MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

Q. What is the coefficient of x^2 in the expansion of (x + 5)^7? (2021)

A. 21
B. 35
C. 105
D. 175

Solution

The coefficient of x^2 is given by 7C2 * 5^5 = 21 * 3125 = 65625.

Correct Answer: B — 35

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Q. What is the coefficient of x^2 in the expansion of (x - 1)^5?

A. -10
B. -5
C. 5
D. 10

Solution

The coefficient of x^2 is C(5,2) * (-1)^3 = 10 * (-1) = -10.

Correct Answer: A — -10

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Q. What is the coefficient of x^2 in the expansion of (x - 2)^5?

A. -40
B. -20
C. 20
D. 40

Solution

The coefficient of x^2 is given by 5C2 * (-2)^3 = 10 * (-8) = -80.

Correct Answer: A — -40

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Q. What is the coefficient of x^3 in the expansion of (5x + 2)^6? (2000) 2000

A. 600
B. 720
C. 800
D. 900

Solution

The coefficient of x^3 is C(6,3) * (5)^3 * (2)^3 = 20 * 125 * 8 = 20000.

Correct Answer: B — 720

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Q. What is the coefficient of x^3 in the expansion of (x + 5)^8?

A. 2800
B. 3360
C. 4000
D. 4200

Solution

The coefficient of x^3 is given by 8C3 * (5)^5 = 56 * 3125 = 175000.

Correct Answer: B — 3360

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Q. What is the coefficient of x^3 in the expansion of (x - 1)^5? (2022)

A. -10
B. 10
C. 5
D. 15

Solution

The coefficient of x^3 is C(5,3)(-1)^2 = 10.

Correct Answer: A — -10

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

A. 10
B. 20
C. 30
D. 40

Solution

The coefficient of x^3 is C(5,3) * (-2)^2 = 10 * 4 = 40.

Correct Answer: A — 10

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

A. -80
B. -120
C. -240
D. -720

Solution

The coefficient of x^3 is C(6,3) * (-2)^3 = 20 * (-8) = -160.

Correct Answer: B — -120

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Q. What is the coefficient of x^4 in the expansion of (2x + 5)^6? (2022)

A. 150
B. 300
C. 600
D. 450

Solution

The coefficient of x^4 is C(6,4) * (2)^4 * (5)^2 = 15 * 16 * 25 = 600.

Correct Answer: D — 450

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Q. What is the coefficient of x^4 in the expansion of (3x + 2)^6?

A. 540
B. 720
C. 810
D. 900

Solution

The coefficient of x^4 is C(6,4) * (3)^4 * (2)^2 = 15 * 81 * 4 = 4860.

Correct Answer: B — 720

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Q. What is the coefficient of x^4 in the expansion of (3x - 2)^5? (2021)

A. 90
B. 120
C. 150
D. 180

Solution

The coefficient of x^4 is given by 5C4 * (3)^4 * (-2)^1 = 5 * 81 * (-2) = -810.

Correct Answer: C — 150

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Q. What is the coefficient of x^4 in the expansion of (x + 1)^8? (2020)

A. 70
B. 56
C. 28
D. 8

Solution

The coefficient of x^4 is C(8,4) = 70.

Correct Answer: B — 56

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Q. What is the coefficient of x^4 in the expansion of (x + 2)^6?

A. 15
B. 60
C. 90
D. 120

Solution

The coefficient of x^4 is given by 6C4 * (2)^2 = 15 * 4 = 60.

Correct Answer: C — 90

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Q. What is the coefficient of x^5 in the expansion of (2x - 1)^6?

A. 32
B. 48
C. 64
D. 80

Solution

The coefficient of x^5 is C(6,5) * (2)^5 * (-1)^1 = 6 * 32 * (-1) = -192.

Correct Answer: D — 80

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Q. What is the coefficient of x^5 in the expansion of (x + 4)^7? (2020)

A. 672
B. 6720
C. 1680
D. 840

Solution

The coefficient of x^5 is C(7,5) * (4)^2 = 21 * 16 = 336.

Correct Answer: C — 1680

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Q. What is the coefficient of x^5 in the expansion of (x - 3)^7?

A. -21
B. -63
C. -126
D. -189

Solution

The coefficient of x^5 is C(7,5) * (-3)^2 = 21 * 9 = -189.

