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Q. If the circumference of a circle is 31.4 cm, what is its radius? (2022)

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

Solution

Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.

Correct Answer: A — 5 cm

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Q. If the circumference of a circle is 31.4 cm, what is its radius? (Use π = 3.14) (2015)

A. 5 cm
B. 7 cm
C. 10 cm
D. 8 cm

Solution

Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Correct Answer: A — 5 cm

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Q. If the circumference of a circle is 31.4 cm, what is the radius? (2020) 2020

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

Solution

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

Correct Answer: A — 5 cm

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Q. If the concentration of a reactant is increased in a system at equilibrium, what will happen according to Le Chatelier's principle?

A. The equilibrium will shift to the right.
B. The equilibrium will shift to the left.
C. The equilibrium will not change.
D. The reaction will stop.

Solution

According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.

Correct Answer: A — The equilibrium will shift to the right.

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Q. If the concentration of a reactant is tripled in a second-order reaction, how does the rate change? (2023)

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
D. Increases by 12 times

Solution

For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.

Correct Answer: C — Increases by 9 times

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Q. If the concentration of Cu²⁺ in a cell is increased, what happens to the cell potential?

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.

Correct Answer: A — Increases

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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 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 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 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 an AC circuit is given by I(t) = I0 cos(ωt), what is the RMS current? (2023)

A. I0/√2
B. I0
C. 2I0
D. I0/2

Solution

RMS current I_rms = I0/√2 for a cosine function.

Correct Answer: A — I0/√2

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Q. If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)

A. 5 A
B. 2.5 A
C. 7.07 A
D. 3.54 A

Solution

The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.

Correct Answer: B — 2.5 A

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Q. If the current through a conductor is doubled, what happens to the heat produced in the conductor? (2020)

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

Solution

The heat produced is proportional to the square of the current (H ∝ I²), so if I is doubled, heat becomes 4 times.

Correct Answer: C — It quadruples

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Q. If the current through a resistor is 2A and the resistance is 5Ω, what is the voltage across the resistor? (2022)

A. 10V
B. 5V
C. 2V
D. 7V

Solution

Using Ohm's Law, V = I * R = 2A * 5Ω = 10V.

Correct Answer: A — 10V

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Q. If the current through a resistor is 5A and the resistance is 10Ω, what is the voltage across the resistor? (2022)

A. 50V
B. 5V
C. 10V
D. 15V

Solution

Using Ohm's Law, V = I * R = 5A * 10Ω = 50V.

Correct Answer: A — 50V

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Q. If the current through a resistor is tripled, what happens to the power dissipated in the resistor? (2022)

A. Increases by 3 times
B. Increases by 9 times
C. Remains the same
D. Decreases by 3 times

Solution

Power is proportional to the square of the current (P = I²R). If I is tripled, P increases by 3² = 9 times.

Correct Answer: B — Increases by 9 times

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Q. If the diameter of a circle is 20 cm, what is its circumference? (2022)

A. 62.83 cm
B. 31.42 cm
C. 20 cm
D. 40 cm

Solution

Circumference = πd; C = π * 20 ≈ 62.83 cm.

Correct Answer: A — 62.83 cm

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Q. If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)

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

Solution

Tensile strength is inversely proportional to the cross-sectional area. Halving the diameter reduces the area to a quarter, thus tensile strength quadruples.

Correct Answer: C — It quadruples

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Q. If the distance between the plates of a capacitor is halved, what happens to the capacitance? (2019)

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

Solution

If the distance d is halved, the capacitance C = εA/d will double.

Correct Answer: A — It doubles

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Q. If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)

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

Solution

If the slit separation d is halved, the angle θ for the first-order maximum (d sin θ = λ) will increase, effectively doubling the angle.

Correct Answer: A — It doubles

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