Q. If the mass of the Earth were to double, what would happen to the gravitational force between two objects on its surface?
A.
It would double
B.
It would remain the same
C.
It would be halved
D.
It would quadruple
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Solution
F = G * (m1 * m2) / r², doubling the mass of Earth doubles the force.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double, what would happen to the gravitational force between the Earth and an object on its surface?
A.
It would double
B.
It would remain the same
C.
It would halve
D.
It would quadruple
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Solution
F ∝ M; if M doubles, F also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double, what would happen to the weight of an object on its surface?
A.
It would double
B.
It would remain the same
C.
It would be halved
D.
It would be quartered
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Solution
Weight is directly proportional to mass. If the Earth's mass doubles, the weight of the object also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to increase while the radius remains constant, what would happen to the gravitational force experienced by an object on its surface?
A.
It would decrease
B.
It would increase
C.
It would remain the same
D.
It would become zero
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Solution
If the mass of the Earth increases, the gravitational force experienced by an object on its surface would increase.
Correct Answer: B — It would increase
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Q. If the mean of a data set is 12 and there are 8 values, what is the total sum of the values?
A.
80
B.
90
C.
100
D.
110
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Solution
Total sum = Mean * Number of values = 12 * 8 = 96.
Correct Answer: A — 80
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Q. If the mean of a data set is 20 and the standard deviation is 4, what is the coefficient of variation?
A.
20%
B.
25%
C.
15%
D.
10%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4 / 20) * 100 = 20%.
Correct Answer: B — 25%
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Q. If the mean of a data set is 30 and there are 10 values, what is the total sum of the values?
A.
300
B.
310
C.
320
D.
330
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Solution
Total sum = Mean * Number of values = 30 * 10 = 300.
Correct Answer: A — 300
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Q. If the mean of a data set is 50 and the standard deviation is 10, what is the coefficient of variation?
A.
20%
B.
10%
C.
15%
D.
25%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (10 / 50) * 100 = 20%.
Correct Answer: A — 20%
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Q. If the mean of a data set is 50 and there are 10 values, what is the total sum of the values?
A.
500
B.
600
C.
700
D.
800
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Solution
Total sum = Mean * Number of values = 50 * 10 = 500.
Correct Answer: A — 500
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Q. If the mean of a dataset is 50 and there are 10 numbers, what is the total sum of the numbers? (2021)
A.
500
B.
600
C.
550
D.
450
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Solution
Total sum = Mean * Number of elements = 50 * 10 = 500.
Correct Answer: A — 500
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Q. If the mean of a set of numbers is 30 and the total number of elements is 6, what is the total sum of the elements? (2023)
A.
180
B.
150
C.
120
D.
200
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Solution
Total sum = Mean * Number of elements = 30 * 6 = 180.
Correct Answer: A — 180
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Q. If the mean of the first five prime numbers is 6, what is the sum of these numbers? (2020)
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Solution
Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.
Correct Answer: A — 30
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Q. If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?
A.
20 degrees
B.
30 degrees
C.
40 degrees
D.
60 degrees
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Solution
Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.
Correct Answer: B — 30 degrees
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Q. If the measured length of a rod is 20 cm with an error of 0.5 cm, what is the relative error in the measurement?
A.
0.025
B.
0.05
C.
0.0025
D.
0.005
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Solution
Relative error = (Absolute error / Measured value) = 0.5 / 20 = 0.025 or 2.5%
Correct Answer: B — 0.05
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Q. If the measured value of a quantity is 100 with a relative error of 0.02, what is the absolute error?
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Solution
Absolute error = Relative error * Measured value = 0.02 * 100 = 2.
Correct Answer: A — 2
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Q. If the measured value of a quantity is 75 with a relative error of 0.04, what is the true value?
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Solution
Relative error = Absolute error / True value. Let true value be x. 0.04 = |75 - x| / x. Solving gives x = 78.
Correct Answer: B — 78
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Q. If the median of the data set 3, 5, 7, 9, x is 7, what is the value of x?
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Solution
For median to be 7, x must be 7 or less, hence x = 7.
Correct Answer: D — 8
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Q. If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)
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Solution
For the median to be 9, x must be 9. The ordered set is 3, 7, 9, 9, 15.
Correct Answer: A — 8
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Q. If the median of the data set {1, 2, 3, 4, 5, 6, 7, 8} is x, what is the value of x?
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Solution
Median = (4 + 5) / 2 = 9 / 2 = 4.5.
Correct Answer: B — 4.5
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Q. If the median of the data set {3, 1, 4, 2, 5} is x, what is the value of x?
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Solution
Sorted data set: {1, 2, 3, 4, 5}. Median = 3.
Correct Answer: B — 3
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Q. If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?
A.
48 cm²
B.
60 cm²
C.
72 cm²
D.
80 cm²
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Solution
Area = (4/3) * √[m1 * m2 * m3] = (4/3) * √[6 * 8 * 10] = 48 cm².
Correct Answer: B — 60 cm²
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Q. If the medians of a triangle are 6, 8, and 10, what is the area of the triangle?
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Solution
Area = (4/3) * √(s(s - m1)(s - m2)(s - m3)), where s = (6 + 8 + 10)/2 = 12. Area = (4/3) * √(12 * 6 * 4 * 2) = 48.
Correct Answer: C — 48
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Q. If the meetings of a project team are scheduled on Monday, Wednesday, and Friday, and no two meetings can occur on consecutive days, which day can be added for an additional meeting without violating the schedule?
A.
Tuesday
B.
Thursday
C.
Saturday
D.
Sunday
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Solution
Thursday can be added as it does not fall on a consecutive day with the existing meetings.
Correct Answer: B — Thursday
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?
A.
(6, 7)
B.
(8, 9)
C.
(4, 5)
D.
(0, 1)
Show solution
Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer: A — (6, 7)
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?
A.
(6, 7)
B.
(8, 9)
C.
(4, 5)
D.
(2, 3)
Show solution
Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer: A — (6, 7)
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Q. If the mode of a data set is 5, which of the following statements is true?
A.
5 occurs most frequently
B.
5 is the average
C.
5 is the middle value
D.
5 is the least value
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Solution
Mode is the value that appears most frequently in a data set.
Correct Answer: A — 5 occurs most frequently
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Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is removed, what will be the new mode?
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Solution
New mode = 2 (as 4 is removed, 2 is the next most frequent).
Correct Answer: A — 2
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Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is?
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Solution
Mode is the number that appears most frequently. Here, 4 appears 3 times.
Correct Answer: D — 4
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Q. If the mode of the data set 2, 3, 3, 5, 7, 8 is 3, what is the mode of the data set 1, 1, 2, 2, 3, 3, 3, 4?
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Solution
Mode = 3 (most frequent value).
Correct Answer: C — 3
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Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is removed, what is the new mode?
A.
4
B.
5
C.
6
D.
No mode
Show solution
Solution
Removing 5 leaves 2, 3, 4, 4, 6. The new mode is 4.
Correct Answer: D — No mode
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