Q. Which of the following fluids is likely to have the highest viscosity?
A.
Water
B.
Honey
C.
Air
D.
Gasoline
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Solution
Honey has a much higher viscosity compared to water, air, and gasoline.
Correct Answer:
B
— Honey
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Q. Which of the following forms of energy is associated with motion? (2023)
A.
Potential Energy
B.
Kinetic Energy
C.
Thermal Energy
D.
Chemical Energy
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Solution
Kinetic Energy is the form of energy associated with motion.
Correct Answer:
B
— Kinetic Energy
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Q. Which of the following frequencies is considered ultrasonic?
A.
20 Hz
B.
20 kHz
C.
20 MHz
D.
200 Hz
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Solution
Ultrasonic sound refers to frequencies above 20 kHz.
Correct Answer:
B
— 20 kHz
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Q. Which of the following functional groups is present in alcohols? (2019)
A.
-OH
B.
-COOH
C.
-NH2
D.
-CHO
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Solution
Alcohols contain the hydroxyl functional group (-OH).
Correct Answer:
A
— -OH
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Q. Which of the following functions has a graph that approaches but never touches the x-axis?
A.
Linear function
B.
Quadratic function
C.
Exponential function
D.
Constant function
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Solution
An exponential function approaches the x-axis as x approaches negative infinity but never actually touches it.
Correct Answer:
C
— Exponential function
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Q. Which of the following functions has a vertical asymptote?
A.
f(x) = x^2 + 1
B.
f(x) = 1/(x - 2)
C.
f(x) = e^x
D.
f(x) = log(x)
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Solution
The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.
Correct Answer:
B
— f(x) = 1/(x - 2)
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Q. Which of the following functions is an even function?
A.
f(x) = x^3
B.
f(x) = x^2
C.
f(x) = x + 1
D.
f(x) = sin(x)
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Solution
An even function satisfies f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer:
B
— f(x) = x^2
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Q. Which of the following functions is continuous at all points?
A.
f(x) = 1/x
B.
f(x) = x^3
C.
f(x) = sqrt(x)
D.
f(x) = tan(x)
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Solution
f(x) = x^3 is a polynomial function, which is continuous everywhere.
Correct Answer:
B
— f(x) = x^3
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Q. Which of the following functions is continuous at x = 0?
A.
f(x) = 1/x
B.
f(x) = e^x
C.
f(x) = tan(x)
D.
f(x) = 1/(x^2 + 1)
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Solution
The function f(x) = e^x is continuous everywhere, including at x = 0.
Correct Answer:
B
— f(x) = e^x
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Q. Which of the following functions is continuous at x = 2?
A.
f(x) = 1/x
B.
f(x) = x^2 - 4
C.
f(x) = sin(1/x)
D.
f(x) =
.
x
.
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Solution
f(x) = x^2 - 4 is a polynomial function and is continuous everywhere, including at x = 2.
Correct Answer:
B
— f(x) = x^2 - 4
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Q. Which of the following functions is continuous at x = 2? f(x) = { x^2 - 4, x < 2; 3x - 6, x >= 2 }
A.
Continuous
B.
Not continuous
C.
Depends on k
D.
None of the above
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Solution
At x = 2, f(2) = 0 and limit from left is 0, limit from right is also 0. Hence, it is continuous.
Correct Answer:
A
— Continuous
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Q. Which of the following functions is continuous at x = 2? f(x) = { x^2, x < 2; 4, x = 2; 2x, x > 2 }
A.
Continuous
B.
Not continuous
C.
Depends on k
D.
None of the above
Show solution
Solution
To check continuity at x = 2, we find the left limit (4), right limit (4), and f(2) (4). All are equal, so f(x) is continuous.
Correct Answer:
A
— Continuous
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Q. Which of the following functions is continuous everywhere?
A.
f(x) = 1/x
B.
f(x) = x^2
C.
f(x) = sin(x)
D.
f(x) =
.
x
.
Show solution
Solution
f(x) = x^2 is a polynomial function and is continuous everywhere.
Correct Answer:
B
— f(x) = x^2
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Q. Which of the following functions is continuous on the interval [0, 1]?
A.
f(x) = 1/x
B.
f(x) = x^3
C.
f(x) = sqrt(x)
D.
f(x) = 1/(x-1)
Show solution
Solution
f(x) = x^3 is a polynomial function and is continuous on the interval [0, 1].
Correct Answer:
B
— f(x) = x^3
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Q. Which of the following functions is differentiable at x = 1? f(x) = { x^2, x < 1; 2x - 1, x >= 1 }
A.
f(1) = 1
B.
f(1) = 0
C.
f(1) = 2
D.
f(1) = 3
Show solution
Solution
Check continuity and differentiability at x = 1 by equating left and right derivatives.