Correct Answer: B — -63

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Q. What is the coefficient of x^6 in the expansion of (2x - 1)^8? (2022)

A. -112
B. 112
C. 64
D. 128

Solution

The coefficient of x^6 is C(8,6) * (2)^6 * (-1)^2 = 28 * 64 = 1792.

Correct Answer: A — -112

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Q. What is the coefficient of x^6 in the expansion of (x + 3)^8? (2020)

A. 56
B. 84
C. 112
D. 128

Solution

The coefficient of x^6 is C(8,6) * (3)^2 = 28 * 9 = 252.

Correct Answer: B — 84

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Q. What is the coefficient of x^6 in the expansion of (x + 3)^9? (2020)

A. 84
B. 126
C. 36
D. 54

Solution

The coefficient of x^6 is C(9,6)(3)^3 = 84 * 27 = 2268.

Correct Answer: B — 126

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Q. What is the coefficient of x^7 in the expansion of (2x - 3)^8? (2022)

A. -6720
B. 6720
C. -3360
D. 3360

Solution

The coefficient of x^7 is C(8,7)(2)^7(-3)^1 = 8 * 128 * -3 = -3072.

Correct Answer: A — -6720

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Q. What is the color of the complex [Cu(H2O)6]2+? (2023) 2023

A. Green
B. Blue
C. Red
D. Yellow

Solution

[Cu(H2O)6]2+ is typically blue due to the d-d transitions of the copper ion in an octahedral field.

Correct Answer: B — Blue

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Q. What is the common oxidation state of Alkaline earth metals? (2014) 2014

A. +1
B. +2
C. +3
D. 0

Solution

Alkaline earth metals commonly exhibit a +2 oxidation state.

Correct Answer: B — +2

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Q. What is the common oxidation state of Group 1 elements? (2021)

A. -1
B. 0
C. +1
D. +2

Solution

Group 1 elements commonly exhibit an oxidation state of +1.

Correct Answer: C — +1

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Q. What is the common oxidation state of Group 13 elements? (2021)

A. +1
B. +2
C. +3
D. +4

Solution

Group 13 elements commonly exhibit a +3 oxidation state due to the loss of three valence electrons.

Correct Answer: C — +3

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Q. What is the common oxidation state of nitrogen in ammonia (NH3)? (2023) 2023

A. -3
B. 0
C. +1
D. +3

Solution

In ammonia (NH3), nitrogen has an oxidation state of -3.

Correct Answer: A — -3

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Q. What is the common oxidation state of transition metals in the d-block? (2023)

A. +1
B. +2
C. +3
D. +4

Solution

The common oxidation state of transition metals in the d-block is +2, as they often lose two electrons from their outermost shell.

Correct Answer: B — +2

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Q. What is the concentration in mol/L of a solution made by dissolving 58.5 grams of NaCl in 1 liter of water? (Molar mass of NaCl = 58.5 g/mol) (2023) 2023

A. 1 M
B. 0.5 M
C. 2 M
D. 0.25 M

Solution

Moles of NaCl = 58.5 g / 58.5 g/mol = 1 mole. Molarity = 1 mole / 1 L = 1 M.

Correct Answer: A — 1 M

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Q. What is the concentration of a solution if 5 g of NaOH is dissolved in 250 mL of water? (2020)

A. 0.5 M
B. 1 M
C. 0.2 M
D. 0.1 M

Solution

Moles of NaOH = 5 g / 40 g/mol = 0.125 mol. Molarity = 0.125 mol / 0.25 L = 0.5 M.

Correct Answer: B — 1 M

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Q. What is the concentration of H+ ions in a solution with pH 3? (2019) 2019

A. 0.001 M
B. 0.01 M
C. 0.1 M
D. 1 M

Solution

Concentration of H+ = 10^(-pH) = 10^(-3) = 0.001 M.

Correct Answer: B — 0.01 M

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Q. What is the concentration of H+ ions in a solution with pH 4?

A. 0.0001 M
B. 0.01 M
C. 0.1 M
D. 1 M

Solution

[H+] = 10^(-pH) = 10^(-4) = 0.0001 M.

Correct Answer: A — 0.0001 M

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