Mathematics Syllabus (JEE Main)
Q. In a bag containing 3 red, 2 blue, and 5 green balls, what is the probability of drawing a blue ball?
A.
1/5
B.
1/4
C.
1/10
D.
1/2
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Solution
Total balls = 3 + 2 + 5 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 2/10 = 1/5.
Correct Answer: B — 1/4
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Q. In a bag of 10 balls, 4 are red and 6 are blue. What is the probability of picking a red ball?
A.
2/5
B.
4/10
C.
3/5
D.
1/2
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Solution
Probability = Number of red balls / Total balls = 4/10 = 2/5.
Correct Answer: B — 4/10
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Q. In a box of 10 balls, 4 are red and 6 are blue. What is the probability of picking a red ball?
A.
0.4
B.
0.5
C.
0.6
D.
0.7
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Solution
Probability = Number of red balls / Total balls = 4/10 = 0.4.
Correct Answer: A — 0.4
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Q. In a box of 100 balls, 30 are red, 50 are blue, and 20 are green. What is the probability of picking a red ball?
A.
0.3
B.
0.5
C.
0.2
D.
0.1
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Solution
Probability = Number of red balls / Total balls = 30/100 = 0.3.
Correct Answer: A — 0.3
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Q. In a box, there are 5 white and 3 black balls. If a ball is drawn and it is black, what is the probability that the next ball drawn is white?
A.
0.625
B.
0.5
C.
0.375
D.
0.25
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Solution
After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/(5+2) = 5/7 ≈ 0.625.
Correct Answer: A — 0.625
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Q. In a class of 30 students, 18 are boys and 12 are girls. If a student is selected at random, what is the probability that the student is a girl given that the student is not a boy?
A.
1/2
B.
2/3
C.
1/3
D.
1/4
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Solution
The total number of students that are not boys is 12 (girls). The probability of selecting a girl given that the student is not a boy is 12/12 = 1.
Correct Answer: B — 2/3
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Q. In a class of 30 students, 18 are boys and 12 are girls. If a student is selected at random, what is the probability that the student is a girl?
A.
2/5
B.
1/3
C.
1/2
D.
3/5
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Solution
The probability of selecting a girl is the number of girls divided by the total number of students, which is 12/30 = 2/5.
Correct Answer: A — 2/5
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Q. In a class of 30 students, 18 are boys and 12 are girls. What is the probability of randomly selecting a girl?
A.
2/5
B.
1/3
C.
1/2
D.
3/5
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Solution
The probability of selecting a girl is the number of girls divided by the total number of students, which is 12/30 = 2/5.
Correct Answer: A — 2/5
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Q. In a class of 30 students, 18 are boys. What is the probability of randomly selecting a girl?
A.
0.4
B.
0.6
C.
0.5
D.
0.3
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Solution
Number of girls = 30 - 18 = 12. Probability = 12/30 = 0.4.
Correct Answer: A — 0.4
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Q. In a class of 30 students, 18 are girls. If a student is selected at random, what is the probability that the student is a girl?
A.
3/5
B.
2/5
C.
1/2
D.
1/3
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Solution
Probability = Number of girls / Total students = 18/30 = 3/5.
Correct Answer: A — 3/5
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Q. In a class of 30 students, the marks obtained are as follows: 45, 50, 55, 60, 65. What is the median?
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Solution
Arranging the data: 45, 50, 55, 60, 65. Median = 55 (middle value).
Correct Answer: B — 55
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Q. In a class of 30 students, the marks obtained are as follows: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. What is the median?
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Solution
Median = (70 + 75) / 2 = 145 / 2 = 72.5, but since we have to choose from options, the closest is 75.
Correct Answer: C — 75
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Q. In a class of 40 students, 25 are girls and 15 are boys. If a student is selected at random, what is the probability that the student is a boy given that the student is not a girl?
A.
1
B.
0.5
C.
0.25
D.
0.75
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Solution
If a student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 15/15 = 1.
Correct Answer: A — 1
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Q. In a class of 40 students, 25 are girls. What is the probability of selecting a boy?
