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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 (1, 2), (4, 6), and (7, 2), what is the length of the side opposite to the vertex (4, 6)? (2023)

A. 5
B. 6
C. 7
D. 8

Solution

Length = √[(1-7)² + (2-2)²] = √[36] = 6.

Correct Answer: B — 6

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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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Q. If the current in a circuit is 5 A and the resistance is 2 ohms, what is the power consumed in the circuit?

A. 10 W
B. 25 W
C. 5 W
D. 2.5 W

Solution

Power (P) can be calculated using P = I^2R = (5 A)^2 * 2 Ω = 25 W.

Correct Answer: B — 25 W

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Q. If the current in a circuit is doubled while the resistance remains constant, what happens to the voltage?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

According to Ohm's Law, if the current (I) is doubled and resistance (R) remains constant, the voltage (V) must also double.

Correct Answer: A — It doubles

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Q. If the current in a circuit is halved, what happens to the power consumed by the circuit?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Power P = I^2 * R. If I is halved, P becomes (1/2)^2 * R = 1/4 * P, so the power is reduced to a quarter, which means it halves.

Correct Answer: B — It halves

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Q. If the current in a circuit is split into two branches with resistances R1 = 2Ω and R2 = 4Ω, what is the current through R1 if the total current is 6A?

A. 2A
B. 3A
C. 4A
D. 6A

Solution

Using the current division rule, I1 = I_total * (R2 / (R1 + R2)) = 6A * (4Ω / (2Ω + 4Ω)) = 6A * (4/6) = 4A.

Correct Answer: B — 3A

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Q. If the current in a circular loop is doubled, how does the magnetic field at the center of the loop change?

A. It remains the same
B. It doubles
C. It quadruples
D. It halves

Solution

The magnetic field at the center of a circular loop is directly proportional to the current; thus, if the current is doubled, the magnetic field also doubles.

Correct Answer: B — It doubles

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Q. If the current in a circular loop is doubled, how does the magnetic field at the center change?

A. Remains the same
B. Doubles
C. Halves
D. Quadruples

Solution

The magnetic field at the center of a loop is directly proportional to the current.

Correct Answer: B — Doubles

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Q. If the current in a circular loop is doubled, what happens to the magnetic field at the center?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

The magnetic field at the center of the loop is directly proportional to the current.

Correct Answer: A — It doubles

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Q. If the current in a circular loop is increased, what happens to the magnetic field at the center of the loop?

A. It decreases
B. It increases
C. It remains the same
D. It becomes zero

Solution

According to the Biot-Savart Law, increasing the current in a circular loop increases the magnetic field at the center of the loop.

Correct Answer: B — It increases

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Q. If the current in a circular loop is reversed, what happens to the direction of the magnetic field at the center of the loop?

A. It remains the same
B. It reverses
C. It doubles
D. It becomes zero

Solution

Reversing the current in a circular loop reverses the direction of the magnetic field at the center.

Correct Answer: B — It reverses

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Q. If the current in a coil is doubled, the magnetic field strength around the coil will?

A. Double
B. Halve
C. Remain the same
D. Increase by four times

Solution

The magnetic field strength around a coil is directly proportional to the current, so if the current is doubled, the magnetic field strength will also double.

Correct Answer: A — Double

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Q. If the current in a coil is reversed, what happens to the direction of the magnetic field produced by the coil?

A. It remains the same
B. It reverses
C. It increases
D. It decreases

Solution

Reversing the current in a coil reverses the direction of the magnetic field produced.

Correct Answer: B — It reverses

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Q. If the current in a solenoid is doubled, what happens to the magnetic field inside the solenoid?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

The magnetic field inside a solenoid is directly proportional to the current.

Correct Answer: A — It doubles

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Major Competitive Exams

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