Engineering Entrance
Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
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A.
10.47 cm
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B.
15.71 cm
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C.
20.94 cm
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D.
25.13 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer: A — 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
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A.
2π cm
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B.
4π cm
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C.
π cm
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D.
8 cm
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.
Correct Answer: A — 2π cm
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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)
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A.
5.24 cm
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B.
3.14 cm
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C.
5.00 cm
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D.
10.47 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer: A — 5.24 cm
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Q. What is the length of an arc of a circle with radius 5 cm and angle 60 degrees? (2020)
-
A.
5.24 cm
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B.
3.14 cm
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C.
5.00 cm
-
D.
6.00 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer: A — 5.24 cm
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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (4, 0), (4, 3), and (0, 3)? (2021)
Solution
Length of diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.
Correct Answer: A — 5
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Q. What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)
Solution
Diagonal length = √[(5-1)² + (4-1)²] = √[16 + 9] = √25 = 5.
Correct Answer: B — 5
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Q. What is the magnetic field inside a long solenoid? (2023)
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A.
Zero
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B.
Uniform and parallel
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C.
Concentric circles
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D.
Decreasing
Solution
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
Correct Answer: B — Uniform and parallel
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Q. What is the main characteristic of elastomers?
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A.
Brittle
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B.
Elastic
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C.
Rigid
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D.
Transparent
Solution
Elastomers are characterized by their elastic properties, allowing them to stretch and return to their original shape.
Correct Answer: B — Elastic
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Q. What is the main component of natural rubber?
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A.
Polyisoprene
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B.
Polystyrene
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C.
Polyethylene
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D.
Polyvinyl acetate
Solution
Natural rubber is primarily composed of polyisoprene, which is derived from latex.
Correct Answer: A — Polyisoprene
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Q. What is the main function of lipids in the body?
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A.
Energy storage
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B.
Genetic information
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C.
Structural support
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D.
Transport
Solution
Lipids serve as a major form of energy storage in the body.
Correct Answer: A — Energy storage
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Q. What is the main product of the combustion of hydrocarbons? (2023) 2023
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A.
Oxygen
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B.
Water
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C.
Carbon Dioxide
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D.
Nitrogen
Solution
The main products of the combustion of hydrocarbons are water (H2O) and carbon dioxide (CO2).
Correct Answer: C — Carbon Dioxide
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Q. What is the main product of the complete combustion of methane? (2023)
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A.
Carbon dioxide and water
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B.
Carbon monoxide and water
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C.
Carbon and hydrogen
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D.
Oxygen and water
Solution
The complete combustion of methane (CH4) produces carbon dioxide (CO2) and water (H2O).
Correct Answer: A — Carbon dioxide and water
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Q. What is the main product of the oxidation of ethanol?
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A.
Acetic acid
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B.
Formic acid
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C.
Butanoic acid
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D.
Propanoic acid
Solution
The main product of the oxidation of ethanol is acetic acid.
Correct Answer: A — Acetic acid
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Q. What is the main product when an amine reacts with an acyl chloride?
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A.
Amide
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B.
Ester
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C.
Alcohol
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D.
Aldehyde
Solution
The reaction of an amine with an acyl chloride produces an amide.
Correct Answer: A — Amide
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Q. What is the main product when an amine reacts with an alkyl halide?
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A.
Amide
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B.
Quaternary ammonium salt
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C.
Alcohol
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D.
Ester
Solution
The main product is a quaternary ammonium salt when an amine reacts with an alkyl halide, as the amine can be further alkylated.
Correct Answer: B — Quaternary ammonium salt
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Q. What is the main product when ethene reacts with bromine?
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A.
Bromethane
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B.
1,2-Dibromoethane
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C.
Ethane
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D.
Bromoethane
Solution
The reaction of ethene with bromine results in the formation of 1,2-dibromoethane.
Correct Answer: B — 1,2-Dibromoethane
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Q. What is the main product when ethene reacts with hydrogen in the presence of a catalyst?
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A.
Ethane
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B.
Ethanol
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C.
Ethyl chloride
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D.
Acetylene
Solution
The main product is ethane, formed by the hydrogenation of ethene.
Correct Answer: A — Ethane
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Q. What is the main product when phenol is treated with bromine?
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A.
Bromobenzene
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B.
