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Q. If the coordinates of a point P are (1, -1, 2), what is the x-coordinate of the point Q if it is reflected across the yz-plane? (2023)

A. 1
B. -1
C. 2
D. 0

Solution

Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).

Correct Answer: B — -1

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Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)

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

Solution

Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

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Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the slope of line AB?

A. 2
B. 1
C. 3
D. 0

Solution

Slope = (6-2)/(4-1) = 4/3.

Correct Answer: A — 2

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Q. If the coordinates of point A are (2, 3) and point B are (4, 7), what is the slope of line AB?

A. 2
B. 1
C. 3
D. 4

Solution

Slope = (7-3)/(4-2) = 4/2 = 2.

Correct Answer: A — 2

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Q. If the coordinates of point C are (5, 5) and point D are (1, 1), what is the slope of CD? (2021)

A. 1
B. 0
C. 2
D. 3

Solution

Slope = (5-1)/(5-1) = 4/4 = 1

Correct Answer: A — 1

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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the distance CD? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Distance CD = |10 - 5| = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the length of CD? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Length CD = |10 - 5| = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)

A. y = x
B. y = 5
C. y = x + 5
D. y = x - 5

Solution

Using point-slope form: y - 5 = 1(x - 5) => y = x

Correct Answer: A — y = x

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Q. If the coordinates of point C are (5, 5) and the slope of the line is 1, what is the equation of the line? (2021) 2021

A. y = x
B. y = 5
C. y = 2x - 5
D. y = x + 5

Solution

Using point-slope form: y - 5 = 1(x - 5) => y = x.

Correct Answer: A — y = x

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Q. If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the distance AB?

A. 2√2
B. √8
C. 2
D. 4

Solution

Distance AB = √((3-1)² + (4-2)²) = √(4) = 2.

Correct Answer: A — 2√2

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Q. If the coordinates of points A and B are (1, 2) and (4, 6) respectively, what is the distance AB?

A. 5
B. 4
C. 3
D. 2

Solution

Distance AB = √((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?

A. 12
B. 14
C. 16
D. 18

Solution

Calculate distances AB, BC, CA and sum them: AB = 5, BC = 5, CA = 7. Perimeter = 5 + 5 + 7 = 17.

Correct Answer: B — 14

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Q. If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?

A. 8
B. 10
C. 12
D. 14

Solution

Perimeter = AB + BC + CA = √[(3-1)² + (4-2)²] + √[(5-3)² + (2-4)²] + √[(1-5)² + (2-2)²] = 2.83 + 2.83 + 4 = 10.

Correct Answer: B — 10

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Q. If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2), what is the perimeter of the triangle?

A. 12
B. 14
C. 16
D. 18

Solution

Perimeter = AB + BC + CA = √[(4-1)² + (6-2)²] + √[(7-4)² + (2-6)²] + √[(1-7)² + (2-2)²] = 3 + √(9 + 16) + 6 = 3 + 5 + 6 = 14.

Correct Answer: B — 14

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Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the area of the triangle?

A. 10
B. 12
C. 14
D. 16

Solution

Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(5-2) + 4(2-1) + 7(1-5) | = 1/2 | 3 + 4 - 28 | = 1/2 * 21 = 10.5.

Correct Answer: B — 12

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Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020)

A. 5
B. 8
C. 12
D. 10

Solution

The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.

Correct Answer: B — 8

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Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020

A. 5
B. 8
C. 12
D. 10

Solution

The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.

Correct Answer: B — 8

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Q. If the cost function is C(x) = 5x^2 + 20x + 100, find the minimum cost. (2020)

A. 100
B. 120
C. 140
D. 160

Solution

The minimum cost occurs at x = -b/(2a) = -20/(2*5) = -2. C(-2) = 5(-2)^2 + 20(-2) + 100 = 120.

Correct Answer: B — 120

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Q. If the cost of 5 kg of rice is Rs. 200, what is the cost of 8 kg of rice? (2020)

A. 320
B. 400
C. 360
D. 280

Solution

Cost per kg = 200 / 5 = 40. Cost of 8 kg = 40 * 8 = 320.

Correct Answer: A — 320

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Q. If the cost of 5 kg of rice is Rs. 200, what is the cost of 8 kg? (2020)

A. 320
B. 400
C. 360
D. 280

Solution

Cost per kg = 200 / 5 = 40. Cost of 8 kg = 40 * 8 = 320.

Correct Answer: A — 320

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Q. If the cost price of an article is Rs. 500 and the selling price is Rs. 600, what is the profit percentage?

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

Solution

Profit = Selling Price - Cost Price = 600 - 500 = 100. Profit Percentage = (Profit/Cost Price) * 100 = (100/500) * 100 = 20%.

Correct Answer: B — 25%

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Q. If the cost price of an item is Rs. 500 and the selling price is Rs. 600, what is the gain percentage?

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

Solution

Gain = Selling Price - Cost Price = 600 - 500 = 100. Gain percentage = (Gain/Cost Price) * 100 = (100/500) * 100 = 20%.

Correct Answer: B — 25%

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Q. If the critical angle for a certain material is 30°, what is the refractive index of that material?

A. 1.00
B. 1.15
C. 1.73
D. 2.00

Solution

The refractive index n can be calculated using n = 1/sin(θc). For θc = 30°, n = 1/sin(30°) = 1/0.5 = 2.00.

Correct Answer: C — 1.73

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Q. If the critical angle for a certain material is 45°, what is the refractive index of that material?

A. 1.41
B. 1.00
C. 1.73
D. 0.71

Solution

Using the formula n = 1/sin(θc), where θc = 45°, we find n = 1/sin(45°) = 1/0.7071 ≈ 1.41.

Correct Answer: A — 1.41

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Q. If the cross-sectional area of a wire is doubled, how does its resistance change?

A. Doubles
B. Halves
C. Remains the same
D. Increases four times

Solution

Resistance is inversely proportional to cross-sectional area; doubling the area halves the resistance.

Correct Answer: B — Halves

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Q. If the cross-sectional area of a wire is doubled, what happens to its resistance?

A. Doubles
B. Halves
C. Remains the same
D. Increases four times

Solution

Resistance (R) is inversely proportional to cross-sectional area (A). Doubling A halves the resistance.

Correct Answer: B — Halves

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Q. If the current flowing through a conductor is 3A and the resistance is 2Ω, what is the voltage across the conductor? (2023)

A. 1.5V
B. 3V
C. 6V
D. 9V

Solution

Using Ohm's Law, V = I * R = 3A * 2Ω = 6V.

Correct Answer: C — 6V

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Q. If the current flowing through a conductor is 3A and the resistance is 6Ω, what is the voltage across the conductor? (2023)

A. 9V
B. 18V
C. 3V
D. 6V

Solution

Using Ohm's Law, V = I * R = 3A * 6Ω = 18V.

Correct Answer: A — 9V

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Q. If the current flowing through a resistor is 2A and the voltage across it is 6V, what is the resistance? (2022)

A. 3Ω
B. 2Ω
C. 6Ω
D. 12Ω

Solution

Using Ohm's Law, R = V / I = 6V / 2A = 3Ω.

Correct Answer: A — 3Ω

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Q. If the current flowing through a resistor is 3A and the voltage across it is 9V, what is the resistance? (2022)

A. 1Ω
B. 2Ω
C. 3Ω
D. 4Ω

Solution

Using Ohm's Law, R = V / I = 9V / 3A = 3Ω.

Correct Answer: C — 3Ω

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Major Competitive Exams

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