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 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
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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
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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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Q. Which of the following is the correct unit for pressure? (2020)
-
A.
Pascal
-
B.
Joule
-
C.
Newton
-
D.
Watt
Solution
The SI unit for pressure is Pascal (Pa), which is equivalent to N/m².
Correct Answer: A — Pascal
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Q. Which of the following is the correct vertex form of the quadratic equation y = x² - 4x + 3?
-
A.
y = (x - 2)² - 1
-
B.
y = (x + 2)² - 1
-
C.
y = (x - 2)² + 1
-
D.
y = (x + 2)² + 1
Solution
Completing the square for the equation y = x² - 4x + 3 results in y = (x - 2)² - 1.
Correct Answer: A — y = (x - 2)² - 1
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Q. Which of the following is the equation of a hyperbola with transverse axis along the x-axis?
-
A.
x^2/a^2 - y^2/b^2 = 1
-
B.
y^2/a^2 - x^2/b^2 = 1
-
C.
x^2/b^2 - y^2/a^2 = 1
-
D.
y^2/b^2 - x^2/a^2 = 1
Solution
The equation of a hyperbola with transverse axis along the x-axis is x^2/a^2 - y^2/b^2 = 1.
Correct Answer: A — x^2/a^2 - y^2/b^2 = 1
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Q. Which of the following is the equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a)?
-
A.
x^2/a^2 + y^2/b^2 = 1
-
B.
y^2/a^2 + x^2/b^2 = 1
-
C.
x^2/b^2 + y^2/a^2 = 1
-
D.
y^2/b^2 + x^2/a^2 = 1
Solution
The equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a) is y^2/a^2 + x^2/b^2 = 1.
Correct Answer: A — x^2/a^2 + y^2/b^2 = 1
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Q. Which of the following is the expanded form of (x + 2)²?
-
A.
x² + 4
-
B.
x² + 4x + 4
-
C.
x² + 2x + 2
-
D.
x² + 2
Solution
(x + 2)² = x² + 2*2*x + 2² = x² + 4x + 4.
Correct Answer: B — x² + 4x + 4
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Q. Which of the following is the functional group of aldehydes?
-
A.
-CHO
-
B.
-CO-
-
C.
-C=O
-
D.
-OH
Solution
Aldehydes contain the functional group -CHO, which is characterized by a carbonyl group (C=O) bonded to a hydrogen atom.
Correct Answer: A — -CHO
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Q. Which of the following is the functional group of aldehydes? (2023) 2023
-
A.
-CHO
-
B.
-CO-
-
C.
-C=O
-
D.
-OH
Solution
Aldehydes contain the functional group -CHO, which is characterized by a carbonyl group (C=O) bonded to a hydrogen atom.
Correct Answer: A — -CHO
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Q. Which of the following is the functional group of carboxylic acids?
-
A.
-OH
-
B.
-COOH
-
C.
-CHO
-
D.
-C=O
Solution
Carboxylic acids contain the -COOH functional group.
Correct Answer: B — -COOH
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Q. Which of the following is the functional group present in alcohols?
-
A.
-OH
-
B.
-COOH
-
C.
-NH2
-
D.
-CHO
Solution
Alcohols contain the hydroxyl group (-OH) as their functional group.
Correct Answer: A — -OH
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Q. Which of the following is the functional unit of skeletal muscle? (2021)
-
A.
Sarcomere
-
B.
Myofibril
-
C.
Muscle Fiber
-
D.
Fascicle
Solution
The sarcomere is the basic functional unit of skeletal muscle, responsible for muscle contraction.
Correct Answer: A — Sarcomere
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Q. Which of the following is the general formula for alkenes?
-
A.
C_nH_(2n)
-
B.
C_nH_(2n+2)
-
C.
C_nH_(2n-2)
-
D.
C_nH_n
Solution
The general formula for alkenes is C_nH_(2n), where n is the number of carbon atoms.
Correct Answer: A — C_nH_(2n)
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Q. Which of the following is the general formula for alkynes?
-
A.
C_nH_(2n+2)
-
B.
C_nH_(2n)
-
C.
C_nH_(2n-2)
-
D.
C_nH_(2n-1)
Solution
The general formula for alkynes is C_nH_(2n-2), where n is the number of carbon atoms.
Correct Answer: C — C_nH_(2n-2)
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