Q. For the reaction: 2SO2(g) + O2(g) ⇌ 2SO3(g), what happens to the equilibrium position if the volume of the container is decreased? (2020)
A.
Shifts to the left
B.
Shifts to the right
C.
No change
D.
Depends on temperature
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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
— Shifts to the right
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Q. For the reaction: 2SO2(g) + O2(g) ⇌ 2SO3(g), what is the effect of increasing temperature on the equilibrium if the reaction is exothermic? (2020)
A.
Equilibrium shifts to the right
B.
Equilibrium shifts to the left
C.
No effect on equilibrium
D.
Equilibrium constant increases
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Solution
For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants.
Correct Answer:
B
— Equilibrium shifts to the left
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Q. For the reaction: 2SO2(g) + O2(g) ⇌ 2SO3(g), what is the effect of removing SO3 on the equilibrium? (2020)
A.
The equilibrium will shift to the right
B.
The equilibrium will shift to the left
C.
The equilibrium will remain unchanged
D.
The reaction will stop
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Solution
Removing SO3 will shift the equilibrium to the right to produce more SO3, according to Le Chatelier's principle.
Correct Answer:
A
— The equilibrium will shift to the right
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Q. For the reaction: 2SO2(g) + O2(g) ⇌ 2SO3(g), what will happen if the volume of the container is increased? (2020)
A.
Equilibrium shifts to the right
B.
Equilibrium shifts to the left
C.
No change in equilibrium
D.
Equilibrium shifts to the center
Show solution
Solution
Increasing the volume decreases the pressure, and according to Le Chatelier's principle, the equilibrium will shift to the side with more moles of gas, which is the left side in this case.
Correct Answer:
B
— Equilibrium shifts to the left
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Q. For the reaction: A(g) + B(g) ⇌ C(g) + D(g), if the volume of the container is decreased, what will be the effect on the equilibrium? (2023)
A.
Shift to the left
B.
Shift to the right
C.
No effect
D.
Increase the concentration of A
Show solution
Solution
Decreasing the volume increases the pressure. According to Le Chatelier's principle, the equilibrium will shift towards the side with fewer moles of gas. If there are more moles of gas on the left side, the equilibrium will shift to the left.
Correct Answer:
A
— Shift to the left
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Q. For which value of k does the equation x² - kx + 9 = 0 have no real roots? (2021)
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Solution
The discriminant must be less than zero: k² - 4*1*9 < 0, thus k² < 36, so k > 6 or k < -6.
Correct Answer:
A
— 6
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Q. For which value of k does the equation x² - kx + 9 = 0 have roots that are both positive? (2023)
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Solution
For both roots to be positive, k must be greater than 0 and k² > 4*9 = 36, thus k > 6.
Correct Answer:
B
— 8
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Q. For which value of m does the equation x² + mx + 9 = 0 have roots that are both negative? (2021)
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Solution
For both roots to be negative, m must be greater than 0 and m² < 36. Thus, m must be in the range (-6, 0). The suitable value is -4.
Correct Answer:
B
— -4
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Q. For which value of m does the equation x² - mx + 9 = 0 have roots 3 and 3? (2023)
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Solution
The sum of the roots is 3 + 3 = 6, hence m = 6.
Correct Answer:
A
— 6
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Q. For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (2022)
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Solution
Using the sum of roots: 2 + (-2) = -p, hence p = 0.
Correct Answer:
C
— -4
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Q. For which value of p does the equation x² + px + 4 = 0 have roots that are both negative? (2022)
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Solution
For both roots to be negative, p must be greater than 0 and p² > 16. Thus, p < -4.
Correct Answer:
C
— -4
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Q. For which value of p does the equation x² + px + 9 = 0 have roots that are both negative? (2021)
Show solution
Solution
For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.
Correct Answer:
B
— -4
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Q. For which value of p does the equation x² - px + 9 = 0 have roots 3 and 3? (2021)
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Solution
The sum of the roots is 3 + 3 = 6, hence p = 6.
Correct Answer:
A
— 6
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Q. How does gravitational potential energy (U) change when the distance from the center of the Earth increases? (2020)
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
Gravitational potential energy increases as the distance from the center of the Earth increases.
