Q. Find the x-intercept of the line 5x - 2y + 10 = 0.
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Solution
Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2. The x-intercept is -2.
Correct Answer:
B
— 2
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Q. Find the y-intercept of the line 4x + y - 8 = 0.
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Solution
Setting x = 0 in the equation gives y = 8. Therefore, the y-intercept is 8.
Correct Answer:
A
— 8
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Q. Find ∫ (5x^4) dx. (2020)
A.
x^5 + C
B.
x^5 + 5C
C.
x^5 + 1
D.
5x^5 + C
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Solution
The integral is (5/5)x^5 + C = x^5 + C.
Correct Answer:
A
— x^5 + C
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Q. Find ∫ (6x^2 - 4) dx. (2019)
A.
2x^3 - 4x + C
B.
2x^3 - 2x + C
C.
2x^3 - 4 + C
D.
3x^3 - 4x + C
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Solution
The integral is (6/3)x^3 - 4x + C = 2x^3 - 4x + C.
Correct Answer:
A
— 2x^3 - 4x + C
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Q. Find ∫ (6x^5) dx. (2022)
A.
x^6 + C
B.
x^6/6 + C
C.
x^6 + 6C
D.
x^6/5 + C
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Solution
The integral is (6/6)x^6 + C = x^6 + C.
Correct Answer:
A
— x^6 + C
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A.
e^x + C
B.
e^x
C.
x e^x + C
D.
ln(e^x) + C
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Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. For a convex lens, if the object is at infinity, the image will be formed at: (2020)
A.
At the focus
B.
At the center of curvature
C.
At infinity
D.
At the optical center
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Solution
When the object is at infinity, the rays converge at the focus of the convex lens.
Correct Answer:
A
— At the focus
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Q. For a convex lens, if the object is at the focus, what type of image is formed? (2020)
A.
Real and inverted
B.
Virtual and erect
C.
No image
D.
Real and erect
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Solution
When the object is at the focus of a convex lens, the rays of light emerge parallel, resulting in no image being formed.
Correct Answer:
C
— No image
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Q. For a monatomic ideal gas, the ratio of specific heats (γ) is approximately: (2019)
A.
1.5
B.
1.67
C.
1.4
D.
2
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Solution
For a monatomic ideal gas, γ = C_p/C_v = 5/3 = 1.67.
Correct Answer:
B
— 1.67
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Q. For a process at constant volume, which of the following is true? (2023)
A.
Work done is zero
B.
Heat added equals change in internal energy
C.
Both A and B
D.
None of the above
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Solution
At constant volume, no work is done (W=0), and the heat added equals the change in internal energy (Q=ΔU).
Correct Answer:
C
— Both A and B
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Q. For a reaction with a rate constant of 0.02 M⁻¹s⁻¹ and initial concentration of 0.5 M, what is the time taken to reach 0.25 M in a second-order reaction? (2023)
A.
25 s
B.
50 s
C.
10 s
D.
20 s
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Solution
Using t = 1 / (k[A₀]) * (1/[A] - 1/[A₀]), t = 1 / (0.02 * 0.5) * (1/0.25 - 1/0.5) = 25 s.
Correct Answer:
A
— 25 s
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Q. For a reaction with an activation energy of 50 kJ/mol, what is the rate constant at 300 K if R = 8.314 J/(mol·K)? (2022)
A.
0.001 M/s
B.
0.01 M/s
C.
0.1 M/s
D.
1 M/s
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Solution
Using the Arrhenius equation, k = Ae^(-Ea/RT). Calculate k using the given values.
Correct Answer:
C
— 0.1 M/s
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Q. For a reaction with an activation energy of 50 kJ/mol, what will happen to the rate if the temperature is increased by 20°C? (2022)
A.
Rate decreases
B.
Rate remains the same
C.
Rate increases significantly
D.
Rate increases slightly
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Solution
Increasing the temperature generally increases the rate of reaction significantly due to higher kinetic energy.
Correct Answer:
C
— Rate increases significantly
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Q. For a zero-order reaction, how does the concentration of reactants change over time? (2020)
A.
Linearly
B.
Exponentially
C.
Quadratically
D.
Logarithmically
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Solution
In a zero-order reaction, the concentration of reactants decreases linearly with time.
Correct Answer:
A
— Linearly
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Q. For a zero-order reaction, if the initial concentration is 0.5 M and the rate constant is 0.1 M/s, how long will it take to reach 0 M? (2019)
A.
5 s
B.
10 s
C.
15 s
D.
20 s
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Solution
For a zero-order reaction, t = [A₀] / k. Here, t = 0.5 M / 0.1 M/s = 5 s.
Correct Answer:
B
— 10 s
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Q. For a zero-order reaction, if the initial concentration is 0.5 M and the rate constant is 0.1 M/s, how long will it take to reach 0.2 M? (2021)
A.
