Q. If a rotating object has a moment of inertia of I and is rotating with an angular velocity ω, what is its rotational kinetic energy?
A.
1/2 Iω
B.
1/2 Iω^2
C.
Iω^2
D.
Iω
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Solution
The rotational kinetic energy is given by KE = 1/2 Iω^2.
Correct Answer:
B
— 1/2 Iω^2
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Q. If a ruler has a least count of 0.1 cm, what is the maximum error in measurement? (2023)
A.
0.05 cm
B.
0.1 cm
C.
0.2 cm
D.
0.01 cm
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Solution
The maximum error is typically taken as the least count of the measuring instrument, which is 0.1 cm.
Correct Answer:
B
— 0.1 cm
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Q. If a ruler has a least count of 0.1 cm, what is the smallest measurement it can accurately provide? (2023)
A.
0.1 cm
B.
0.05 cm
C.
0.01 cm
D.
1 cm
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Solution
The least count of a measuring instrument is the smallest value that can be measured accurately, which in this case is 0.1 cm.
Correct Answer:
A
— 0.1 cm
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Q. If a runner completes a 10 km race in 40 minutes, what is his average speed in km/h? (2021)
A.
12 km/h
B.
13 km/h
C.
14 km/h
D.
15 km/h
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Solution
Time = 40 minutes = 40/60 hours = 2/3 hours. Speed = Distance / Time = 10 km / (2/3) hours = 10 * (3/2) = 15 km/h.
Correct Answer:
C
— 14 km/h
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Q. If a salary is increased by 25% and the new salary is $50,000, what was the original salary?
A.
$40,000
B.
$45,000
C.
$35,000
D.
$30,000
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Solution
Let the original salary be x. Then, x + 0.25x = 50000 => 1.25x = 50000 => x = 50000 / 1.25 = $40,000.
Correct Answer:
A
— $40,000
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Q. If a salary of $50,000 is increased by 10% and then decreased by 10%, what is the final salary?
A.
$50,000
B.
$49,500
C.
$51,000
D.
$52,000
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Solution
New salary after increase = 50000 * 1.10 = $55,000. After decrease = 55000 * 0.90 = $49,500.
Correct Answer:
B
— $49,500
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Q. If a satellite is in a geostationary orbit, what is its orbital period?
A.
24 hours
B.
12 hours
C.
6 hours
D.
1 hour
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Solution
A geostationary satellite has an orbital period equal to the Earth's rotation period, which is 24 hours.
Correct Answer:
A
— 24 hours
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Q. If a satellite is in a stable orbit, what can be said about the net force acting on it?
A.
It is zero
B.
It is equal to the gravitational force
C.
It is equal to the centripetal force
D.
It is equal to the sum of gravitational and centripetal forces
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Solution
In a stable orbit, the net force acting on the satellite is zero because the gravitational force provides the necessary centripetal force.
Correct Answer:
A
— It is zero
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Q. If a satellite is launched into a higher orbit, how does its potential energy change compared to its initial orbit?
A.
It decreases
B.
It remains the same
C.
It increases
D.
It becomes zero
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Solution
The potential energy of a satellite increases when it is moved to a higher orbit due to the increase in distance from the Earth's center.
Correct Answer:
C
— It increases
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Q. If a satellite is moved to a higher orbit, what happens to its orbital period?
A.
It decreases.
B.
It increases.
C.
It remains the same.
D.
It becomes zero.
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Solution
The orbital period of a satellite increases when it is moved to a higher orbit, according to Kepler's third law.
Correct Answer:
B
— It increases.
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Q. If a satellite is moving in a circular orbit, what is the relationship between its centripetal acceleration and gravitational acceleration?
A.
Centripetal = Gravitational
B.
Centripetal > Gravitational
C.
Centripetal < Gravitational
D.
No relationship
Show solution
Solution
For a satellite in a stable circular orbit, the centripetal acceleration is equal to the gravitational acceleration.
Correct Answer:
A
— Centripetal = Gravitational
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Q. If a satellite is moving in a circular orbit, what type of energy does it possess?
A.
Only kinetic energy
B.
Only potential energy
C.
Both kinetic and potential energy
D.
Neither kinetic nor potential energy
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Solution
A satellite in a circular orbit possesses both kinetic energy due to its motion and potential energy due to its position in the gravitational field.
Correct Answer:
C
— Both kinetic and potential energy
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Q. If a satellite's altitude is doubled, how does its orbital speed change?
A.
Increases by √2
B.
Decreases by √2
C.
Remains the same
D.
Increases by 2
Show solution
Solution
If a satellite's altitude is doubled, its orbital speed decreases by √2.
Correct Answer:
B
— Decreases by √2
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Q. If a satellite's altitude is increased, what happens to its orbital period?
A.
It decreases
B.
It increases
C.
It remains constant
D.
It becomes zero
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Solution
As the altitude increases, the orbital period increases due to the greater distance from the Earth's center.
Correct Answer:
B
— It increases
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Q. If a satellite's speed is greater than the escape velocity, what will happen?
A.
It will enter a stable orbit
B.
