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Q. Calculate the pH of a 0.01 M solution of NaHCO3. (2023)

A. 8.3
B. 9.0
C. 7.5
D. 8.0

Solution

NaHCO3 is a weak base. The pH can be calculated using the formula pH = 7 + 0.5(pKa - log[C]). pKa of HCO3- is about 10.3, so pH ≈ 8.3.

Correct Answer: A — 8.3

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Q. Calculate the pH of a 0.05 M NH4Cl solution (Kb for NH3 = 1.8 x 10^-5).

A. 4.75
B. 5.25
C. 5.75
D. 6.25

Solution

Using the formula for weak bases, pH = 14 - 0.5(pKb - logC) = 14 - 0.5(4.74 - log(0.05)) = 5.25.

Correct Answer: B — 5.25

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Q. Calculate the pH of a 0.1 M NaOH solution.

A. 12
B. 13
C. 14
D. 11

Solution

pOH = -log[OH-] = -log(0.1) = 1, thus pH = 14 - pOH = 14 - 1 = 13.

Correct Answer: C — 14

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Q. Calculate the pH of a 0.2 M solution of KOH.

A. 12
B. 13
C. 14
D. 11

Solution

pOH = -log(0.2) = 0.7, thus pH = 14 - 0.7 = 13.3.

Correct Answer: B — 13

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Q. Calculate the term containing x^3 in the expansion of (2x + 5)^6. (2000)

A. 1500
B. 1800
C. 2000
D. 2500

Solution

The term containing x^3 is C(6,3) * (2)^3 * (5)^(6-3) = 20 * 8 * 125 = 20000.

Correct Answer: B — 1800

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Q. Calculate the term containing x^3 in the expansion of (x + 2)^7.

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

Solution

The term containing x^3 is C(7,3) * (2)^4 = 35 * 16 = 560.

Correct Answer: B — 84

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Q. Calculate the term independent of x in the expansion of (2x - 3)^5.

A. -243
B. 0
C. 243
D. 81

Solution

The term independent of x is C(5,5) * (2x)^0 * (-3)^5 = 1 * 1 * (-243) = -243.

Correct Answer: A — -243

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Q. Calculate the term independent of x in the expansion of (2x^2 - 3x + 4)^3.

A. 12
B. 24
C. 36
D. 48

Solution

The term independent of x occurs when the powers of x cancel out. The term is C(3,0)(4)^3 + C(3,1)(-3x)(4)^2 + C(3,2)(-3x)^2(4) + C(3,3)(-3x)^3 = 64 - 36 + 0 + 0 = 28.

Correct Answer: B — 24

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Q. Calculate the term independent of x in the expansion of (2x^2 - 3x + 4)^5.

A. 80
B. 120
C. 160
D. 200

Solution

The term independent of x occurs when the powers of x cancel out. This can be calculated using the binomial expansion.

Correct Answer: C — 160

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Q. Calculate the term independent of x in the expansion of (2x^2 - 3x)^4.

A. -81
B. 108
C. -108
D. 81

Solution

The term independent of x occurs when 2k = 4, k = 2. The term is C(4,2) * (2x^2)^2 * (-3x)^2 = 6 * 4 * 9 = -216.

Correct Answer: C — -108

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Q. Calculate the term independent of x in the expansion of (x/2 - 3)^6.

A. 729
B. 729/64
C. 729/32
D. 729/16

Solution

The term independent of x occurs when k = 3, which gives C(6,3) * (x/2)^3 * (-3)^3 = 20 * (1/8) * (-27) = -67.5.

Correct Answer: B — 729/64

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Q. Calculate the term independent of x in the expansion of (x/2 - 3)^8.

A. -3
B. -8
C. 0
D. 256

Solution

The term independent of x occurs when k = 4. Thus, the term is C(8,4) * (x/2)^4 * (-3)^4 = 70 * (1/16) * 81 = 256.

Correct Answer: D — 256

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Q. Calculate the term independent of x in the expansion of (x^2 - 3x + 2)^4.

