Major Competitive Exams

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Q. Determine the values of x that satisfy the equation sin^2(x) - sin(x) = 0.

A. 0, π
B. 0, π/2, π
C. 0, π/2, 3π/2
D. 0, π/2, π, 3π/2

Solution

Factoring gives sin(x)(sin(x) - 1) = 0, so x = 0, π/2, π, 3π/2.

Correct Answer: D — 0, π/2, π, 3π/2

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Q. Determine the x-intercept of the line 4x - 2y + 8 = 0.

A. -2
B. 2
C. 4
D. 0

Solution

Setting y = 0 in the equation gives 4x + 8 = 0, thus x = -2.

Correct Answer: B — 2

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Q. Determine the x-intercept of the line 4x - 5y + 20 = 0.

A. -5
B. 5
C. 4
D. -4

Solution

Setting y = 0 in the equation gives 4x + 20 = 0, thus x = -5.

Correct Answer: D — -4

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Q. Determine the x-intercept of the line 5x + 2y - 10 = 0.

A. 2
B. 5
C. 10
D. 0

Solution

Setting y = 0 in the equation gives 5x - 10 = 0, thus x = 2.

Correct Answer: B — 5

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Q. Determine the x-intercept of the line given by the equation 2x - 3y + 6 = 0.

A. -3
B. 3
C. 2
D. 0

Solution

Set y = 0 in the equation: 2x + 6 = 0 => x = -3.

Correct Answer: B — 3

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Q. Determine the x-intercept of the line given by the equation 5x + 2y - 10 = 0. (2023)

A. 2
B. 0
C. 5
D. 10

Solution

Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.

Correct Answer: C — 5

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Q. Determine the y-intercept of the line given by the equation 5x + 2y - 10 = 0. (2021)

A. 5
B. 2
C. 10
D. 0

Solution

Setting x = 0 in the equation gives 2y = 10, thus y = 5. The y-intercept is 5.

Correct Answer: B — 2

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Q. Differentiate f(x) = 4x^2 * e^x. (2022)

A. 4e^x + 4x^2e^x
B. 4x^2e^x + 4xe^x
C. 4e^x + 2x^2e^x
D. 8xe^x

Solution

Using the product rule, f'(x) = 4e^x + 4x^2e^x.

Correct Answer: A — 4e^x + 4x^2e^x

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Q. Differentiate f(x) = 4x^2 + 3x - 5. (2019)

A. 8x + 3
B. 4x + 3
C. 2x + 3
D. 8x - 3

Solution

Using the power rule, f'(x) = 8x + 3.

Correct Answer: A — 8x + 3

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Q. Differentiate f(x) = 4x^5 - 2x^3 + x. (2022)

A. 20x^4 - 6x^2 + 1
B. 20x^4 - 6x^2
C. 4x^4 - 2x^2 + 1
D. 5x^4 - 2x^2

Solution

Using the power rule, f'(x) = 20x^4 - 6x^2 + 1.

Correct Answer: A — 20x^4 - 6x^2 + 1

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Q. Differentiate f(x) = ln(x^2 + 1). (2022)

A. 2x/(x^2 + 1)
B. 1/(x^2 + 1)
C. 2x/(x^2 - 1)
D. x/(x^2 + 1)

Solution

Using the chain rule, f'(x) = 2x/(x^2 + 1).

Correct Answer: A — 2x/(x^2 + 1)

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Q. Differentiate f(x) = x^2 * e^x. (2022)

A. x^2 * e^x + 2x * e^x
B. 2x * e^x + x^2 * e^x
C. x^2 * e^x + e^x
D. 2x * e^x

Solution

Using the product rule, f'(x) = x^2 * e^x + 2x * e^x.

Correct Answer: A — x^2 * e^x + 2x * e^x

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Q. Differentiate f(x) = x^2 * ln(x).

A. 2x * ln(x) + x
B. x * ln(x) + 2x
C. 2x * ln(x)
D. x^2/x

Solution

Using the product rule, f'(x) = 2x * ln(x) + x.

Correct Answer: A — 2x * ln(x) + x

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Q. Differentiate the function f(x) = ln(x^2 + 1).

A. 2x/(x^2 + 1)
B. 2/(x^2 + 1)
C. 1/(x^2 + 1)
D. x/(x^2 + 1)

Solution

Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).

Correct Answer: A — 2x/(x^2 + 1)

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Q. Differentiate the function f(x) = x^2 * e^x.

A. x^2 * e^x + 2x * e^x
B. 2x * e^x + x^2 * e^x
C. x^2 * e^x + e^x
D. 2x * e^x + e^x

Solution

Using the product rule, f'(x) = (x^2)' * e^x + x^2 * (e^x)' = 2x * e^x + x^2 * e^x.

