Q. What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at a frequency (f)? (2020)
A.
R
B.
√(R² + (2πfL)²)
C.
R + 2πfL
D.
R - 2πfL
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Solution
The impedance Z in a series RL circuit is given by Z = √(R² + (2πfL)²).
Correct Answer:
B
— √(R² + (2πfL)²)
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Q. What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at angular frequency ω? (2020)
A.
R
B.
√(R² + (ωL)²)
C.
R + jωL
D.
R + L
Show solution
Solution
The impedance Z in a series R-L circuit is given by Z = √(R² + (ωL)²).
Correct Answer:
B
— √(R² + (ωL)²)
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Q. What is the impedance of a series circuit containing a resistor and an inductor?
A.
R
B.
√(R^2 + (ωL)^2)
C.
R + jωL
D.
R - jωL
Show solution
Solution
The impedance Z in a series R-L circuit is given by Z = √(R^2 + (ωL)^2).
Correct Answer:
B
— √(R^2 + (ωL)^2)
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Q. What is the impedance of a series circuit with a resistor of 4Ω and an inductor of 3Ω at resonance? (2020)
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Solution
At resonance, the impedance is equal to the resistance, which is 4Ω.
Correct Answer:
C
— 4Ω
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Q. What is the impedance of a series RLC circuit at resonance?
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Solution
At resonance, the impedance of a series RLC circuit is equal to the resistance R.
Correct Answer:
A
— R
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Q. What is the implication of the author's argument regarding education and inequality?
A.
Education is the sole solution to inequality.
B.
Improving education alone will not suffice to reduce inequality.
C.
Education exacerbates inequality.
D.
Inequality has no relation to education.
Show solution
Solution
The author implies that while education is important, it must be accompanied by other measures to effectively reduce inequality.
Correct Answer:
B
— Improving education alone will not suffice to reduce inequality.
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Q. What is the implication of the author's statement regarding practice tests?
A.
They are unnecessary for CAT preparation.
B.
They should be the only focus of study.
C.
They are a valuable tool for assessing readiness.
D.
They can lead to overconfidence.
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Solution
The author implies that practice tests are important for gauging one's preparedness for the exam, making option 2 the correct choice.
Correct Answer:
C
— They are a valuable tool for assessing readiness.
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Q. What is the implication of the phrase 'the tip of the iceberg' in the context of the passage?
A.
The issue is more complex than it appears.
B.
The problem is nearly resolved.
C.
The situation is improving.
D.
The topic is irrelevant.
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Solution
The phrase 'the tip of the iceberg' implies that the issue is more complex and extensive than it initially seems.
Correct Answer:
A
— The issue is more complex than it appears.
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Q. What is the implied message of the passage regarding consumerism? (2023)
A.
It is essential for economic growth
B.
It leads to environmental degradation
C.
It fosters community engagement
D.
It is a personal choice
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Solution
The passage implies that consumerism contributes to environmental degradation, highlighting its negative impact.
Correct Answer:
B
— It leads to environmental degradation
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Q. What is the indefinite integral of e^x? (2020)
A.
e^x + C
B.
e^x
C.
x e^x + C
D.
x^2 e^x + C
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Solution
The indefinite integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. What is the indirect speech of the sentence: 'She said, I am going to the market.'? (2021)
A.
She said that she is going to the market.
B.
She said that she was going to the market.
C.
She said that she goes to the market.
D.
She said that she had gone to the market.
Show solution
Solution
In indirect speech, the present continuous tense changes to past continuous tense.
Correct Answer:
B
— She said that she was going to the market.
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Q. What is the indirect speech of: 'He said, I am reading a book.'? (2019)
A.
He said that he was reading a book.
B.
He said that he is reading a book.
C.
He said that he read a book.
D.
He said that he has read a book.
Show solution
Solution
In indirect speech, the present continuous tense changes to past continuous tense.
Correct Answer:
A
— He said that he was reading a book.
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Q. What is the indirect speech of: 'He said, I have finished my work.'? (2021)
A.
He said that he has finished his work.
B.
He said that he had finished his work.
C.
He said that he finished his work.
D.
He said that he was finishing his work.
Show solution
Solution
In indirect speech, the present perfect tense changes to past perfect tense.
Correct Answer:
B
— He said that he had finished his work.
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Q. What is the indirect speech of: 'She said, I am tired.'? (2023)
A.
She said that she is tired.
B.
She said that she was tired.
C.
She said that she tired.
D.
She said that she has been tired.
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Solution
In indirect speech, the present tense changes to past tense.
Correct Answer:
B
— She said that she was tired.
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Q. What is the indirect speech of: 'The teacher said, You must complete your homework.'? (2022)
A.
The teacher said that we must complete our homework.
B.
The teacher said that we had to complete our homework.
C.
The teacher said that we should complete our homework.
D.
The teacher said that we could complete our homework.
