y= a cos t - b cos(at/b), both a, b> 0, is a) a- b b) a+ b c) √(a²+ b²) d) √(a²- b²) 8) Let x and y be two variables and x...
Read more