A. 8
B. 12
C. 16
D. 20

Solution

The term independent of x occurs when the powers of x cancel out. The term is C(4,2) * (2)^2 * (-3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 12

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Q. Calculate the value of (1 + 3)^5 using the binomial theorem.

A. 81
B. 243
C. 125
D. 256

Solution

(1 + 3)^5 = 4^5 = 1024.

Correct Answer: B — 243

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Q. Calculate the value of 100 - (25 × 3). (2015)

A. 25
B. 75
C. 50
D. 70

Solution

25 × 3 = 75, then 100 - 75 = 25.

Correct Answer: B — 75

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Q. Calculate the value of 12 × 3 - 4 × 2. (2023) 2023

A. 28
B. 32
C. 34
D. 30

Solution

12 × 3 = 36 and 4 × 2 = 8, so 36 - 8 = 28.

Correct Answer: A — 28

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Q. Calculate the value of 12 × 3 - 4. (2021)

A. 32
B. 28
C. 36
D. 24

Solution

12 × 3 = 36, then 36 - 4 = 32.

Correct Answer: B — 28

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Q. Calculate the value of 12 × 5 - 8. (2021)

A. 52
B. 60
C. 56
D. 48

Solution

12 × 5 = 60, then 60 - 8 = 52.

Correct Answer: C — 56

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Q. Calculate the value of 12 × 8 - 10. (2021)

A. 86
B. 82
C. 78
D. 80

Solution

12 × 8 = 96, then 96 - 10 = 86.

Correct Answer: B — 82

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Q. Calculate the value of 12 × 8 - 24. (2021)

A. 72
B. 96
C. 48
D. 60

Solution

12 × 8 = 96, then 96 - 24 = 72.

Correct Answer: A — 72

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Q. Calculate the value of 12 × 8 - 4 × 6. (2021)

A. 72
B. 60
C. 48
D. 54

Solution

12 × 8 = 96 and 4 × 6 = 24, so 96 - 24 = 72.

Correct Answer: B — 60

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Q. Calculate the value of 25% of 200. (2015)

A. 50
B. 25
C. 75
D. 100

Solution

25% of 200 = (25/100) × 200 = 50.

Correct Answer: A — 50

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Q. Calculate the value of 5! (5 factorial). (2020)

A. 120
B. 100
C. 60
D. 24

Solution

5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: A — 120

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Q. Calculate the value of 5! - 4!. (2019)

A. 20
B. 24
C. 120
D. 96

Solution

5! = 120 and 4! = 24, so 120 - 24 = 96.

Correct Answer: D — 96

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Q. Calculate the value of 6^2 - 4^2. (2023) 2023

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

Solution

6^2 = 36 and 4^2 = 16, so 36 - 16 = 20.

Correct Answer: A — 20

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Q. Calculate the value of 8 + 2 × 5. (2015)

A. 18
B. 20
C. 10
D. 16

Solution

According to BODMAS, 2 × 5 = 10, then 8 + 10 = 18.

Correct Answer: D — 16

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Q. Calculate the value of 8 × (2 + 3). (2015)

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

Solution

2 + 3 = 5, then 8 × 5 = 40.

Correct Answer: A — 40

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Q. Calculate the value of 8^2 - 4^2. (2021)

A. 48
B. 60
C. 50
D. 40

Solution

8^2 = 64 and 4^2 = 16, so 64 - 16 = 48.

Correct Answer: A — 48

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Q. Calculate the weight of a 10 kg object on the surface of Mars, where the acceleration due to gravity is 3.7 m/s².

A. 37 N
B. 74 N
C. 10 N
D. 100 N

Solution

Weight = mass * gravity = 10 kg * 3.7 m/s² = 37 N

Correct Answer: A — 37 N

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Q. Calculate the weight of a 10 kg object on the surface of the Earth (g = 9.8 m/s²).

A. 98 N
B. 10 N
C. 9.8 N
D. 100 N

Solution

Weight W = m * g = 10 kg * 9.8 m/s² = 98 N.

Correct Answer: A — 98 N

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