Q. A bag contains 4 white and 6 black balls. If two balls are drawn at random, what is the probability that both are black?
A.
0.5
B.
0.24
C.
0.36
D.
0.4
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Solution
P(both black) = (6/10) * (5/9) = 30/90 = 1/3 ≈ 0.333.
Correct Answer: B — 0.24
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Q. A bag contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is not blue?
A.
0.5
B.
0.6
C.
0.7
D.
0.8
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Solution
The total number of balls is 10. The number of non-blue balls is 7 (5 red + 2 green). Thus, the probability is 7/10 = 0.7.
Correct Answer: C — 0.7
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Q. A box contains 3 red, 2 blue, and 5 green balls. If one ball is drawn at random, what is the probability that it is either red or blue?
A.
0.5
B.
0.25
C.
0.625
D.
0.75
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Solution
Total balls = 3 + 2 + 5 = 10. Probability of red or blue = (3 + 2) / 10 = 5 / 10 = 0.5.
Correct Answer: C — 0.625
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Q. A box contains 4 white and 6 black balls. If two balls are drawn at random, what is the probability that both are white?
A.
1/15
B.
2/15
C.
1/10
D.
1/5
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Solution
The probability of drawing 2 white balls is (4/10) * (3/9) = 12/90 = 1/15.
Correct Answer: A — 1/15
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a queen?
A.
1/4
B.
1/13
C.
4/52
D.
17/52
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Solution
There are 13 hearts and 4 queens, but one of the queens is a heart. Thus, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.
Correct Answer: D — 17/52
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Q. A group of friends consists of 12 who play football, 8 who play basketball, and 5 who play both. How many play only football?
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Solution
To find the number of friends who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.
Correct Answer: C — 7
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Q. A group of friends consists of 5 who like football, 4 who like basketball, and 2 who like both. How many friends like only football?
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Solution
The number of friends who like only football is calculated as: Only Football = Total Football - Both = 5 - 2 = 3.
Correct Answer: A — 3
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Q. From a group of 8 people, how many ways can a team of 4 be selected?
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Solution
The number of ways to choose 4 people from 8 is given by 8C4 = 70.
Correct Answer: B — 56
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Q. How many ways can 5 different colored balls be placed in 3 different boxes if each box can hold any number of balls?
A.
243
B.
125
C.
256
D.
3125
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Solution
Each ball has 3 choices (boxes), so for 5 balls, the total arrangements = 3^5 = 243.
Correct Answer: A — 243
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Q. How many ways can 5 students be seated in a row of 5 chairs?
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Solution
The number of ways to arrange 5 students in 5 chairs is 5! = 120.
Correct Answer: A — 120
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Q. If 25% of a group like tea, 35% like coffee, and 10% like both, what percentage like only tea?
A.
15%
B.
25%
C.
10%
D.
20%
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Solution
The percentage who like only tea is 25% - 10% = 15%.
Correct Answer: A — 15%
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Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either fruit?
A.
35%
B.
30%
C.
25%
D.
20%
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Solution
Using inclusion-exclusion, the percentage that likes either fruit is 25% + 15% - 5% = 35%.
Correct Answer: A — 35%
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Q. If 40 students like Mathematics, 30 like Science, and 10 like both subjects, how many students like only Mathematics?
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Solution
The number of students who like only Mathematics is 40 - 10 = 30.
Correct Answer: B — 20
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Q. If 6 different colored balls are to be arranged in a row, how many arrangements are possible?
A.
720
B.
600
C.
360
D.
480
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Solution
The number of arrangements of 6 different colored balls is 6! = 720.
Correct Answer: A — 720
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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only writing?
A.
30%
B.
40%
C.
10%
D.
50%
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Solution
The percentage of students who like only writing is 40% - 10% = 30%.
Correct Answer: A — 30%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play only one sport?
A.
90%
B.
80%
C.
70%
D.
60%
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Solution
The percentage playing only cricket is 60% - 10% = 50%, and only football is 40% - 10% = 30%. Thus, total playing only one sport is 50% + 30% = 80%.
