Q. If the perimeter of a rectangle is 30 cm and the length is 10 cm, what is the width?
A.
5 cm
B.
10 cm
C.
7.5 cm
D.
15 cm
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Solution
Perimeter P = 2(length + width). So, 30 = 2(10 + width). Dividing by 2 gives 15 = 10 + width. Thus, width = 15 - 10 = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width? (2020)
A.
10 cm
B.
12.5 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Perimeter = 2(length + width). So, 50 = 2(15 + width). Solving gives width = 10 cm.
Correct Answer:
B
— 12.5 cm
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Q. If the perimeter of a regular hexagon is 72 cm, what is the length of each side?
A.
10 cm
B.
12 cm
C.
14 cm
D.
8 cm
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Solution
The perimeter of a regular hexagon is the sum of the lengths of its 6 equal sides. Therefore, each side is 72 cm / 6 = 12 cm.
Correct Answer:
B
— 12 cm
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Q. If the perimeter of a regular octagon is 64 cm, what is the length of each side? (2023)
A.
6 cm
B.
8 cm
C.
10 cm
D.
12 cm
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Solution
The perimeter of a regular octagon is 8 times the length of one side. Therefore, each side is 64 cm / 8 = 8 cm.
Correct Answer:
B
— 8 cm
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Q. If the perimeter of a square is 36 cm, what is the length of one side? (2023)
A.
9 cm
B.
12 cm
C.
6 cm
D.
15 cm
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Solution
The perimeter of a square is given by 4 times the length of one side. Therefore, if the perimeter is 36 cm, the length of one side is 36 cm / 4 = 9 cm.
Correct Answer:
B
— 12 cm
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Q. If the perimeter of a square is 40 cm, what is the length of one side? (2018)
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Perimeter = 4 × side, so side = 40/4 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. If the perimeter of a square is 64 cm, what is the length of one side? (2023)
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
Show solution
Solution
Perimeter of a square = 4 × side. Therefore, 4 × side = 64 cm, giving side = 64/4 = 16 cm.
Correct Answer:
C
— 16 cm
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Q. If the perimeter of a triangle is 30 cm and the lengths of two sides are 10 cm and 12 cm, what is the length of the third side? (2020)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
Show solution
Solution
Let the third side be x. Then, 10 + 12 + x = 30, so x = 30 - 22 = 8 cm.
Correct Answer:
A
— 8 cm
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Q. If the perimeter of an equilateral triangle is 36 cm, what is the length of each side?
A.
9 cm
B.
12 cm
C.
15 cm
D.
18 cm
Show solution
Solution
In an equilateral triangle, all sides are equal. Therefore, if the perimeter is 36 cm, each side is 36/3 = 12 cm.
Correct Answer:
B
— 12 cm
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Q. If the perimeter of an isosceles triangle is 24 cm and the length of the base is 8 cm, what is the length of each of the equal sides?
A.
8 cm
B.
10 cm
C.
12 cm
D.
6 cm
Show solution
Solution
Let the length of each equal side be x. The perimeter is given by 2x + 8 = 24. Solving for x gives 2x = 16, so x = 8 cm.
Correct Answer:
B
— 10 cm
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Q. If the perimeter of an isosceles triangle is 24 cm and the lengths of the two equal sides are 10 cm each, what is the length of the base?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
The perimeter is the sum of all sides. Therefore, base = 24 - (10 + 10) = 4 cm.
Correct Answer:
B
— 6 cm
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Q. If the perimeter of triangle DEF is 36 cm and the lengths of sides DE and EF are 10 cm and 12 cm respectively, what is the length of side DF? (2020)
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Perimeter = DE + EF + DF. Therefore, DF = 36 - (10 + 12) = 14 cm.
Correct Answer:
C
— 14 cm
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Q. If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?
A.
T ∝ r
B.
T ∝ r²
C.
T ∝ √r
D.
T ∝ 1/√r
Show solution
Solution
T = 2π√(r³/GM), thus T ∝ √r.
Correct Answer:
C
— T ∝ √r
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Q. If the pH of a river is measured to be 7.5, what type of water is it considered? (2020)
A.
Acidic
B.
Neutral
C.
Alkaline
D.
Distilled
Show solution
Solution
A pH greater than 7 is considered alkaline.
Correct Answer:
C
— Alkaline
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Q. If the pH of a river water is 8, what type of soil is likely to be found in the surrounding area?
A.
Acidic soil
B.
Neutral soil
C.
Alkaline soil
D.
Saline soil
Show solution
Solution
A pH of 8 indicates alkaline soil.
