Q. The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
A.
Discriminant > 0
B.
Discriminant = 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant must be equal to zero.
Correct Answer: B — Discriminant = 0
Learn More →
Q. The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must be zero.
Correct Answer: A — Discriminant = 0
Learn More →
Q. The condition for the lines represented by the equation x^2 + y^2 - 4x - 6y + 9 = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must equal zero.
Correct Answer: A — Discriminant = 0
Learn More →
Q. The coordinates of the centroid of a triangle with vertices at (0, 0), (6, 0), and (3, 6) are:
A.
(3, 2)
B.
(3, 3)
C.
(2, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((x1+x2+x3)/3, (y1+y2+y3)/3) = (9/3, 6/3) = (3, 2).
Correct Answer: B — (3, 3)
Learn More →
Q. The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 1) are:
A.
(4, 3)
B.
(4, 4)
C.
(3, 3)
D.
(5, 3)
Show solution
Solution
Centroid = ((2+4+6)/3, (3+5+1)/3) = (4, 3).
Correct Answer: A — (4, 3)
Learn More →
Q. The coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6) are:
A.
(3, 2)
B.
(2, 3)
C.
(3, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer: A — (3, 2)
Learn More →
Q. The coordinates of the centroid of the triangle with vertices (2, 3), (4, 5), and (6, 7) are:
A.
(4, 5)
B.
(3, 4)
C.
(5, 6)
D.
(6, 5)
Show solution
Solution
Centroid = ((2+4+6)/3, (3+5+7)/3) = (4, 5).
Correct Answer: B — (3, 4)
Learn More →
Q. The critical points of the function f(x) = x^3 - 6x^2 + 9x + 1 are:
A.
x = 1, 3
B.
x = 0, 2
C.
x = 2, 4
D.
x = 1, 2
Show solution
Solution
Finding f'(x) = 3x^2 - 12x + 9 and solving gives critical points at x = 1 and x = 3.
Correct Answer: A — x = 1, 3
Learn More →
Q. The dimensional formula for work is:
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-1]
C.
[M^0 L^2 T^-1]
D.
[M^1 L^0 T^0]
Show solution
Solution
The dimensional formula for work is [M^1 L^2 T^-2].
Correct Answer: A — [M^1 L^2 T^-2]
Learn More →
Q. The displacement of a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What is the maximum displacement?
Show solution
Solution
The maximum displacement in SHM is equal to the amplitude A.
Correct Answer: A — A
Learn More →
Q. The distance from the point (1, 2) to the line 2x + 3y - 6 = 0 is:
Show solution
Solution
Distance = |2(1) + 3(2) - 6| / √(2² + 3²) = |2 + 6 - 6| / √13 = 2/√13.
Correct Answer: B — 2
Learn More →
Q. The distance from the point (3, 4) to the line 2x + 3y - 6 = 0 is:
Show solution
Solution
Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.
Correct Answer: B — 2
Learn More →
Q. The eccentricity of an ellipse is defined as e = c/a. If a = 10 and c = 6, what is the eccentricity?
A.
0.6
B.
0.8
C.
0.4
D.
0.5
Show solution
Solution
Eccentricity e = c/a = 6/10 = 0.6.
Correct Answer: B — 0.8
Learn More →
Q. The electric potential due to a uniformly charged sphere at a point outside the sphere is equivalent to that of?
A.
A point charge at the center
B.
A point charge at the surface
C.
A point charge at the edge
D.
A hollow sphere
Show solution
Solution
The electric potential outside a uniformly charged sphere is the same as that due to a point charge located at the center of the sphere.
Correct Answer: A — A point charge at the center
Learn More →
Q. The energy of a simple harmonic oscillator is proportional to which of the following?
A.
Displacement
B.
Velocity
C.
Square of amplitude
D.
Frequency
Show solution
Solution
The total energy of a simple harmonic oscillator is proportional to the square of the amplitude.
Correct Answer: C — Square of amplitude
Learn More →
Q. The enthalpy change for a reaction can be calculated using which of the following?
A.
Bond energies
B.
Standard enthalpies of formation
C.
Calorimetry
D.
All of the above
Show solution
Solution
The enthalpy change for a reaction can be calculated using bond energies, standard enthalpies of formation, and calorimetry.
Correct Answer: D — All of the above
Learn More →
Q. The enthalpy change for the reaction A + B → C is +50 kJ/mol. What can be said about the reaction?
A.
It is exothermic
B.
