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Q. If a radar system can detect objects up to 100 km away, how many meters is that? (2023)

A. 5000 m
B. 10000 m
C. 15000 m
D. 20000 m

Solution

100 km = 100 × 1000 m = 100000 m

Correct Answer: B — 10000 m

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Q. If a radar system can detect objects up to 100 km away, what is the maximum area it can cover? (2022)

A. 31415.93 km²
B. 7853.98 km²
C. 10000 km²
D. 5000 km²

Solution

Area = πr² = π(100 km)² ≈ 31415.93 km²

Correct Answer: A — 31415.93 km²

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Q. If a ray of light passes from air into a medium with a refractive index of 2, what is the angle of refraction if the angle of incidence is 30°?

A. 15°
B. 30°
C. 45°
D. 60°

Solution

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). 1 * sin(30°) = 2 * sin(θ2) => sin(θ2) = 0.25 => θ2 = 15°.

Correct Answer: C — 45°

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Q. If a ray of light passes through the optical center of a lens, what happens to the ray?

A. It bends towards the normal.
B. It bends away from the normal.
C. It continues in a straight line.
D. It converges to a point.

Solution

A ray of light passing through the optical center of a lens continues in a straight line without bending.

Correct Answer: C — It continues in a straight line.

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Q. If a reaction has a ΔG of +5 kJ/mol, what can be inferred?

A. The reaction is spontaneous
B. The reaction is non-spontaneous
C. The reaction is at equilibrium
D. The reaction is exothermic

Solution

A ΔG of +5 kJ/mol indicates that the reaction is non-spontaneous.

Correct Answer: B — The reaction is non-spontaneous

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Q. If a reaction has ΔH = 100 kJ and ΔS = -200 J/K, what is ΔG at 298 K?

A. 0 kJ
B. 100 kJ
C. 200 kJ
D. 300 kJ

Solution

ΔG = ΔH - TΔS = 100 kJ - 298 K * (-0.2 kJ/K) = 100 kJ + 59.6 kJ = 159.6 kJ.

Correct Answer: D — 300 kJ

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Q. If a recipe requires 2 cups of flour for 4 servings, how much flour is needed for 10 servings?

A. 4 cups
B. 5 cups
C. 6 cups
D. 7 cups

Solution

Flour needed = (2 cups / 4 servings) × 10 servings = 5 cups.

Correct Answer: B — 5 cups

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Q. If a recipe requires 2 cups of flour for every 3 cups of sugar, how many cups of flour are needed for 9 cups of sugar?

A. 4
B. 5
C. 6
D. 7

Solution

Using the ratio, if 3 cups of sugar require 2 cups of flour, then 9 cups of sugar require (2/3) * 9 = 6 cups of flour.

Correct Answer: C — 6

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Q. If a recipe requires 3 cups of flour for 12 cookies, how many cups are needed for 30 cookies?

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

Solution

Cups needed = (3 cups / 12 cookies) × 30 cookies = 7.5 cups.

Correct Answer: B — 6 cups

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Q. If a recipe requires 3 cups of flour for every 2 cups of sugar, how many cups of flour are needed for 8 cups of sugar?

A. 10 cups
B. 12 cups
C. 9 cups
D. 6 cups

Solution

The ratio of flour to sugar is 3:2. For 8 cups of sugar, the amount of flour needed is (3/2) × 8 = 12 cups.

Correct Answer: B — 12 cups

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Q. If a rectangle has a length of 10 and a width of 5, what is its area? (2017)

A. 50
B. 60
C. 55
D. 45

Solution

Area = length × width = 10 × 5 = 50.

Correct Answer: A — 50

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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is its area? (2017)

A. 50 cm²
B. 60 cm²
C. 40 cm²
D. 30 cm²

Solution

Area = length × width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is its perimeter? (2022)

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

Solution

Perimeter of a rectangle = 2(length + width) = 2(10 + 5) = 30 cm.

Correct Answer: A — 30 cm

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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is the area of the rectangle? (2022)

A. 50 cm²
B. 55 cm²
C. 60 cm²
D. 65 cm²

Solution

Area = length × width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

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Q. If a rectangle has a length of 10 m and a width of 5 m, what is its perimeter? (2023)

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

Solution

Perimeter = 2(length + width) = 2(10 + 5) = 30 m.

Correct Answer: A — 30 m

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Q. If a rectangle has a length of 10 units and a width of 5 units, what is its perimeter?