A.
0.375
B.
0.625
C.
0.5
D.
0.25
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Solution
Number of boys = 40 - 25 = 15. Probability = 15/40 = 0.375.
Correct Answer: B — 0.625
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Q. In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and 10 are taking both. What is the probability that a student is taking Physics given that they are taking Mathematics?
A.
1/4
B.
1/3
C.
1/2
D.
1/5
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Solution
P(Physics | Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 10/25 = 2/5.
Correct Answer: C — 1/2
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Q. In a class of 5 students, their scores are 10, 20, 30, 40, and 50. What is the median score?
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Solution
Median = 30 (middle value when arranged in order: 10, 20, 30, 40, 50).
Correct Answer: B — 30
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Q. In a class of 5 students, their scores are 12, 15, 18, 20, and 25. What is the median score?
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Solution
Arranging the scores: 12, 15, 18, 20, 25. Median = 18 (middle value).
Correct Answer: B — 18
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Q. In a class of 5 students, their scores are 12, 15, 20, 25, and 28. What is the median score?
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Solution
Arranging the scores: 12, 15, 20, 25, 28. Median = 20 (middle value).
Correct Answer: B — 20
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Q. In a class of 5 students, their scores are 80, 90, 70, 85, and 95. What is the median score?
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Solution
Arranging the scores: 70, 80, 85, 90, 95. Median = 85 (middle value).
Correct Answer: B — 85
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Q. In a data set, if the mean is 30 and the median is 25, what can be inferred about the data?
A.
Skewed right
B.
Skewed left
C.
Symmetrical
D.
Uniform
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Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer: A — Skewed right
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Q. In a data set, if the mean is 30 and the median is 25, what can be inferred?
A.
Data is skewed right
B.
Data is skewed left
C.
Data is symmetric
D.
Data is uniform
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Solution
Since the mean is greater than the median, the data is skewed to the right.
Correct Answer: A — Data is skewed right
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Q. In a data set, if the mean is 50 and the median is 45, what can be inferred about the data?
A.
Skewed right
B.
Skewed left
C.
Symmetric
D.
Uniform
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Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer: A — Skewed right
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Q. In a data set, if the mean is 50 and the sum of all values is 500, how many values are there?
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Solution
Number of values = Sum / Mean = 500 / 50 = 10.
Correct Answer: C — 10
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Q. In a data set, if the mode is 15 and the mean is 20, what can be said about the data?
A.
Positively skewed
B.
Negatively skewed
C.
Symmetrical
D.
Uniform
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Solution
Since the mean is greater than the mode, the data is positively skewed.
Correct Answer: A — Positively skewed
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Q. In a data set, if the values are 2, 4, 4, 4, 5, 5, 7, what is the mode?
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Solution
Mode = 4 (most frequently occurring value).
Correct Answer: A — 4
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Q. In a data set, the mean is 10 and the standard deviation is 2. What is the coefficient of variation?
A.
20%
B.
10%
C.
5%
D.
15%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (2/10) * 100 = 20%.
Correct Answer: A — 20%
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Q. In a data set, the mean is 20 and the median is 18. What can be inferred about the data?
A.
Skewed right
B.
Skewed left
C.
Symmetric
D.
Uniform
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Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer: A — Skewed right
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Q. In a data set, the mean is 20 and the median is 18. What can be said about the data?
A.
Positively skewed
B.
Negatively skewed
C.
Symmetrical
D.
Uniform
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Solution
Since the mean is greater than the median, the data is positively skewed.
Correct Answer: A — Positively skewed
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Q. In a data set, the mean is 20 and the standard deviation is 4. What is the coefficient of variation?
A.
20%
B.
15%
C.
10%
D.
5%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4/20) * 100 = 20%.
Correct Answer: A — 20%
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Q. In a data set, the mean is 50 and the number of observations is 10. What is the sum of all observations?
A.
400
B.
500
C.
600
D.
700
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Solution
Sum = Mean * Number of Observations = 50 * 10 = 500.
Correct Answer: B — 500
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