Q. Which of the following is the correct representation of the decimal number 15 in base-4?
Solution
15 in decimal is represented as '33' in base-4 (3*4^1 + 3*4^0 = 12 + 3 = 15).
Correct Answer:
A
— 33
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Q. Which of the following is the correct representation of the decimal number 15 in hexadecimal?
Solution
In hexadecimal, the decimal number 15 is represented as F.
Correct Answer:
A
— F
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Q. Which of the following is the correct representation of the decimal number 15 in base 8?
Solution
In base 8, the decimal number 15 is represented as '17'.
Correct Answer:
A
— 17
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Q. Which of the following is the correct representation of the decimal number 25 in base-8?
Solution
25 in decimal is represented as '31' in base-8 (3*8^1 + 1*8^0 = 24 + 1 = 25).
Correct Answer:
A
— 31
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Q. Which of the following is the correct representation of the speed of light?
-
A.
3.00 × 10^8 m/s
-
B.
3.00 × 10^6 m/s
-
C.
3.00 × 10^10 m/s
-
D.
3.00 × 10^9 m/s
Solution
The speed of light in vacuum is approximately 3.00 × 10^8 m/s.
Correct Answer:
A
— 3.00 × 10^8 m/s
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Q. Which of the following is the correct representation of the unit of energy? (2019)
-
A.
Joule
-
B.
Newton-meter
-
C.
Both A and B
-
D.
None of the above
Solution
Both Joule and Newton-meter represent the same unit of energy.
Correct Answer:
C
— Both A and B
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Q. Which of the following is the correct simplification of (x^2y^3)/(xy^2)?
-
A.
x^(2-1)y^(3-2)
-
B.
x^1y^1
-
C.
x^2y^5
-
D.
x^3y^1
Solution
Using the quotient rule for exponents, (x^2y^3)/(xy^2) simplifies to x^(2-1)y^(3-2) = xy.
Correct Answer:
A
— x^(2-1)y^(3-2)
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Q. Which of the following is the correct simplification of (x^3 * y^2) / (x^2 * y)?
-
A.
x^(3-2) * y^(2-1)
-
B.
x^(5) * y^(1)
-
C.
x^(1) * y^(1)
-
D.
x^(1) * y^(3)
Solution
Using the property of exponents for division, we subtract the exponents: x^(3-2) * y^(2-1) = x^1 * y^1.
Correct Answer:
A
— x^(3-2) * y^(2-1)
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Q. Which of the following is the correct simplification of (x^3 * y^2)^(2)?
-
A.
x^6 * y^4
-
B.
x^5 * y^2
-
C.
x^3 * y^2
-
D.
x^2 * y^3
Solution
Using the power of a product property, (a*b)^n = a^n * b^n, we get (x^3)^2 * (y^2)^2 = x^6 * y^4.
Correct Answer:
A
— x^6 * y^4
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Q. Which of the following is the correct simplification of (x^3y^2)^2?
-
A.
x^6y^4
-
B.
x^5y^2
-
C.
x^3y^2
-
D.
x^2y^3
Solution
Using the power of a product property, (x^3y^2)^2 = x^(3*2)y^(2*2) = x^6y^4.
Correct Answer:
A
— x^6y^4
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Q. Which of the following is the correct simplification of log_10(1000) + log_10(0.01)?
Solution
log_10(1000) = 3 and log_10(0.01) = -2, thus 3 + (-2) = 1.
Correct Answer:
B
— 0
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Q. Which of the following is the correct simplification of log_10(1000) - log_10(10)?
Solution
Using the property of logarithms, log_10(1000) = 3 and log_10(10) = 1. Therefore, log_10(1000) - log_10(10) = 3 - 1 = 2.
Correct Answer:
C
— 3
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Q. Which of the following is the correct simplification of log_10(1000) using properties of logarithms?
Solution
log_10(1000) = log_10(10^3) = 3.
Correct Answer:
A
— 3
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Q. Which of the following is the correct simplification of log_2(8) + log_2(4)?
-
A.
log_2(32)
-
B.
log_2(12)
-
C.
log_2(16)
-
D.
log_2(6)
Solution
Using the property of logarithms, log_2(8) + log_2(4) = log_2(8*4) = log_2(32) = log_2(16).
Correct Answer:
C
— log_2(16)
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Q. Which of the following is the correct simplification of log_5(25) - log_5(5)?
Solution
log_5(25) = 2 and log_5(5) = 1, thus log_5(25) - log_5(5) = 2 - 1 = 1.
Correct Answer:
A
— 1
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Q. Which of the following is the correct simplification of log_a(b^2)?
-
A.
