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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?

A. 62
B. 67
C. 72
D. 77

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 15th term of an arithmetic progression where the first term is 7 and the common difference is 2? (2023)

A. 27
B. 29
C. 31
D. 33

Solution

Using the formula for the nth term, the 15th term = 7 + (15-1) * 2 = 7 + 28 = 35.

Correct Answer: C — 31

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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 (a + b)^6?

A. 15ab^5
B. 20ab^5
C. 30ab^5
D. 6ab^5

Solution

The 3rd term is given by 6C2 * a^4 * b^2 = 15 * a^4 * b^2 = 15ab^5.

Correct Answer: B — 20ab^5

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Q. What is the 3rd term in the expansion of (x + 2)^5? (2021)

A. 40
B. 80
C. 60
D. 20

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)^6?

A. 60x^4
B. 90x^4
C. 120x^4
D. 180x^4

Solution

The 3rd term is given by C(6, 2) * (x)^2 * (2)^4 = 15 * x^2 * 16 = 240x^2.

Correct Answer: B — 90x^4

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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 4th term in the expansion of (3x + 2)^6?

A. 540x^4
B. 540x^3
C. 720x^4
D. 720x^3

Solution

The 4th term is given by C(6,3) * (3x)^3 * (2)^3 = 20 * 27x^3 * 8 = 4320x^3.

Correct Answer: A — 540x^4

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Q. What is the 4th term of the arithmetic progression where the first term is 10 and the common difference is 5?

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

Solution

The nth term is given by a + (n-1)d. Here, a = 10, d = 5, and n = 4. So, the 4th term = 10 + (4-1) * 5 = 10 + 15 = 25.

Correct Answer: A — 25

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Q. What is the 4th term of the arithmetic sequence where the first term is 10 and the common difference is -2? (2023)

A. 6
B. 4
C. 2
D. 0

Solution

The 4th term is given by a + (n-1)d = 10 + (4-1)(-2) = 10 - 6 = 4.

Correct Answer: B — 4

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Q. What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)

A. 24
B. 30
C. 36
D. 42

Solution

For n = 4, a_4 = 4^2 + 2*4 = 16 + 8 = 24.

Correct Answer: A — 24

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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 (2x - 3)^7?

A. -1134x^5
B. 1134x^5
C. -1458x^5
D. 1458x^5

Solution

The 5th term is given by C(7, 4)(2x)^4(-3)^3 = 35 * 16x^4 * (-27) = -1134x^5.

Correct Answer: A — -1134x^5

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Q. What is the 5th term in the expansion of (3x - 2)^6?

A. -540x^5
B. 540x^5
C. -486x^5
D. 486x^5

Solution

The 5th term is given by C(6, 4) * (3x)^4 * (-2)^2 = 15 * 81x^4 * 4 = 4860x^4.

Correct Answer: A — -540x^5

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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?

A. 45
B. 47
C. 49
D. 51

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 6th term of the sequence defined by a_n = n^2 + n? (2023)

A. 36
B. 42
C. 30
D. 24

Solution

For n = 6, a_6 = 6^2 + 6 = 36 + 6 = 42.

Correct Answer: B — 42

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Q. What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)

A. 31
B. 35
C. 36
D. 30

Solution

Substituting n = 6 gives a_6 = 6^2 - 6 + 1 = 36 - 6 + 1 = 31.

Correct Answer: C — 36

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Q. What is the 75th percentile of the data set {10, 20, 30, 40, 50}?

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

Solution

The 75th percentile (Q3) is the value below which 75% of the data falls, which is 40.

Correct Answer: A — 40

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Q. What is the 7th term of the sequence defined by a_n = 2^n + 3^n?

A. 2187
B. 243
C. 256
D. 729

Solution

a_7 = 2^7 + 3^7 = 128 + 2187 = 2315.

Correct Answer: A — 2187

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Q. What is the 8th term of the sequence defined by a_n = 3n - 2?

A. 22
B. 24
C. 26
D. 28

Solution

Substituting n = 8 into the formula: a_8 = 3(8) - 2 = 24 - 2 = 22.

Correct Answer: A — 22

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