Q. What is the relationship between the work function and the threshold frequency?
A.
Φ = hν₀
B.
Φ = ν₀/h
C.
Φ = h/ν₀
D.
Φ = ν₀²/h
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Solution
The work function (Φ) is directly proportional to the threshold frequency (ν₀) as Φ = hν₀.
Correct Answer:
A
— Φ = hν₀
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Q. What is the relationship between torque (τ), moment of inertia (I), and angular acceleration (α)?
A.
τ = Iα
B.
τ = α/I
C.
τ = I/α
D.
τ = I + α
Show solution
Solution
The relationship is given by τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.
Correct Answer:
A
— τ = Iα
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Q. What is the relationship between verbal ability and overall performance in the CAT exam as suggested in the passage?
A.
Verbal ability is secondary to quantitative skills.
B.
Verbal ability directly impacts overall performance.
C.
Verbal ability is irrelevant to the exam's success.
D.
Verbal ability is only important for certain sections.
Show solution
Solution
The passage suggests that strong verbal ability is crucial and directly influences overall performance in the CAT exam.
Correct Answer:
B
— Verbal ability directly impacts overall performance.
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Q. What is the relationship between voltage, current, and resistance according to Ohm's Law?
A.
V = I * R
B.
V = I / R
C.
V = R / I
D.
V = I + R
Show solution
Solution
Ohm's Law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with resistance (R) as the proportionality constant: V = I * R.
Correct Answer:
A
— V = I * R
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Q. What is the relationship between voltage, current, and resistance as described by Ohm's Law? (2021)
A.
V = I + R
B.
V = I * R
C.
V = I / R
D.
V = R / I
Show solution
Solution
Ohm's Law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with the resistance (R) being the constant of proportionality. Therefore, V = I * R.
Correct Answer:
B
— V = I * R
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Q. What is the relationship between voltage, current, and resistance as stated by Ohm's Law? (2021)
A.
V = I + R
B.
V = I * R
C.
V = I / R
D.
V = R / I
Show solution
Solution
Ohm's Law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with the resistance (R) being the constant of proportionality. Therefore, V = I * R.
Correct Answer:
B
— V = I * R
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Q. What is the relationship between voltage, current, and resistance in a circuit according to Ohm's Law?
A.
V = I + R
B.
V = I - R
C.
V = I * R
D.
V = I / R
Show solution
Solution
According to Ohm's Law, the relationship is given by V = I * R.
Correct Answer:
C
— V = I * R
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Q. What is the relationship between voltage, current, and resistance in an electrical circuit?
A.
Ohm's Law
B.
Kirchhoff's Law
C.
Faraday's Law
D.
Ampere's Law
Show solution
Solution
Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R) as V = IR.
Correct Answer:
A
— Ohm's Law
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Q. What is the relationship between ΔG and equilibrium constant K?
A.
ΔG = -RT ln K
B.
ΔG = RT ln K
C.
ΔG = KRT
D.
ΔG = K/R
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Solution
The relationship is given by ΔG = -RT ln K, where R is the gas constant and T is temperature.
Correct Answer:
A
— ΔG = -RT ln K
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Q. What is the relationship between ΔG and the equilibrium constant (K)?
A.
ΔG = -RT ln(K)
B.
ΔG = RT ln(K)
C.
ΔG = KRT
D.
ΔG = K - RT
Show solution
Solution
The relationship is given by ΔG = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.
Correct Answer:
A
— ΔG = -RT ln(K)
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Q. What is the relationship between ΔG, ΔH, and ΔS at constant temperature?
A.
ΔG = ΔH + TΔS
B.
ΔG = ΔH - TΔS
C.
ΔG = TΔS - ΔH
D.
ΔG = ΔH/ΔS
Show solution
Solution
The relationship is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.
Correct Answer:
B
— ΔG = ΔH - TΔS
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Q. What is the relationship between ΔH and ΔG at equilibrium?
A.
ΔG = 0
B.
ΔH = 0
C.
ΔG = ΔH
D.
ΔG = ΔH + TΔS
Show solution
Solution
At equilibrium, the change in Gibbs free energy (ΔG) is zero.
Correct Answer:
A
— ΔG = 0
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Q. What is the relationship between ΔH and ΔU for a reaction at constant pressure?
A.
ΔH = ΔU + PΔV
B.
ΔH = ΔU - PΔV
C.
