Q. What is the measure of each angle in a square? (2023)
A.
90 degrees
B.
60 degrees
C.
120 degrees
D.
45 degrees
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Solution
Each angle in a square measures 90 degrees.
Correct Answer: A — 90 degrees
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Q. What is the measure of each angle in a triangle if one angle is 40 degrees and the other is 60 degrees? (2019)
A.
80 degrees
B.
100 degrees
C.
120 degrees
D.
140 degrees
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Solution
The sum of angles in a triangle is always 180 degrees. If one angle is 40 degrees and another is 60 degrees, the third angle is 180 - (40 + 60) = 80 degrees.
Correct Answer: A — 80 degrees
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Q. What is the measure of each angle in a triangle if one angle is 50 degrees and the other is 60 degrees? (2019)
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.
Correct Answer: A — 70 degrees
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Q. What is the measure of the exterior angle of a triangle if the interior angles are 50 degrees and 60 degrees? (2021)
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
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Solution
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, the exterior angle = 50 + 60 = 110 degrees.
Correct Answer: B — 80 degrees
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Q. What is the measure of the exterior angle of a triangle if the two interior opposite angles are 50 degrees and 60 degrees? (2023)
A.
110 degrees
B.
100 degrees
C.
120 degrees
D.
130 degrees
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Solution
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, the exterior angle = 50 + 60 = 110 degrees.
Correct Answer: A — 110 degrees
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Q. What is the median of the following data set: 12, 15, 14, 10, 18? (2023)
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Solution
First, arrange the data in ascending order: 10, 12, 14, 15, 18. The median is the middle value, which is 14.
Correct Answer: B — 14
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Q. What is the median of the following numbers: 10, 20, 30, 40, 50, 60, 70? (2022)
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Solution
The numbers are in order. The median is the 4th number, which is 40.
Correct Answer: B — 40
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Q. What is the median of the following numbers: 22, 18, 25, 30, 20? (2021)
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Solution
Arranging the numbers: 18, 20, 22, 25, 30. The median is the middle number, which is 22.
Correct Answer: A — 20
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Q. What is the median of the following numbers: 8, 3, 5, 12, 7, 10? (2023)
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Solution
Arrange the numbers: 3, 5, 7, 8, 10, 12. The median is the average of the 3rd and 4th numbers: (7 + 8) / 2 = 7.5.
Correct Answer: C — 8
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Q. What is the median of the following set of numbers: 3, 7, 5, 9, 1? (2021)
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Solution
To find the median, first arrange the numbers in ascending order: 1, 3, 5, 7, 9. The median is the middle number, which is 5.
Correct Answer: B — 5
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Q. What is the median of the following set: 4, 1, 7, 3, 9, 2? (2022)
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Solution
Arranging the numbers: 1, 2, 3, 4, 7, 9. The median is the average of the 3rd and 4th numbers: (3 + 4) / 2 = 3.5.
Correct Answer: A — 3
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Q. What is the minimum value of f(x) = 2x^2 - 8x + 10? (2021)
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Solution
The minimum occurs at x = -b/(2a) = 8/(2*2) = 2. f(2) = 2(2^2) - 8(2) + 10 = 2.
Correct Answer: A — 1
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Q. What is the minimum value of the function f(x) = 2x^2 + 4x + 1? (2023)
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Solution
The vertex is at x = -4/(2*2) = -1. The minimum value is f(-1) = 2(-1)^2 + 4(-1) + 1 = -1.
Correct Answer: B — 1
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Q. What is the mode of the following data set: 2, 3, 4, 2, 5, 2, 3? (2023)
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Solution
Mode is the number that appears most frequently. Here, 2 appears 3 times.
Correct Answer: A — 2
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Q. What is the mode of the following data set: 2, 3, 4, 4, 5, 5, 5, 6? (2023)
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Solution
Mode is the number that appears most frequently. Here, 5 appears 3 times.
Correct Answer: B — 5
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Q. What is the mode of the following data set: 4, 1, 2, 4, 3, 4, 2? (2023)
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Solution
The number 4 appears most frequently (3 times). Hence, mode = 4.
Correct Answer: D — 4
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Q. What is the mode of the following data set: 4, 1, 2, 4, 3, 4, 5? (2019)
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Solution
The mode is the number that appears most frequently. Here, 4 appears 3 times, so the mode is 4.
Correct Answer: C — 4
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Q. What is the mode of the following numbers: 1, 1, 2, 3, 3, 3, 4, 4?
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Solution
The mode is 3, as it appears 3 times, more than any other number.
Correct Answer: C — 3
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Q. What is the mode of the numbers: 1, 1, 2, 3, 3, 3, 4, 4?
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Solution
The mode is 3, as it appears most frequently (three times) in the data set.
Correct Answer: C — 3
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Q. What is the order of a matrix with 3 rows and 4 columns? (2021)
A.
3x4
B.
4x3
C.
3x3
D.
4x4
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Solution
The order of a matrix is given by the number of rows followed by the number of columns. Therefore, a matrix with 3 rows and 4 columns is of order 3x4.
Correct Answer: A — 3x4
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Q. What is the perimeter of a rectangle with length 10 cm and width 5 cm? (2021)
A.
30 cm
B.
25 cm
C.
20 cm
D.
15 cm
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Solution
The perimeter of a rectangle is given by P = 2(length + width). Here, P = 2(10 + 5) = 30 cm.
Correct Answer: B — 25 cm
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Q. What is the probability of drawing a heart from a standard deck of cards? (2022)
A.
1/4
B.
1/13
C.
1/52
D.
3/52
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Solution
There are 13 hearts in a deck of 52 cards. Probability = 13/52 = 1/4.
Correct Answer: A — 1/4
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Q. What is the product of the first five prime numbers? (2023)
A.
30
B.
60
C.
210
D.
120
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Solution
The first five prime numbers are 2, 3, 5, 7, and 11. Their product is 2 × 3 × 5 × 7 × 11 = 2310.
Correct Answer: C — 210
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Q. What is the product of the roots of the equation 2x^2 - 8x + 6 = 0?
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Solution
The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 6 and a = 2, so the product is 6/2 = 3.
Correct Answer: A — 3
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Q. What is the product of the roots of the equation x² - 4x + 3 = 0? (2021)
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Solution
The product of the roots is given by c/a = 3/1 = 3.
Correct Answer: A — 3
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Q. What is the product of the roots of the equation x² - 7x + 10 = 0? (2023)
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Solution
The product of the roots is given by c/a = 10/1 = 10.
Correct Answer: A — 10
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Q. What is the product of the roots of the quadratic equation x^2 - 7x + 10 = 0? (2023)
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Solution
Using Vieta's formulas, the product of the roots is c/a = 10/1 = 10.
Correct Answer: A — 10
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Q. What is the projection of vector A = 3i + 4j onto vector B = 1i + 2j?
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Solution
Projection = (A · B / |B|^2) * B = (11 / 5) * (1i + 2j) = 2.5.
Correct Answer: A — 2.5
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Q. What is the projection of vector A = 3i + 4j onto vector B = 2i + 2j?
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Solution
Projection = (A · B / |B|^2) * B = (14 / 8) * (2i + 2j) = (7/4)(2i + 2j) = 3.5i + 3.5j.
Correct Answer: A — 5
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Q. What is the projection of vector A = 6i + 8j onto vector B = 2i + 2j?
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Solution
Projection of A onto B = (A · B / |B|^2) * B = ((6*2 + 8*2) / (2^2 + 2^2)) * (2i + 2j) = (28/8)(2i + 2j) = 7i + 7j.
Correct Answer: A — 8
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