It is endothermic
C.
It is spontaneous
D.
It is at equilibrium
Show solution
Solution
A positive enthalpy change indicates that the reaction absorbs heat, thus it is endothermic.
Correct Answer: B — It is endothermic
Learn More →
Q. The enthalpy of vaporization of a substance is defined as:
A.
The heat required to melt the substance
B.
The heat required to convert a liquid into a gas
C.
The heat released during condensation
D.
The heat required to raise the temperature of a substance
Show solution
Solution
The enthalpy of vaporization is the heat required to convert a liquid into a gas at constant temperature and pressure.
Correct Answer: B — The heat required to convert a liquid into a gas
Learn More →
Q. The enthalpy of vaporization of water is approximately ____ kJ/mol.
A.
40.79
B.
60.79
C.
80.79
D.
100.79
Show solution
Solution
The enthalpy of vaporization of water is approximately 40.79 kJ/mol.
Correct Answer: A — 40.79
Learn More →
Q. The enthalpy of vaporization of water is approximately:
A.
40.79 kJ/mol
B.
2260 kJ/mol
C.
100 kJ/mol
D.
60 kJ/mol
Show solution
Solution
The enthalpy of vaporization of water is approximately 2260 kJ/mol.
Correct Answer: B — 2260 kJ/mol
Learn More →
Q. The entropy change for a phase transition at constant temperature is given by:
A.
ΔS = ΔH/T
B.
ΔS = T/ΔH
C.
ΔS = ΔH*T
D.
ΔS = ΔH + T
Show solution
Solution
For a phase transition at constant temperature, the change in entropy is given by ΔS = ΔH/T, where ΔH is the enthalpy change.
Correct Answer: A — ΔS = ΔH/T
Learn More →
Q. The entropy change for a reaction can be calculated using which of the following?
A.
ΔS = ΣS(products) - ΣS(reactants)
B.
ΔS = ΣS(reactants) - ΣS(products)
C.
ΔS = Q/T
D.
ΔS = W/T
Show solution
Solution
The change in entropy for a reaction is calculated using the formula ΔS = ΣS(products) - ΣS(reactants).
Correct Answer: A — ΔS = ΣS(products) - ΣS(reactants)
Learn More →
Q. The entropy of a perfect crystal at absolute zero is given by:
Show solution
Solution
According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is zero.
Correct Answer: B — 0
Learn More →
Q. The entropy of a perfect crystal at absolute zero is:
A.
Maximum
B.
Minimum
C.
Undefined
D.
Infinite
Show solution
Solution
According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is zero, which is the minimum value.
Correct Answer: B — Minimum
Learn More →
Q. The entropy of a perfect crystal at absolute zero temperature is given by which law?
A.
Third law of thermodynamics
B.
First law of thermodynamics
C.
Second law of thermodynamics
D.
Zeroth law of thermodynamics
Show solution
Solution
The third law of thermodynamics states that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero.
Correct Answer: A — Third law of thermodynamics
Learn More →
Q. The entropy of a perfect crystal at absolute zero temperature is given by:
A.
0
B.
1
C.
Infinity
D.
Depends on the substance
Show solution
Solution
According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is exactly zero.
Correct Answer: A — 0
Learn More →
Q. The entropy of a perfect crystalline substance at absolute zero is given by which law?
A.
Third law of thermodynamics
B.
First law of thermodynamics
C.
Second law of thermodynamics
D.
Zeroth law of thermodynamics
Show solution
Solution
The third law of thermodynamics states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero.
Correct Answer: A — Third law of thermodynamics
Learn More →
Q. The entropy of a perfect crystalline substance at absolute zero is:
A.
Zero
B.
Maximum
C.
Undefined
D.
Infinite
Show solution
Solution
According to the third law of thermodynamics, the entropy of a perfect crystalline substance at absolute zero is zero.
Correct Answer: A — Zero
Learn More →
Q. The equation of a line parallel to y = 2x + 3 and passing through (1, 1) is?
A.
y = 2x - 1
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 1 = 2(x - 1) => y = 2x - 1.
Correct Answer: A — y = 2x - 1
Learn More →
Q. The equation of a line passing through (1, 2) and (3, 6) is:
A.
y = 2x
B.
y = 3x - 1
C.
y = x + 1
D.
y = 4x - 2
Show solution
Solution
Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.
Correct Answer: A — y = 2x
Learn More →
Showing 5551 to 5580 of 10700 (357 Pages)