ΔH = ΔU
D.
ΔH = PΔV
Show solution
Solution
At constant pressure, the relationship is given by ΔH = ΔU + PΔV.
Correct Answer:
A
— ΔH = ΔU + PΔV
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Q. What is the remainder when 1000 is divided by 6?
Show solution
Solution
1000 divided by 6 gives a quotient of 166 and a remainder of 4.
Correct Answer:
A
— 4
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Q. What is the remainder when 1000 is divided by 9? (2023)
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Solution
1000 divided by 9 gives a remainder of 1 (1000 = 9*111 + 1).
Correct Answer:
B
— 2
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Q. What is the remainder when 123456 is divided by 10? (2023)
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Solution
The remainder when a number is divided by 10 is the last digit of the number, which is 6.
Correct Answer:
D
— 6
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Q. What is the remainder when 123456 is divided by 11? (2023)
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Solution
123456 mod 11 = 0, as 123456 is divisible by 11.
Correct Answer:
A
— 0
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Q. What is the remainder when 144 is divided by 11?
Show solution
Solution
144 divided by 11 gives a remainder of 1.
Correct Answer:
A
— 0
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Q. What is the remainder when 145 is divided by 12?
Show solution
Solution
145 divided by 12 gives a remainder of 1.
Correct Answer:
B
— 2
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Q. What is the remainder when 250 is divided by 7?
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Solution
250 divided by 7 gives a quotient of 35 and a remainder of 5.
Correct Answer:
A
— 1
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Q. What is the remainder when 256 is divided by 11?
Show solution
Solution
256 divided by 11 gives a quotient of 23 and a remainder of 3.
Correct Answer:
A
— 2
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Q. What is the remainder when 256 is divided by 7?
Show solution
Solution
256 divided by 7 gives a quotient of 36 and a remainder of 4.
Correct Answer:
B
— 4
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Q. What is the remainder when 256 is divided by 9?
Show solution
Solution
256 divided by 9 gives a quotient of 28 and a remainder of 4.
Correct Answer:
B
— 2
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Q. What is the remainder when 987654 is divided by 9?
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Solution
The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the remainder when 987654321 is divided by 9? (2023)
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Solution
The remainder when a number is divided by 9 can be found by summing its digits. The sum of the digits of 987654321 is 45, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the repeating unit in polyethylene?
A.
-CH2-CH2-
B.
-C6H5-
C.
-C3H6-
D.
-C2H4-
Show solution
Solution
The repeating unit in polyethylene is -CH2-CH2-, derived from ethylene monomers.
Correct Answer:
A
— -CH2-CH2-
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Q. What is the repeating unit of polystyrene? (2021)
A.
-CH2-CH2-
B.
-CH=CH2-
C.
-C6H5-
D.
-C3H6-
Show solution
Solution
The repeating unit of polystyrene is derived from the monomer styrene, which has the structure -CH=CH2-.
Correct Answer:
B
— -CH=CH2-
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Q. What is the resistance of a circuit if a current of 5A flows through it when a voltage of 25V is applied? (2022)
A.
5Ω
B.
10Ω
C.
15Ω
D.
20Ω
Show solution
Solution
Using Ohm's law (R = V/I), R = 25V / 5A = 5Ω.
Correct Answer:
B
— 10Ω
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Q. What is the resistance of a wire of length 2 m and cross-sectional area 1 mm² if the resistivity of the material is 1.7 x 10^-8 Ωm?
A.
0.034 Ω
B.
0.017 Ω
C.
0.068 Ω
D.
0.085 Ω
Show solution
Solution
Resistance R = ρ * (L/A). Here, R = (1.7 x 10^-8 Ωm) * (2 m / (1 x 10^-6 m²)) = 0.034 Ω.
Correct Answer:
A
— 0.034 Ω
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Q. What is the resistivity of a material if a 5 m long wire with a cross-sectional area of 1 mm² has a resistance of 10 Ω?
A.
2 x 10^-6 Ω·m
B.
5 x 10^-6 Ω·m
C.
1 x 10^-5 Ω·m
D.
2 x 10^-5 Ω·m
Show solution
Solution
Resistivity ρ = R * (A / L) = 10 * (1 x 10^-6 / 5) = 2 x 10^-5 Ω·m.
Correct Answer:
C
— 1 x 10^-5 Ω·m
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