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Q. If the roots of the quadratic equation x^2 - 3x + p = 0 are 1 and 2, what is the value of p?

A. 1
B. 2
C. 3
D. 6

Solution

Using Vieta's formulas, sum of roots = 1 + 2 = 3 and product of roots = 1*2 = 2. Thus, p = 2.

Correct Answer: D — 6

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Q. If the roots of the quadratic equation x² + px + q = 0 are both negative, which of the following must be true?

A. p > 0 and q > 0
B. p < 0 and q < 0
C. p < 0 and q > 0
D. p > 0 and q < 0

Solution

For both roots to be negative, the sum (p) must be positive and the product (q) must also be positive.

Correct Answer: A — p > 0 and q > 0

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Q. If the roots of the quadratic equation x² - 5x + k = 0 are equal, what is the value of k? (2023)

A. 6
B. 5
C. 4
D. 3

Solution

For the roots to be equal, the discriminant must be zero. Thus, (-5)² - 4(1)(k) = 0, giving k = 25/4 = 6.25.

Correct Answer: A — 6

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Q. If the sales of Product A in Q1 were 200 units, what was the percentage increase in sales by Q2?

A. 50%
B. 100%
C. 25%
D. 75%

Solution

The sales increased to 350 units in Q2, which is a 75% increase from Q1.

Correct Answer: D — 75%

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Q. If the sales of Product A in Q3 are 300 units, what is the percentage increase from Q2?

A. 50%
B. 100%
C. 75%
D. 25%

Solution

The percentage increase from Q2 (200 units) to Q3 (300 units) is 50%.

Correct Answer: C — 75%

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Q. If the sales of Product A in Q4 are projected to be 20% higher than in Q3, and Q3 sales were 300 units, what will be the projected sales for Q4?

A. 360
B. 320
C. 300
D. 280

Solution

Projected sales for Q4 would be 300 + (20% of 300) = 300 + 60 = 360 units.

Correct Answer: A — 360

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Q. If the sales of Product B in Q3 are projected to increase by 20% from Q2, what will be the new sales figure?

A. 600 units
B. 720 units
C. 800 units
D. 900 units

Solution

If Product B sold 600 units in Q2, a 20% increase would result in 720 units in Q3.

Correct Answer: B — 720 units

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Q. If the sales of Product B in Q3 were to decrease by 20%, what would be the new sales figure?

A. 400
B. 450
C. 480
D. 500

Solution

If Product B sold 600 units in Q3, a 20% decrease would result in 480 units.

Correct Answer: C — 480

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Q. If the sales of Product B in Q4 are projected to be 600 units, what will be the total sales for Product B over the four quarters?

A. 1800
B. 1600
C. 1400
D. 1200

Solution

The total sales for Product B over the four quarters would be 1600 units (400 + 500 + 400 + 600).

Correct Answer: B — 1600

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Q. If the sales of Product B in Q4 are projected to be 600 units, what would be the total sales for the year? (2000)

A. 2000
B. 2200
C. 2400
D. 2600

Solution

Adding the projected Q4 sales of 600 to the previous quarters gives a total of 2200 units for the year.

Correct Answer: B — 2200

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Q. If the sales of Product B in Q4 were 600 units, what was the percentage increase from Q3 if Q3 sales were 500 units?

A. 20%
B. 25%
C. 30%
D. 15%

Solution

The percentage increase from Q3 to Q4 is ((600 - 500) / 500) * 100 = 20%.

Correct Answer: B — 25%

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Q. If the sales of Product C in Q3 were to increase by 20%, what would be the new sales figure?

A. 240 units
B. 300 units
C. 360 units
D. 420 units

Solution

The original sales figure for Product C in Q3 was 300 units; a 20% increase would result in 360 units.

Correct Answer: C — 360 units

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Q. If the sales of Product C in Q4 are projected to be 200 units, what is the expected total sales for the year?

A. 1200
B. 1300
C. 1400
D. 1500

Solution

If Product C sells 200 units in Q4, the expected total sales for the year would be 1300 units.

Correct Answer: B — 1300

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Q. If the sales of Product C in Q4 are projected to be 200 units, what would be the total sales for the year?

A. 1200
B. 1300
C. 1400
D. 1500

Solution

If Product C sells 200 units in Q4, the total sales for the year would be 1300 units.

Correct Answer: B — 1300

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Q. If the sales of Product C increased by 50 units, what would be the new total sales?