3 s
B.
5 s
C.
2 s
D.
4 s
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Solution
For a zero-order reaction, t = [A₀ - A] / k. Here, t = (0.5 - 0.2) / 0.1 = 3 s.
Correct Answer:
D
— 4 s
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Q. For an ideal gas, the work done during an isobaric process is given by which formula? (2022)
A.
W = PΔV
B.
W = nRT
C.
W = ΔU + Q
D.
W = 0
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Solution
In an isobaric process, the work done is calculated using the formula W = PΔV, where P is pressure and ΔV is the change in volume.
Correct Answer:
A
— W = PΔV
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Q. For an ideal gas, which law relates pressure, volume, and temperature? (2023) 2023
A.
Boyle's Law
B.
Charles's Law
C.
Ideal Gas Law
D.
Avogadro's Law
Show solution
Solution
The Ideal Gas Law (PV = nRT) relates pressure (P), volume (V), and temperature (T) for an ideal gas.
Correct Answer:
C
— Ideal Gas Law
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Q. For the equation x² + 4x + k = 0 to have real roots, what must be the minimum value of k? (2023)
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Solution
The discriminant must be non-negative: 4² - 4*1*k ≥ 0, thus k ≤ 4.
Correct Answer:
A
— -4
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Q. For the equation x² + 6x + k = 0 to have real roots, what is the minimum value of k? (2021)
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Solution
The discriminant must be non-negative: 6² - 4*1*k ≥ 0, which gives k ≤ 9, so the minimum value is -9.
Correct Answer:
A
— -9
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Q. For the equation x² + 6x + k = 0 to have real roots, what must be the minimum value of k? (2023)
A.
-9
B.
-6
C.
-12
D.
-15
Show solution
Solution
The discriminant must be non-negative: 6² - 4*1*k ≥ 0, thus k ≤ 9.
Correct Answer:
A
— -9
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Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is decreased, what will happen to the equilibrium? (2020)
A.
Shift to the left
B.
Shift to the right
C.
No change
D.
Depends on temperature
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Solution
Decreasing the volume increases the pressure, and the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.
Correct Answer:
B
— Shift to the right
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Q. For the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), what is the effect of decreasing the volume of the container? (2021)
A.
Shift to the left
B.
Shift to the right
C.
No effect
D.
Increase in temperature
Show solution
Solution
Decreasing the volume increases the pressure, and according to Le Chatelier's principle, the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.
Correct Answer:
B
— Shift to the right
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Q. For the equilibrium reaction A ⇌ B, if the concentration of B is increased, what will be the effect on the equilibrium? (2023)
A.
Shift to the right
B.
Shift to the left
C.
No change
D.
Increase in temperature
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Solution
Increasing the concentration of B will shift the equilibrium to the left to produce more A, according to Le Chatelier's principle.
Correct Answer:
B
— Shift to the left
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Q. For the equilibrium reaction: 2NO2(g) ⇌ N2O4(g), what is the effect of increasing the pressure? (2021)
A.
Shift to the left
B.
Shift to the right
C.
No effect
D.
Increase Kp
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Solution
Increasing the pressure will shift the equilibrium to the side with fewer moles of gas, which is the right side (N2O4) in this case.
Correct Answer:
A
— Shift to the left
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Q. For the exothermic reaction A + B ⇌ C + D, what effect does increasing the temperature have on the equilibrium? (2020)
A.
Shifts to the left
B.
Shifts to the right
C.
No change
D.
Increases Kc
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Solution
For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants.
Correct Answer:
A
— Shifts to the left
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Q. For the exothermic reaction A + B ⇌ C + heat, what will happen if the temperature is increased? (2020)
A.
Equilibrium will shift to the right
B.
Equilibrium will shift to the left
C.
No change in equilibrium
D.
Equilibrium will shift to the center
Show solution
Solution
For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants, as the system tries to absorb the added heat.
Correct Answer:
B
— Equilibrium will shift to the left
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Q. For the exothermic reaction: N2(g) + 3H2(g) ⇌ 2NH3(g), what will happen if the temperature is increased? (2023)
A.
The equilibrium will shift to the right
B.
The equilibrium will shift to the left
C.
No change in equilibrium
D.
The reaction will stop
Show solution
Solution
According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium to the left, favoring the reactants.
Correct Answer:
B
— The equilibrium will shift to the left
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Q. For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (2023)
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Solution
The vertex x-coordinate is given by -b/(2a) = -4/(2*-1) = 2.
Correct Answer:
A
— 2
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Q. For the function f(x) = -x^2 + 6x, find the x-coordinate of the vertex. (2022)
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Solution
The vertex x-coordinate is found using x = -b/(2a) = -6/(-2) = 3.
Correct Answer:
A
— 3
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