Correct Answer:
C
— Alkaline soil
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Q. If the pH of a solution is 11, what is the concentration of hydroxide ions [OH-] in the solution?
A.
1 x 10^-3 M
B.
1 x 10^-11 M
C.
1 x 10^-2 M
D.
1 x 10^-14 M
Show solution
Solution
pOH = 14 - pH = 3, [OH-] = 10^-3 M.
Correct Answer:
C
— 1 x 10^-2 M
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Q. If the pH of a solution is 3, what is the concentration of H+ ions? (2023)
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
0.0001 M
Show solution
Solution
pH = 3 means [H+] = 10^-3 M = 0.001 M.
Correct Answer:
B
— 0.01 M
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Q. If the pH of a solution is 3, what is the concentration of hydrogen ions [H+] in moles per liter?
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
1 M
Show solution
Solution
The concentration of hydrogen ions [H+] is 10^(-pH) = 10^(-3) = 0.001 M.
Correct Answer:
C
— 0.1 M
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Q. If the photoelectric effect is observed, what can be inferred about the incident light?
A.
It has a frequency below the threshold
B.
It has a frequency equal to the threshold
C.
It has a frequency above the threshold
D.
It has any frequency
Show solution
Solution
The photoelectric effect occurs only when the frequency of the incident light is above the threshold frequency.
Correct Answer:
C
— It has a frequency above the threshold
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Q. If the phrase 'to err is human' is paraphrased, which of the following is the best alternative?
A.
Humans are prone to mistakes.
B.
Only humans make errors.
C.
Mistakes are a sign of humanity.
D.
Humans never make mistakes.
Show solution
Solution
The paraphrase captures the essence of the original phrase, emphasizing human fallibility.
Correct Answer:
A
— Humans are prone to mistakes.
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Q. If the phrase 'to err is human' is paraphrased, which of the following options conveys the same meaning?
A.
Humans are perfect.
B.
Making mistakes is a human trait.
C.
Only humans can make mistakes.
D.
Humans never make mistakes.
Show solution
Solution
The paraphrase captures the essence of the original phrase, emphasizing that making mistakes is a common human characteristic.
Correct Answer:
B
— Making mistakes is a human trait.
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Q. If the phrase 'to err is human' is rephrased, which of the following is the best alternative?
A.
Humans are prone to mistakes.
B.
Only humans make errors.
C.
Mistakes are a sign of humanity.
D.
Humans never make mistakes.
Show solution
Solution
The rephrased statement captures the essence of the original phrase.
Correct Answer:
A
— Humans are prone to mistakes.
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Q. If the phrase 'to pull someone's leg' means to tease or joke with someone, what is the synonym of 'tease'?
A.
Annoy
B.
Bother
C.
Mock
D.
Praise
Show solution
Solution
'Mock' is a synonym of 'tease', as both involve making fun of someone.
Correct Answer:
C
— Mock
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Q. If the phrase 'to pull someone's leg' means to tease someone, which of the following is a synonym for this idiom?
A.
To annoy
B.
To joke
C.
To criticize
D.
To support
Show solution
Solution
To joke is a synonym for teasing someone.
Correct Answer:
B
— To joke
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Q. If the phrase 'to sit on the fence' means to remain neutral, which of the following is a synonym?
A.
To take sides
B.
To be indecisive
C.
To be assertive
D.
To be confrontational
Show solution
Solution
Being indecisive is synonymous with remaining neutral, as it implies not making a decision.
Correct Answer:
B
— To be indecisive
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Q. If the pKa of acetic acid is 4.76, what is the pH of a 0.1 M solution?
A.
4.76
B.
5.76
C.
6.76
D.
3.76
Show solution
Solution
For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.
Correct Answer:
A
— 4.76
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Q. If the point (x, y) lies on the line 3x - 4y = 12, what is the value of y when x = 4? (2023)
Show solution
Solution
Substituting x = 4 gives 3(4) - 4y = 12 => 12 - 4y = 12 => y = 0.
Correct Answer:
D
— 2
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Q. If the point (x, y) lies on the line 4x - 5y = 20, what is the value of y when x = 0?
Show solution
Solution
Substituting x = 0: 4(0) - 5y = 20 => -5y = 20 => y = -4.
Correct Answer:
B
— 5
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Q. If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
A.
1
B.
2
C.
0
D.
undefined
Show solution
Solution
Slope = (4-2)/(3-1) = 1, and it remains the same for other points.
Correct Answer:
A
— 1
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Q. If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?
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Solution
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 0.
Correct Answer:
A
— 0
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