Correct Answer: A — x^2 * e^x + 2x * e^x

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Q. During a badminton tournament, if Player A wins against Player B and Player B wins against Player C, what can be concluded about Player A and Player C?

A. Player A is better than Player C.
B. Player C is better than Player A.
C. The outcome between Player A and Player C is uncertain.
D. Player A and Player C have never played against each other.

Solution

The transitive property does not apply in sports; thus, we cannot conclude the relationship between Player A and Player C.

Correct Answer: C — The outcome between Player A and Player C is uncertain.

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Q. During a badminton tournament, if player A won against player B, and player B won against player C, which of the following can be inferred?

A. Player A is better than player C
B. Player C is better than player A
C. Player A and C are equally skilled
D. Player B is the weakest

Solution

If A beats B and B beats C, it can be inferred that A is better than C.

Correct Answer: A — Player A is better than player C

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Q. During a badminton tournament, Player A won 3 matches, lost 2, and had 1 match that was a draw. What is Player A's win-loss record?

A. 3-2-1
B. 2-3-1
C. 1-3-2
D. 3-1-2

Solution

Player A's record is expressed as wins-losses-draws, which is 3-2-1.

Correct Answer: A — 3-2-1

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Q. During a global conference, 40% of the attendees were women. If there were 500 attendees, how many were men? (2023)

A. 200
B. 250
C. 300
D. 350

Solution

Number of women = 40% of 500 = 200. Number of men = 500 - 200 = 300.

Correct Answer: C — 300

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Q. During a national celebration, 25% of the attendees are children. If there are 800 attendees, how many are adults? (2020)

A. 600
B. 200
C. 400
D. 300

Solution

Number of children = 25% of 800 = 0.25 * 800 = 200. Number of adults = 800 - 200 = 600.

Correct Answer: A — 600

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Q. During a national event, 25% of the attendees are from outside the country. If there are 800 attendees, how many are from outside the country? (2021)

A. 200
B. 250
C. 300
D. 350

Solution

Number of attendees from outside = 25% of 800 = 0.25 * 800 = 200.

Correct Answer: A — 200

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Q. During a national event, 25% of the attendees are from outside the country. If there are 1,200 attendees, how many are from outside the country?

A. 300
B. 250
C. 400
D. 350

Solution

Number of attendees from outside = 25% of 1,200 = 0.25 * 1,200 = 300.

Correct Answer: A — 300

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Q. During a national event, 25% of the attendees are from rural areas. If there are 800 attendees, how many are from urban areas?

A. 600
B. 200
C. 400
D. 300

Solution

Number of attendees from urban areas = 800 * (1 - 0.25) = 800 * 0.75 = 600.

Correct Answer: A — 600

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Q. During a national event, 25% of the attendees are students. If there are 1,600 attendees, how many are not students?

A. 1,200
B. 1,000
C. 1,400
D. 1,600

Solution

Number of non-students = 1,600 * (1 - 0.25) = 1,600 * 0.75 = 1,200.

Correct Answer: A — 1,200

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Q. During a national event, 30% of the attendees are from abroad. If there are 1,000 attendees, how many are from abroad? (2021)

A. 300
B. 400
C. 500
D. 600

Solution

Number of attendees from abroad = 30% of 1,000 = 0.3 * 1,000 = 300.

Correct Answer: A — 300

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Q. During a national event, if 70% of the attendees are adults and there are 350 attendees, how many are children?

A. 105
B. 245
C. 70
D. 140

Solution

Number of adults = 70% of 350 = 0.70 * 350 = 245. Number of children = 350 - 245 = 105.

Correct Answer: A — 105

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Q. During a national event, if 70% of the attendees are adults and there are 500 attendees, how many are children? (2022)

A. 150
B. 200
C. 100
D. 250

Solution

Number of adults = 70% of 500 = 0.70 * 500 = 350. Number of children = 500 - 350 = 150.

Correct Answer: B — 200

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Q. During a peacekeeping mission, 120 soldiers were deployed. If 25% of them were from country A, how many soldiers were from country A?

A. 20
B. 25
C. 30
D. 35

Solution

Number of soldiers from country A = 25% of 120 = 0.25 * 120 = 30.

Correct Answer: C — 30

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Q. During a phase change, the temperature of a substance:

A. Increases
B. Decreases
C. Remains constant
D. Varies unpredictably

Solution

During a phase change, the temperature of a substance remains constant while the substance absorbs or releases heat.

Correct Answer: C — Remains constant

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Q. During a tournament, if a player has a win-loss record of 8-2, what is the player's winning percentage? (2023)

A. 80%
B. 75%
C. 70%
D. 85%

Solution

Winning percentage = (number of wins / total matches) * 100 = (8 / (8+2)) * 100 = 80%.

Correct Answer: A — 80%

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Major Competitive Exams

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