Correct Answer: B — 80%
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Q. If a committee of 3 is to be formed from 5 people, how many different committees can be formed?
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Solution
The number of ways to choose 3 people from 5 is given by 5C3 = 10.
Correct Answer: B — 15
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Q. If a committee of 3 members is to be formed from a group of 5 people, how many different committees can be formed?
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Solution
The number of ways to choose 3 members from 5 is given by 5C3 = 10.
Correct Answer: A — 10
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using 26 letters and 10 digits?
A.
676000
B.
6760000
C.
67600
D.
6760
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Solution
The number of passwords is 26^3 * 10^2 = 17576000.
Correct Answer: A — 676000
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 3 letters of the alphabet and the first 5 digits?
A.
150
B.
180
C.
120
D.
100
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Solution
The number of ways to choose 3 letters from 3 is 3! and 2 digits from 5 is 5P2. Total = 3! * 5P2 = 6 * 20 = 120.
Correct Answer: B — 180
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Q. If a sequence is defined as a_n = 3n + 2, what is the value of a_5?
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Solution
Substituting n = 5 into the equation gives a_5 = 3(5) + 2 = 15 + 2 = 17.
Correct Answer: B — 17
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Q. If a team of 4 is to be selected from 10 players, how many different teams can be formed?
A.
210
B.
120
C.
300
D.
150
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Solution
The number of ways to choose 4 players from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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Q. If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?
A.
{2, 4, 6, 8}
B.
{2}
C.
{2, 3, 5, 7}
D.
{2, 3, 5, 7, 4, 6, 8}
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Solution
The intersection A ∩ B includes elements that are both even and prime, which is {2}.
Correct Answer: B — {2}
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Q. If set A contains the elements {1, 2, 3, 4} and set B contains the elements {3, 4, 5, 6}, what is the intersection of sets A and B?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 3, 4, 5, 6}
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Solution
The intersection of sets A and B is the set of elements that are common to both sets. Therefore, the intersection is {3, 4}.
Correct Answer: B — {3, 4}
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Q. If set A contains the numbers {1, 2, 3, 4, 5} and set B contains the numbers {4, 5, 6, 7, 8}, what is the intersection of sets A and B?
A.
{1, 2, 3}
B.
{4, 5}
C.
{6, 7, 8}
D.
{1, 2, 3, 4, 5, 6, 7, 8}
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Solution
The intersection of sets A and B is the set of elements that are common to both sets, which is {4, 5}.
Correct Answer: B — {4, 5}
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Q. If set P = {1, 2, 3, 4} and set Q = {3, 4, 5, 6}, what is the difference P - Q?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 5, 6}
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Solution
The difference P - Q includes elements in P that are not in Q, which is {1, 2}.
Correct Answer: A — {1, 2}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the intersection of sets P and Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
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Solution
The intersection of sets P and Q includes elements that are both even and prime. The only even prime number is 2.
Correct Answer: C — {2}
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Q. If set R = {1, 2, 3, 4, 5} and set S = {4, 5, 6, 7}, what is the symmetric difference of sets R and S?
A.
{1, 2, 3, 6, 7}
B.
{4, 5}
C.
{1, 2, 3, 4, 5, 6, 7}
D.
{6, 7}
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Solution
The symmetric difference of sets R and S includes elements that are in either set but not in both. Thus, it is {1, 2, 3, 6, 7}.
Correct Answer: A — {1, 2, 3, 6, 7}
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Q. If set X = {a, b, c} and set Y = {b, c, d}, what is the union of sets X and Y?
A.
{a, b, c, d}
B.
{b, c}
C.
{a, b}
D.
{c, d}
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Solution
The union of sets X and Y includes all unique elements from both sets. Thus, the union is {a, b, c, d}.
Correct Answer: A — {a, b, c, d}
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Q. If the Binomial Theorem is applied to (x + 2)^4, what is the term containing x^2?
A.
12x^2
B.
24x^2
C.
36x^2
D.
48x^2
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Solution
The term containing x^2 is C(4,2) * x^2 * 2^2 = 6 * x^2 * 4 = 24x^2.
Correct Answer: B — 24x^2
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