Correct Answer:
A
— f(1) = 1
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Q. Which of the following functions is differentiable everywhere?
A.
f(x) =
B.
x
C.
D.
f(x) = x^2
.
f(x) = sqrt(x)
.
f(x) = 1/x
Show solution
Solution
f(x) = x^2 is a polynomial and differentiable everywhere.
Correct Answer:
B
— x
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Q. Which of the following functions is even?
A.
f(x) = x^3
B.
f(x) = x^2
C.
f(x) = x + 1
D.
f(x) = sin(x)
Show solution
Solution
A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer:
B
— f(x) = x^2
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Q. Which of the following functions is not a polynomial function?
A.
f(x) = x^2 + 3x + 1
B.
g(x) = 2x^3 - 4
C.
h(x) = sqrt(x)
D.
k(x) = 5
Show solution
Solution
h(x) = sqrt(x) is not a polynomial function.
Correct Answer:
C
— h(x) = sqrt(x)
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Q. Which of the following functions is not a polynomial?
A.
f(x) = x^3 + 2x^2 - 5
B.
g(x) = 1/x
C.
h(x) = 4x - 7
D.
k(x) = 2
Show solution
Solution
g(x) = 1/x is not a polynomial because it has a negative exponent.
Correct Answer:
B
— g(x) = 1/x
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Q. Which of the following functions is not continuous at x = 0?
A.
f(x) = x^3
B.
f(x) = e^x
C.
f(x) = 1/x
D.
f(x) = ln(x)
Show solution
Solution
The function f(x) = 1/x is not defined at x = 0, hence it is not continuous there.
Correct Answer:
C
— f(x) = 1/x
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Q. Which of the following functions is not continuous at x = 1?
A.
f(x) = x^2
B.
f(x) = 1/x
C.
f(x) = sin(x)
D.
f(x) = { x, x < 1; 2, x >= 1 }
Show solution
Solution
The function has a jump discontinuity at x = 1, hence it is not continuous.
Correct Answer:
D
— f(x) = { x, x < 1; 2, x >= 1 }
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Q. Which of the following functions is not continuous?
A.
f(x) = x^2
B.
f(x) = 1/x
C.
f(x) = sin(x)
D.
f(x) = e^x
Show solution
Solution
f(x) = 1/x is not continuous at x = 0.
Correct Answer:
B
— f(x) = 1/x
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Q. Which of the following functions is not differentiable at x = 0? f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0.
A.
f(x)
B.
g(x) =
C.
x
D.
.
h(x) = x^3
.
k(x) = x^2
Show solution
Solution
The function f(x) is not differentiable at x = 0 due to the oscillatory nature of sin(1/x) as x approaches 0.
Correct Answer:
A
— f(x)
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Q. Which of the following functions is periodic?
A.
f(x) = x
B.
f(x) = cos(x)
C.
f(x) = e^x
D.
f(x) = ln(x)
Show solution
Solution
The cosine function is periodic with a period of 2π.
Correct Answer:
B
— f(x) = cos(x)
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Q. Which of the following gases behaves most ideally under standard conditions?
A.
NH3
B.
CO2
C.
He
D.
H2O
Show solution
Solution
Helium (He) behaves most ideally under standard conditions due to its low intermolecular forces.
Correct Answer:
C
— He
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Q. Which of the following gases behaves most like an ideal gas? (2023)
A.
Helium
B.
Carbon dioxide
C.
Water vapor
D.
Ammonia
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Solution
Helium behaves most like an ideal gas due to its low intermolecular forces and small size, making it closer to the ideal gas behavior.
Correct Answer:
A
— Helium
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Q. Which of the following gases has the highest density at STP?
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Solution
CO2 has the highest density at STP among the given gases.
Correct Answer:
D
— CO2
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Q. Which of the following gases has the highest rate of diffusion at the same temperature?
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Solution
According to Graham's law, lighter gases diffuse faster; H2 has the lowest molar mass.
Correct Answer:
D
— H2
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Q. Which of the following gases has the highest RMS speed at the same temperature?
A.
Oxygen (O2)
B.
Nitrogen (N2)
C.
Hydrogen (H2)
D.
Carbon Dioxide (CO2)
Show solution
Solution
RMS speed is inversely proportional to the square root of molar mass. Hydrogen (H2) has the lowest molar mass among the options, thus it has the highest RMS speed.
Correct Answer:
C
— Hydrogen (H2)
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Q. Which of the following gases is most abundant in the Earth's atmosphere?
A.
Oxygen
B.
Nitrogen
C.
Carbon Dioxide
D.
Argon
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Solution
Nitrogen makes up about 78% of the Earth's atmosphere, making it the most abundant gas.
Correct Answer:
B
— Nitrogen
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