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

Solution

Perimeter = 2 * (length + width) = 2 * (10 + 5) = 30 units.

Correct Answer: A — 30

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Q. If a rectangle has a length of 12 cm and a width of 4 cm, what is its perimeter? (2019)

A. 32 cm
B. 28 cm
C. 24 cm
D. 30 cm

Solution

Perimeter = 2(length + width) = 2(12 + 4) = 32 cm.

Correct Answer: A — 32 cm

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Q. If a rectangle has a length of 15 cm and a width of 10 cm, what is its perimeter? (2022)

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

Solution

Perimeter = 2(length + width) = 2(15 + 10) = 50 cm.

Correct Answer: A — 50 cm

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Q. If a rectangle has a length of 8 cm and a width of 3 cm, what is its area? (2015)

A. 24 cm²
B. 30 cm²
C. 20 cm²
D. 18 cm²

Solution

Area = length × width = 8 × 3 = 24 cm².

Correct Answer: A — 24 cm²

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Q. If a rectangle has a length of 8 cm and a width of 3 cm, what is its perimeter? (2019)

A. 22 cm
B. 24 cm
C. 20 cm
D. 26 cm

Solution

Perimeter = 2(length + width) = 2(8 + 3) = 22 cm.

Correct Answer: A — 22 cm

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Q. If a rectangle has a length of 8 cm and a width of 5 cm, what is its perimeter? (2022)

A. 26 cm
B. 30 cm
C. 40 cm
D. 20 cm

Solution

Perimeter = 2(length + width) = 2(8 + 5) = 26 cm.

Correct Answer: A — 26 cm

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Q. If a rectangle has a length of 8 m and a width of 3 m, what is its perimeter? (2021)

A. 22 m
B. 24 m
C. 26 m
D. 30 m

Solution

Perimeter = 2(length + width) = 2(8 m + 3 m) = 22 m.

Correct Answer: A — 22 m

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Q. If a rectangle has a length of 8 units and a width of 3 units, what is its perimeter? (2023)

A. 22
B. 24
C. 20
D. 18

Solution

The perimeter of a rectangle is given by 2(length + width). Thus, perimeter = 2(8 + 3) = 22 units.

Correct Answer: A — 22

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Q. If a rectangle has a length of 8 units and a width of 5 units, what is its perimeter? (2023)

A. 26
B. 30
C. 20
D. 24

Solution

The perimeter of a rectangle is given by 2(length + width). Thus, perimeter = 2(8 + 5) = 2 * 13 = 26.

Correct Answer: A — 26

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Q. If a rectangle has a length that is twice its width and the perimeter is 48 cm, what is the area of the rectangle?

A. 96 cm²
B. 144 cm²
C. 192 cm²
D. 256 cm²

Solution

Let width = w, then length = 2w. Perimeter = 2(length + width) = 48. Thus, 2(2w + w) = 48, leading to 6w = 48, so w = 8 cm. Area = length * width = 2w * w = 2*8*8 = 128 cm².

Correct Answer: B — 144 cm²

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Q. If a region receives 1200 mm of rainfall in a year, what is the average monthly rainfall? (2022)

A. 100 mm
B. 120 mm
C. 150 mm
D. 200 mm

Solution

Average monthly rainfall = Total annual rainfall / 12 = 1200 mm / 12 = 100 mm.

Correct Answer: B — 120 mm

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Q. If a resistor has a current of 2A flowing through it and a voltage of 10V across it, what is the resistance? (2023)

A. 2Ω
B. 5Ω
C. 10Ω
D. 20Ω

Solution

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

Correct Answer: B — 5Ω

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Q. If a resistor has a resistance of 10Ω and a current of 2A flows through it, what is the voltage across the resistor? (2023)

A. 5V
B. 10V
C. 20V
D. 30V

Solution

Using Ohm's Law, V = I * R = 2A * 10Ω = 20V.

Correct Answer: C — 20V

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Q. If a resistor has a resistance of 10Ω and a current of 5A flows through it, what is the voltage across the resistor? (2023)

A. 10V
B. 20V
C. 30V
D. 50V

Solution

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

Correct Answer: B — 20V

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Q. If a resistor has a resistance of 5 ohms and a current of 2 amperes flows through it, what is the voltage across the resistor?

A. 10 V
B. 5 V
C. 2.5 V
D. 1 V

Solution

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

Correct Answer: A — 10 V

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Major Competitive Exams

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