Correct Answer:
A
— It increases
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Q. How does the gravitational force between two objects change if the mass of one object is halved?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It becomes zero
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Solution
Gravitational force is directly proportional to the product of the masses. Halving one mass halves the force.
Correct Answer:
B
— It halves
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Q. How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
A.
5040
B.
10000
C.
9000
D.
7200
Show solution
Solution
The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.
Correct Answer:
A
— 5040
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Q. How many different 4-digit PINs can be formed using the digits 0-9 if repetition is allowed? (2020)
A.
10000
B.
1000
C.
100
D.
1000
Show solution
Solution
Each digit can be any of the 10 digits (0-9), so the total number of PINs is 10^4 = 10000.
Correct Answer:
A
— 10000
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Q. How many different 4-digit PINs can be formed using the digits 0-9 without repetition?
A.
5040
B.
9000
C.
10000
D.
1000
Show solution
Solution
The number of 4-digit PINs is P(10, 4) = 5040.
Correct Answer:
A
— 5040
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Q. How many different ways can 2 out of 5 different fruits be chosen?
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Solution
The number of ways to choose 2 from 5 is C(5, 2) = 10.
Correct Answer:
A
— 10
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Q. How many different ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
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Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer:
C
— 120
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Q. How many different ways can 4 different colored balls be arranged in a row? (2020)
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Solution
The number of arrangements of 4 different colored balls is 4! = 24.
Correct Answer:
B
— 24
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Q. How many different ways can 4 prizes be distributed among 10 students? (2020)
A.
5040
B.
10000
C.
2100
D.
120
Show solution
Solution
The number of ways to distribute 4 prizes among 10 students is 10P4 = 10! / (10-4)! = 5040.
Correct Answer:
A
— 5040
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Q. How many different ways can 6 people be seated in a row? (2020)
A.
720
B.
600
C.
360
D.
480
Show solution
Solution
The number of arrangements of 6 people is 6! = 720.
Correct Answer:
A
— 720
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Q. How many different ways can the letters of the word 'BOOK' be arranged? (2014)
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Solution
The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.
Correct Answer:
B
— 24
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Q. How many different ways can the letters of the word 'MATH' be arranged?
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Solution
The number of arrangements of the letters in 'MATH' is 4! = 24.
Correct Answer:
B
— 24
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Q. How many grams are in 0.5 moles of glucose (C6H12O6)? (2023)
A.
90 g
B.
180 g
C.
45 g
D.
60 g
Show solution
Solution
Molar mass of C6H12O6 = 6*12 + 12*1 + 6*16 = 180 g/mol. Mass = 0.5 moles x 180 g/mol = 90 g.
Correct Answer:
A
— 90 g
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Q. How many grams are in 4 moles of potassium chloride (KCl)? (2022)
A.
74 g
B.
148 g
C.
296 g
D.
37 g
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Solution
Molar mass of KCl = 39 + 35.5 = 74.5 g/mol. Mass = 4 moles x 74.5 g/mol = 298 g.
Correct Answer:
C
— 296 g
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Q. How many grams are in 4 moles of sulfuric acid (H2SO4)? (2023)
A.
196 g
B.
98 g
C.
392 g
D.
294 g
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Solution
Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 4 moles x 98 g/mol = 392 g.
Correct Answer:
C
— 392 g
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Q. How many grams of KCl are needed to prepare 0.5 M solution in 500 mL of water? (2023)
A.
14.9 g
B.
7.45 g
C.
29.8 g
D.
3.73 g
Show solution
Solution
Molarity = moles/volume(L). Moles = 0.5 mol/L * 0.5 L = 0.25 mol. Mass = moles * molar mass = 0.25 mol * 74.5 g/mol = 18.625 g.
Correct Answer:
B
— 7.45 g
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Q. How many grams of KCl are needed to prepare 250 mL of a 0.5 M solution? (2023) 2023
A.
7.45 g
B.
12.5 g
C.
9.25 g
D.
5.25 g
Show solution
Solution
Molar mass of KCl = 74.55 g/mol. Grams = Molarity * Volume (L) * Molar mass = 0.5 M * 0.25 L * 74.55 g/mol = 9.31 g.
Correct Answer:
A
— 7.45 g
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