It will escape Earth's gravitational pull
C.
It will crash into the Earth
D.
It will remain in a circular orbit
Show solution
Solution
If a satellite's speed exceeds the escape velocity, it will escape Earth's gravitational pull and move away into space.
Correct Answer:
B
— It will escape Earth's gravitational pull
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Q. If a satellite's speed is less than the required orbital speed, what will happen?
A.
It will remain in orbit.
B.
It will fall back to Earth.
C.
It will escape into space.
D.
It will move to a higher orbit.
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Solution
If a satellite's speed is less than the required orbital speed, it will not have enough centripetal force to maintain its orbit and will fall back to Earth.
Correct Answer:
B
— It will fall back to Earth.
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Q. If a scheme provides ₹1000 per month to 500 families for 6 months, what is the total amount disbursed?
A.
₹3 lakhs
B.
₹2 lakhs
C.
₹4 lakhs
D.
₹5 lakhs
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Solution
Total amount = ₹1000 * 500 families * 6 months = ₹3,000,000 or ₹3 lakhs.
Correct Answer:
A
— ₹3 lakhs
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Q. If a scholarship fund increases by 15% each year and starts with $10,000, what will be the amount after 2 years? (2023)
A.
$12,000
B.
$12,250
C.
$12,500
D.
$12,800
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Solution
After 1 year: 10000 * 1.15 = $11500. After 2 years: 11500 * 1.15 = $13225.
Correct Answer:
C
— $12,500
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Q. If a school awards $1000 to each of the top 10 students, what is the total amount awarded? (2019)
A.
$5000
B.
$8000
C.
$10000
D.
$12000
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Solution
Total amount awarded = 1000 * 10 = $10000.
Correct Answer:
C
— $10000
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Q. If a school awards a total of $1200 in scholarships, and the first place receives $600, the second place receives $300, and the third place receives $200, how much is left for the fourth place? (2023)
A.
$100
B.
$200
C.
$300
D.
$400
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Solution
Total awarded = 600 + 300 + 200 = 1100. Amount left for fourth place = 1200 - 1100 = $100.
Correct Answer:
A
— $100
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Q. If a seller incurs a loss of 10% on selling a bicycle for $450, what was the cost price?
A.
$500
B.
$450
C.
$400
D.
$350
Show solution
Solution
Let the cost price be x. Then, 450 = x - 10% of x => 450 = x - 0.1x => 450 = 0.9x => x = 500.
Correct Answer:
A
— $500
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Q. If a seller incurs a loss of 15% on selling a bicycle for $255, what was the cost price? (2023)
A.
$300
B.
$280
C.
$270
D.
$250
Show solution
Solution
Let the cost price be x. Selling Price = x - (15/100 * x) = 255. Thus, 0.85x = 255, x = 300.
Correct Answer:
A
— $300
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Q. If a seller marks a product at $400 and gives a discount of 25%, what is the profit if the cost price is $250? (2023)
A.
$50
B.
$75
C.
$100
D.
$125
Show solution
Solution
Selling Price = $400 - (25% of $400) = $400 - $100 = $300. Profit = Selling Price - Cost Price = $300 - $250 = $50.
Correct Answer:
C
— $100
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Q. If a seller marks up the price of a product by 50% and then offers a discount of 20%, what is the effective percentage increase in the price?
A.
30%
B.
25%
C.
20%
D.
15%
Show solution
Solution
Let the cost price be $100. Marked Price = $100 + ($100 * 0.50) = $150. Selling Price after discount = $150 - ($150 * 0.20) = $120. Effective increase = (($120 - $100) / $100) * 100 = 20%.
Correct Answer:
B
— 25%
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Q. If a sequence is defined as a_n = 3n + 1, what is the value of a_7? (2023)
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Solution
Substituting n = 7 into the formula gives a_7 = 3(7) + 1 = 21 + 1 = 22.
Correct Answer:
A
— 22
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Q. If a sequence is defined as a_n = 3n + 2, what is the value of a_5?
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Solution
Substituting n = 5 into the equation gives a_5 = 3(5) + 2 = 15 + 2 = 17.
Correct Answer:
B
— 17
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Q. If a sequence is defined by a_n = 2n + 3, what is a_5?
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Solution
a_5 = 2(5) + 3 = 13.
Correct Answer:
C
— 13
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Q. If a sequence is defined by the formula a_n = 3n + 2, what is the value of a_7? (2023)
Show solution
Solution
Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.
Correct Answer:
A
— 23
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Q. If a set A contains elements {1, 2, 3, 4, 5} and a constraint states that only even numbers can be included, what will be the resulting set?
A.
{2, 4}
B.
{1, 3, 5}
C.
{1, 2, 3, 4, 5}
D.
{}
Show solution
Solution
The resulting set will be {2, 4} as these are the only even numbers in set A.
Correct Answer:
A
— {2, 4}
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Q. If a set A is defined by the constraints x > 5 and x < 10, which of the following numbers is NOT a member of set A?
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Solution
The number 10 does not satisfy the constraint x < 10, hence it is not a member of set A.
Correct Answer:
C
— 10
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