Q. What happens to the particles in a solid when it is heated? (2023)
-
A.
They move closer together.
-
B.
They vibrate more vigorously.
-
C.
They become gas.
-
D.
They stop moving.
Solution
When a solid is heated, its particles gain energy and vibrate more vigorously, potentially leading to a change in state.
Correct Answer:
B
— They vibrate more vigorously.
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Q. What happens to the particles of a solid when it is heated? (2023)
-
A.
They move closer together
-
B.
They vibrate faster
-
C.
They become a gas
-
D.
They lose mass
Solution
When a solid is heated, its particles gain energy and vibrate faster, which can lead to a change in state.
Correct Answer:
B
— They vibrate faster
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Q. What happens to the particles of a substance when it changes from a solid to a liquid? (2023)
-
A.
They lose energy
-
B.
They gain energy
-
C.
They remain unchanged
-
D.
They become more ordered
Solution
When a solid melts into a liquid, the particles gain energy, allowing them to overcome some of the forces holding them in fixed positions.
Correct Answer:
B
— They gain energy
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Q. What happens to the pressure of a gas if the volume is decreased while the temperature remains constant?
-
A.
Increases
-
B.
Decreases
-
C.
Remains the same
-
D.
Doubles
Solution
According to Boyle's Law, if the volume decreases and temperature is constant, the pressure increases.
Correct Answer:
A
— Increases
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Q. What happens to the temperature of a gas during an isothermal expansion? (2021)
-
A.
Increases
-
B.
Decreases
-
C.
Remains constant
-
D.
Varies with pressure
Solution
During an isothermal expansion, the temperature of the gas remains constant as the system absorbs heat to do work.
Correct Answer:
C
— Remains constant
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Q. What happens to the total current in a parallel circuit if one branch is removed? (2021)
-
A.
Increases
-
B.
Decreases
-
C.
Remains the same
-
D.
Depends on the branch
Solution
Removing a branch in a parallel circuit decreases the total current.
Correct Answer:
B
— Decreases
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Q. What happens to the volume of a gas when its temperature increases at constant pressure? (2020)
-
A.
Volume decreases
-
B.
Volume remains constant
-
C.
Volume increases
-
D.
Volume fluctuates
Solution
According to Charles's Law, the volume of a gas increases with an increase in temperature at constant pressure.
Correct Answer:
C
— Volume increases
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Q. What is 100 - (25 × 3)? (2022)
Solution
25 × 3 = 75, then 100 - 75 = 25.
Correct Answer:
C
— 75
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Q. What is 100 ÷ 4 + 25? (2018)
Solution
100 ÷ 4 = 25, then 25 + 25 = 50.
Correct Answer:
B
— 75
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Q. What is 25 × 4? (2014)
Q. What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?
Solution
The nth term of an arithmetic sequence is given by a_n = a + (n-1)d. Here, a = 5, d = 3, n = 10. So, a_10 = 5 + (10-1) * 3 = 5 + 27 = 32.
Correct Answer:
B
— 35
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Q. What is the 12th term of the arithmetic sequence where the first term is 7 and the common difference is 5?
Solution
Using the formula a_n = a + (n-1)d, we have a_12 = 7 + (12-1) * 5 = 7 + 55 = 62.
Correct Answer:
A
— 62
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Q. What is the 3rd term in the expansion of (2x + 3)^4?
-
A.
108x^2
-
B.
216x^2
-
C.
324x^2
-
D.
432x^2
Solution
The 3rd term is given by C(4,2) * (2x)^2 * (3)^2 = 6 * 4x^2 * 9 = 216x^2.
Correct Answer:
B
— 216x^2
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Q. What is the 3rd term in the expansion of (2x + 5)^6? (2000)
-
A.
600x^4
-
B.
1500x^4
-
C.
1800x^4
-
D.
2000x^4
Solution
The 3rd term is given by C(6,2) * (2x)^2 * (5)^4 = 15 * 4 * 625 = 37500.
Correct Answer:
B
— 1500x^4
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Q. What is the 3rd term in the expansion of (2x - 3)^5? (2022)
-
A.
-90x^3
-
B.
90x^3
-
C.
-60x^3
-
D.
60x^3
Solution
The 3rd term is C(5,2) * (2x)^3 * (-3)^2 = 10 * 8x^3 * 9 = -720x^3.