Bromophenol
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C.
Benzene
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D.
Bromobutane
Solution
Bromine reacts with phenol to form bromophenol, which is a substitution product.
Correct Answer: B — Bromophenol
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Q. What is the main product when phenol reacts with bromine? (2019)
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A.
Bromobenzene
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B.
Bromophenol
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C.
Benzene
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D.
No reaction
Solution
Phenol reacts with bromine to form Bromophenol, which is a brominated derivative of phenol.
Correct Answer: B — Bromophenol
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Q. What is the main product when phenol reacts with sodium hydroxide?
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A.
Sodium phenoxide
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B.
Sodium benzoate
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C.
Benzene
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D.
Phenyl acetate
Solution
Phenol reacts with sodium hydroxide to form sodium phenoxide, which is a salt of phenol.
Correct Answer: A — Sodium phenoxide
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Q. What is the main product when propan-2-one is treated with iodine in the presence of a base?
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A.
Iodoform
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B.
Acetone
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C.
Bromoform
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D.
Chloroform
Solution
Propan-2-one (acetone) reacts with iodine in the presence of a base to form Iodoform.
Correct Answer: A — Iodoform
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Q. What is the main reaction of phenols with sodium hydroxide? (2020)
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A.
Formation of sodium phenoxide
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B.
Formation of ether
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C.
Formation of alcohol
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D.
Formation of ketone
Solution
Phenols react with sodium hydroxide to form sodium phenoxide, which is a salt of phenol.
Correct Answer: A — Formation of sodium phenoxide
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Q. What is the main type of reaction that haloalkanes undergo? (2020)
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A.
Addition
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B.
Substitution
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C.
Elimination
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D.
Redox
Solution
Haloalkanes primarily undergo nucleophilic substitution reactions due to the presence of a good leaving group (halogen).
Correct Answer: B — Substitution
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Q. What is the main use of citric acid?
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A.
Preservative
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B.
Flavoring agent
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C.
Cleaning agent
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D.
All of the above
Solution
Citric acid is used as a preservative, flavoring agent, and cleaning agent.
Correct Answer: D — All of the above
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Q. What is the major product when 2-bromobutane is treated with KOH in ethanol?
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A.
But-1-ene
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B.
But-2-ene
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C.
Butane
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D.
No reaction
Solution
The major product is But-2-ene due to the more stable double bond formed during elimination.
Correct Answer: B — But-2-ene
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Q. What is the mass of 3 moles of NaCl? (2020) 2020
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A.
87 g
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B.
58.5 g
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C.
174 g
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D.
3 g
Solution
Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol. Mass = moles x molar mass = 3 moles x 58.5 g/mol = 174 g.
Correct Answer: C — 174 g
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Q. What is the mass of 3 moles of sodium chloride (NaCl)? (2023)
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A.
58.5 g
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B.
117 g
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C.
175.5 g
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D.
29.25 g
Solution
The molar mass of NaCl is 58.5 g/mol. Therefore, 3 moles of NaCl weigh 3 x 58.5 g = 175.5 g.
Correct Answer: B — 117 g
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Q. What is the mass of NaOH required to prepare 0.5 L of a 1 M solution? (2023)
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A.
20 g
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B.
40 g
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C.
10 g
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D.
30 g
Solution
Molar mass of NaOH = 40 g/mol; grams = moles × molar mass = (1 mole/L × 0.5 L) × 40 g/mol = 20 g
Correct Answer: B — 40 g
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Q. What is the mass of solute in grams in a 3 M solution of NaCl in 1 L of solution? (2023)
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A.
58.44 g
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B.
174.32 g
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C.
29.22 g
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D.
87.16 g
Solution
Molar mass of NaCl = 58.44 g/mol; mass = moles × molar mass = 3 moles × 58.44 g/mol = 175.32 g
Correct Answer: B — 174.32 g
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Q. What is the mass of solute in grams required to make 1 L of a 0.1 M solution of NaCl? (Molar mass of NaCl = 58.5 g/mol) (2021)
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A.
5.85 g
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B.
10 g
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C.
1 g
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D.
2 g
Solution
Mass = moles × molar mass = (0.1 moles/L × 1 L) × 58.5 g/mol = 5.85 g.
Correct Answer: A — 5.85 g
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