2 log_a(b)
-
B.
log_a(2b)
-
C.
log_a(b) + 2
-
D.
log_a(b) - 2
Solution
Using the power rule of logarithms, log_a(b^2) simplifies to 2 log_a(b).
Correct Answer:
A
— 2 log_a(b)
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Q. Which of the following is the correct simplification of log_a(b^c)?
-
A.
c * log_a(b)
-
B.
log_a(c) * log_a(b)
-
C.
log_a(b) / c
-
D.
log_a(c^b)
Solution
The property of logarithms states that log_a(b^c) = c * log_a(b).
Correct Answer:
A
— c * log_a(b)
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Q. Which of the following is the correct structure for 2,3-dimethyl-2-butanol?
-
A.
CH3C(CH3)(OH)C(CH3)CH3
-
B.
CH3C(CH3)C(OH)CH2CH3
-
C.
CH3C(OH)(CH3)C(CH3)CH3
-
D.
CH3C(CH3)C(CH3)CH2OH
Solution
The correct structure has the hydroxyl group on the second carbon with two methyl groups on the same carbon.
Correct Answer:
A
— CH3C(CH3)(OH)C(CH3)CH3
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Q. Which of the following is the correct structure for 2-butyne?
-
A.
CH3-C≡C-CH3
-
B.
CH3-CH≡C-CH3
-
C.
CH3-C=C-CH3
-
D.
C≡C-CH2-CH3
Solution
2-butyne has the structure CH3-CH≡C-CH3, with the triple bond between the second and third carbon.
Correct Answer:
B
— CH3-CH≡C-CH3
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Q. Which of the following is the correct structure for 2-methylpropane?
-
A.
CH3-CH(CH3)-CH2-CH3
-
B.
CH3-CH2-CH(CH3)-CH3
-
C.
CH3-CH(CH3)-CH(CH3)-CH3
-
D.
CH3-CH2-CH2-CH(CH3)
Solution
2-methylpropane has a branched structure with a methyl group on the second carbon.
Correct Answer:
B
— CH3-CH2-CH(CH3)-CH3
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Q. Which of the following is the correct structure for propan-2-one? (2020)
-
A.
CH3COCH3
-
B.
CH3CHO
-
C.
C2H5CHO
-
D.
C3H6O
Solution
Propan-2-one, also known as acetone, has the structure CH3COCH3, indicating it is a ketone.
Correct Answer:
A
— CH3COCH3
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Q. Which of the following is the correct unit for measuring area?
-
A.
Square meter
-
B.
Cubic meter
-
C.
Liter
-
D.
Joule
Solution
The correct unit for measuring area is square meter.
Correct Answer:
A
— Square meter
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Q. Which of the following is the correct unit for measuring electric charge?
-
A.
Coulomb
-
B.
Ampere
-
C.
Volt
-
D.
Ohm
Solution
The SI unit for electric charge is Coulomb (C).
Correct Answer:
A
— Coulomb
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Q. Which of the following is the correct unit for measuring electric current?
-
A.
Volt
-
B.
Ohm
-
C.
Ampere
-
D.
Watt
Solution
The SI unit for measuring electric current is the Ampere.
Correct Answer:
C
— Ampere
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Q. Which of the following is the correct unit for measuring energy?
-
A.
Joule
-
B.
Newton
-
C.
Watt
-
D.
Pascal
Solution
The correct unit for measuring energy is Joule (J).
Correct Answer:
A
— Joule
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Q. Which of the following is the correct unit for measuring frequency? (2022)
-
A.
Hertz
-
B.
Joule
-
C.
Watt
-
D.
Newton
Solution
The unit for measuring frequency is Hertz (Hz).
Correct Answer:
A
— Hertz
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Q. Which of the following is the correct unit for measuring pressure? (2020)
-
A.
Pascal
-
B.
Joule
-
C.
Newton
-
D.
Watt
Solution
The SI unit for measuring pressure is Pascal (Pa).
Correct Answer:
A
— Pascal
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Q. Which of the following is the correct unit for measuring the amount of substance?
-
A.
Liter
-
B.
Gram
-
C.
Mole
-
D.
Cubic meter
Solution
The mole is the SI unit for measuring the amount of substance.
Correct Answer:
C
— Mole
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Q. Which of the following is the correct unit for molality?
-
A.
mol/L
-
B.
mol/kg
-
C.
mol/mL
-
D.
mol/1000g
Solution
Molality is defined as moles of solute per kilogram of solvent, hence the unit is mol/kg.
Correct Answer:
B
— mol/kg
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Q. Which of the following is the correct unit for molarity?
-
A.
mol/L
-
B.
mol/kg
-
C.
g/L
-
D.
g/mol
Solution
Molarity is defined as moles of solute per liter of solution, hence the unit is mol/L.
Correct Answer:
A
— mol/L
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