Show solution
Solution
In indirect speech, 'must' changes to 'had to'.
Correct Answer:
B
— The teacher said that we had to complete our homework.
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Q. What is the induced EMF in a loop of wire if the magnetic field through the loop changes at a rate of dB/dt?
A.
-A(dB/dt)
B.
A(dB/dt)
C.
-L(dB/dt)
D.
L(dB/dt)
Show solution
Solution
The induced EMF (ε) is given by Faraday's law as ε = -A(dB/dt), where A is the area of the loop.
Correct Answer:
A
— -A(dB/dt)
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Q. What is the induced EMF in a loop of wire if the magnetic flux through it changes at a rate of dΦ/dt?
A.
-dΦ/dt
B.
dΦ/dt
C.
Φ
D.
0
Show solution
Solution
According to Faraday's law of electromagnetic induction, the induced EMF is given by ε = -dΦ/dt.
Correct Answer:
A
— -dΦ/dt
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Q. What is the induced EMF in a loop of wire when the magnetic field changes at a rate of 5 T/s?
A.
0 V
B.
5 V
C.
10 V
D.
15 V
Show solution
Solution
The induced EMF (ε) is given by Faraday's law of electromagnetic induction: ε = -dΦ/dt. If the change in magnetic field is 5 T/s, then ε = 5 V.
Correct Answer:
B
— 5 V
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Q. What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of dB/dt?
A.
-dB/dt
B.
dB/dt
C.
μ₀dB/dt
D.
0
Show solution
Solution
According to Faraday's law of electromagnetic induction, the induced EMF is given by ε = -dΦ/dt, where Φ is the magnetic flux.
Correct Answer:
A
— -dB/dt
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Q. What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of 5 T/s?
A.
0 V
B.
5 V
C.
10 V
D.
15 V
Show solution
Solution
The induced EMF (ε) is given by Faraday's law of electromagnetic induction: ε = -dΦ/dt. If the rate of change of magnetic field is 5 T/s, then ε = 5 V.
Correct Answer:
B
— 5 V
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Q. What is the inradius of a triangle with sides 7 cm, 8 cm, and 9 cm?
A.
3 cm
B.
4 cm
C.
5 cm
D.
6 cm
Show solution
Solution
Using the formula r = A/s, where A is the area and s is the semi-perimeter. Area = 26 cm², s = 12 cm, so r = 26/12 = 4 cm.
Correct Answer:
B
— 4 cm
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Q. What is the integral form of Ampere's Law?
A.
∮B·dl = μ₀I_enclosed
B.
∮E·dl = -dΦ/dt
C.
∮F·dl = m*a
D.
∮V·dl = Q/C
Show solution
Solution
The integral form of Ampere's Law states that the line integral of the magnetic field B around a closed loop is equal to μ₀ times the enclosed current I.
Correct Answer:
A
— ∮B·dl = μ₀I_enclosed
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Q. What is the integral of 1/x dx?
A.
ln
B.
x
C.
+ C
D.
x + C
.
1/x + C
.
x^2/2 + C
Show solution
Solution
The integral of 1/x dx is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of 1/x with respect to x? (2022)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
e^x + C
Show solution
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of 1/x? (2022)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
x^2 + C
Show solution
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of cos(2x) dx? (2021)
A.
(1/2)sin(2x) + C
B.
sin(2x) + C
C.
(1/2)cos(2x) + C
D.
2sin(2x) + C
Show solution
Solution
The integral of cos(2x) is (1/2)sin(2x) + C.
Correct Answer:
A
— (1/2)sin(2x) + C
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Q. What is the integral of cos(3x) dx?
A.
(1/3)sin(3x) + C
B.
3sin(3x) + C
C.
(1/3)cos(3x) + C
D.
sin(3x) + C
Show solution
Solution
The integral of cos(3x) is (1/3)sin(3x) + C, where C is the constant of integration.
Correct Answer:
A
— (1/3)sin(3x) + C
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Q. What is the integral of cos(x)dx?
A.
sin(x) + C
B.
cos(x) + C
C.
-sin(x) + C
D.
-cos(x) + C
Show solution
Solution
The integral of cos(x) is sin(x) + C.
Correct Answer:
A
— sin(x) + C
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Q. What is the integral of e^(2x) dx?
A.
(1/2)e^(2x) + C
B.
2e^(2x) + C
C.
e^(2x) + C
D.
(1/2)e^(x) + C
Show solution
Solution
The integral of e^(2x) is (1/2)e^(2x) + C, where C is the constant of integration.
Correct Answer:
A
— (1/2)e^(2x) + C
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Q. What is the integral of e^(2x)? (2023)
A.
(1/2)e^(2x) + C
B.
2e^(2x) + C
C.
e^(2x) + C
D.
(1/2)e^(x) + C
Show solution
Solution
The integral of e^(2x) is (1/2)e^(2x) + C.
Correct Answer:
A
— (1/2)e^(2x) + C
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