Correct Answer:
A
— -90x^3
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Q. What is the 3rd term in the expansion of (x + 2)^5? (2021)
Solution
The 3rd term is given by C(5,2) * (x)^3 * (2)^2 = 10 * x^3 * 4 = 40.
Correct Answer:
C
— 60
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Q. What is the 3rd term in the expansion of (x + 2)^8? (2022)
-
A.
112
-
B.
128
-
C.
256
-
D.
64
Solution
The 3rd term is given by 8C2 * (2)^2 * (x)^6 = 28 * 4 * x^6 = 112x^6.
Correct Answer:
A
— 112
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Q. What is the 3rd term in the expansion of (x + 3)^4? (2023)
-
A.
36x^2
-
B.
54x^2
-
C.
72x^2
-
D.
108x^2
Solution
The 3rd term is C(4,2) * (3)^2 * (x)^2 = 6 * 9 * x^2 = 54x^2.
Correct Answer:
B
— 54x^2
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Q. What is the 3rd term in the expansion of (x + 3)^5? (2023)
-
A.
45
-
B.
90
-
C.
135
-
D.
180
Solution
The 3rd term is C(5,2) * (3)^2 * (x)^3 = 10 * 9 * x^3 = 90.
Correct Answer:
B
— 90
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Q. What is the 3rd term in the expansion of (x + 3)^7? (2023)
-
A.
189
-
B.
441
-
C.
729
-
D.
1024
Solution
The 3rd term is C(7,2) * (3)^2 * (x)^5 = 21 * 9 * x^5 = 189.
Correct Answer:
B
— 441
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Q. What is the 3rd term in the expansion of (x + 4)^5? (2023)
-
A.
80x^3
-
B.
160x^3
-
C.
240x^3
-
D.
320x^3
Solution
The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Correct Answer:
C
— 240x^3
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Q. What is the 3rd term in the expansion of (x + 4)^6? (2020)
-
A.
240x^4
-
B.
360x^4
-
C.
480x^4
-
D.
600x^4
Solution
The 3rd term is C(6,2) * (4)^2 * (x)^4 = 15 * 16 * x^4 = 240x^4.
Correct Answer:
B
— 360x^4
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Q. What is the 4th term in the expansion of (2x - 3)^6? (2020)
-
A.
-540
-
B.
540
-
C.
-720
-
D.
720
Solution
The 4th term is C(6,3) * (2x)^3 * (-3)^3 = 20 * 8x^3 * -27 = -540.
Correct Answer:
A
— -540
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Q. What is the 5th term in the expansion of (2 + 3x)^6? (2023)
-
A.
486
-
B.
540
-
C.
729
-
D.
810
Solution
The 5th term is given by 6C4 * (2)^(6-4) * (3x)^4 = 15 * 4 * 81x^4 = 4860x^4.
Correct Answer:
B
— 540
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Q. What is the 5th term in the expansion of (3x - 2)^7? (2023)
-
A.
-1680x^3
-
B.
1680x^3
-
C.
-2520x^3
-
D.
2520x^3
Solution
The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Correct Answer:
A
— -1680x^3
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Q. What is the 5th term in the expansion of (x - 1)^8? (2022)
-
A.
-56x^4
-
B.
56x^4
-
C.
-70x^4
-
D.
70x^4
Solution
The 5th term corresponds to k=4. Using the binomial theorem, it is given by 8C4 * (x)^4 * (-1)^4 = 70x^4.
Correct Answer:
A
— -56x^4
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Q. What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?
Solution
To find the 5th term, substitute n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.
Correct Answer:
B
— 47
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Q. What is the 8th term of the sequence defined by a_n = 3n - 2?
Solution
Substituting n = 8 into the formula: a_8 = 3(8) - 2 = 24 - 2 = 22.
Correct Answer:
A
— 22
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Q. What is the angle between the lines y = 2x + 1 and y = -1/2x + 3?
-
A.
90 degrees
-
B.
60 degrees
-
C.
45 degrees
-
D.
30 degrees
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/4) which is approximately 60 degrees.
Correct Answer:
B
— 60 degrees
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Q. What is the angle subtended at the center of a circle by an arc of length 5 cm if the radius is 10 cm? (2022)
-
A.
30 degrees
-
B.
60 degrees
-
C.
90 degrees
-
D.
45 degrees
Solution
Arc length = (θ/360) * 2πr; 5 = (θ/360) * 2π * 10; θ = (5 * 360) / (20π) = 30 degrees.
Correct Answer:
B
— 60 degrees
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