A. 2050
B. 2100
C. 2150
D. 2200

Solution

The new total sales would be 2000 + 50 = 2050.

Correct Answer: B — 2100

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Q. If the sales of Product D in Q1 were 200 units, what was the percentage increase in sales by Q3?

A. 50%
B. 100%
C. 150%
D. 200%

Solution

The sales increased to 400 units in Q3, which is a 100% increase from Q1.

Correct Answer: B — 100%

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Q. If the sales of Product D in Q1 were 200 units, what was the percentage increase in sales by Q2?

A. 50%
B. 100%
C. 25%
D. 75%

Solution

The sales increased to 400 units in Q2, which is a 100% increase from Q1.

Correct Answer: B — 100%

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Q. If the sales of Product D in Q1 were 300 units, what was the percentage increase in Q2?

A. 20%
B. 30%
C. 40%
D. 50%

Solution

The sales in Q2 were 420 units, which is a 40% increase from Q1.

Correct Answer: C — 40%

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Q. If the sales of Product D in Q3 were to double in Q4, what would be the new sales figure?

A. 200
B. 300
C. 400
D. 500

Solution

If Product D sold 200 units in Q3, doubling that would result in 400 units in Q4.

Correct Answer: C — 400

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Q. If the sales of Product D in Q3 were to double, what would be the new total for that quarter?

A. 200 units
B. 300 units
C. 400 units
D. 500 units

Solution

If Product D's sales in Q3 were 200 units, doubling it would result in 400 units.

Correct Answer: C — 400 units

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Q. If the sales of Product D in Q3 were to increase by 20%, what would be the new sales figure?

A. 240 units
B. 300 units
C. 360 units
D. 420 units

Solution

The original sales figure for Product D in Q3 was 300 units; a 20% increase results in 360 units.

Correct Answer: C — 360 units

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Q. If the sales of Product D in Q4 were 300 units, what was the average sales per quarter for Product D?

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

Solution

The average sales per quarter for Product D is 250 units, calculated from the total sales.

Correct Answer: A — 250 units

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Q. If the scalar product of two vectors A and B is 0, what can be inferred about the vectors?

A. They are equal
B. They are parallel
C. They are orthogonal
D. They are collinear

Solution

If A · B = 0, then A and B are orthogonal (perpendicular) to each other.

Correct Answer: C — They are orthogonal

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Q. If the scalar product of two vectors A and B is 0, what can be said about the vectors?

A. They are parallel
B. They are orthogonal
C. They are equal
D. They are collinear

Solution

If A · B = 0, then the vectors are orthogonal.

Correct Answer: B — They are orthogonal

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Q. If the scalar product of two vectors A and B is 15 and the magnitudes are |A| = 5 and |B| = 3, find the angle between them.

A. 60°
B. 45°
C. 30°
D. 90°

Solution

A · B = |A||B|cos(θ) => 15 = 5*3*cos(θ) => cos(θ) = 1, θ = 0°.

Correct Answer: B — 45°

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Q. If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?

A. They are perpendicular
B. They are parallel
C. They are equal
D. They are opposite

Solution

If A · B = |A||B|, then the angle between them is 0°, meaning they are parallel.

Correct Answer: B — They are parallel

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Q. If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?

A. 2x - y + 3z = 10
B. 2x + y + 3z = 10
C. 2x - y - 3z = 10
D. 2x + y - 3z = 10

Solution

A · B = 2x - y + 3z = 10.

Correct Answer: A — 2x - y + 3z = 10

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Q. If the scalar product of vectors A and B is equal to the product of their magnitudes, what can be said about the angle between them?

A. 0°
B. 90°
C. 180°
D. 45°

Solution

If A · B = |A||B|, then cos(θ) = 1, which means θ = 0°.

Correct Answer: A — 0°

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Q. If the scores of 10 students are: 50, 60, 70, 80, 90, 100, 50, 60, 70, 80, what is the mode?

A. 50
B. 60
C. 70
D. 80

Solution

Mode is the value that appears most frequently. Here, 50, 60, 70, and 80 all appear twice, but 50 is the smallest.

Correct Answer: A — 50

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Q. If the scores of 5 students are 10, 20, 30, 40, and x, and the mean is 30, what is the value of x?

A. 30
B. 40
C. 50
D. 60

Solution

Mean = (10 + 20 + 30 + 40 + x) / 5 = 30. Solving gives x = 50.

Correct Answer: C — 50

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Major Competitive Exams

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