Q. If 200 g of water at 80°C is mixed with 300 g of water at 20°C, what will be the final temperature of the mixture? (Assume no heat loss to the surroundings)
A.
30°C
B.
40°C
C.
50°C
D.
60°C
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Solution
Using the formula m1c1T1 + m2c2T2 = (m1 + m2)cTfinal, we find Tfinal = 40°C.
Correct Answer: B — 40°C
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Q. If 200 g of water at 80°C is mixed with 300 g of water at 20°C, what will be the final temperature of the mixture? (2019)
A.
30°C
B.
40°C
C.
50°C
D.
60°C
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Solution
Using the formula m1c1T1 + m2c2T2 = (m1 + m2)cT, we find T = (200*80 + 300*20) / (200 + 300) = 40°C.
Correct Answer: B — 40°C
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Q. If 200 J of heat is added to a system and 50 J of work is done by the system, what is the change in internal energy? (2023)
A.
150 J
B.
250 J
C.
200 J
D.
100 J
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Solution
According to the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.
Correct Answer: A — 150 J
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Q. If 200 J of heat is added to a system and 50 J of work is done by the system, what is the change in internal energy of the system?
A.
150 J
B.
250 J
C.
200 J
D.
100 J
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Solution
According to the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.
Correct Answer: A — 150 J
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Q. If 2000 J of heat is added to a system and 500 J of work is done by the system, what is the change in internal energy of the system? (2021)
A.
1500 J
B.
2000 J
C.
2500 J
D.
3000 J
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Solution
Using the first law of thermodynamics: ΔU = Q - W = 2000 J - 500 J = 1500 J.
Correct Answer: A — 1500 J
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Q. If 25% of a group like tea, 35% like coffee, and 10% like both, what percentage like only tea?
A.
15%
B.
25%
C.
10%
D.
20%
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Solution
The percentage who like only tea is 25% - 10% = 15%.
Correct Answer: A — 15%
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Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either apples or oranges?
A.
35%
B.
30%
C.
25%
D.
20%
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Solution
Using inclusion-exclusion, the percentage is 25% + 15% - 5% = 35%.
Correct Answer: A — 35%
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Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either fruit?
A.
35%
B.
30%
C.
25%
D.
20%
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Solution
Using inclusion-exclusion, the percentage that likes either fruit is 25% + 15% - 5% = 35%.
Correct Answer: A — 35%
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Q. If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
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Solution
From the second equation, x = 10 - 2y. Substituting into the first gives 2(10 - 2y) + 3y = 12, solving gives y = 2, x = 6.
Correct Answer: C — 4
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Q. If 2x = 10, what is the value of x? (2015)
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Solution
Dividing both sides by 2 gives x = 10/2 = 5.
Correct Answer: A — 5
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Q. If 2y - 7 = 13, what is the value of y? (2023)
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Solution
2y - 7 = 13 => 2y = 20 => y = 10.
Correct Answer: A — 10
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Q. If 2^(x+1) = 16, what is the value of x?
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Solution
16 = 2^4 => x + 1 = 4 => x = 3
Correct Answer: B — 3
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Q. If 3 moles of a gas occupy 60 liters at STP, what is the molar volume of the gas?
A.
20 L
B.
30 L
C.
40 L
D.
60 L
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Solution
Molar volume = total volume / number of moles = 60 L / 3 moles = 20 L/mole.
Correct Answer: B — 30 L
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Q. If 3 moles of a gas occupy 60 liters, what is the volume occupied by 1 mole of the gas at the same conditions?
A.
20 L
B.
30 L
C.
15 L
D.
10 L
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Solution
Volume per mole = total volume / number of moles = 60 L / 3 moles = 20 L/mole.
Correct Answer: A — 20 L
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Q. If 3 moles of glucose are dissolved in 1 liter of solution, what is the molality of the solution? (2023)
A.
3 m
B.
1 m
C.
2 m
D.
0.5 m
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Solution
Molality (m) = moles of solute / kg of solvent; assuming 1 L of water = 1 kg, m = 3 moles / 1 kg = 3 m
Correct Answer: A — 3 m
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Q. If 30% of the members of the Rajya Sabha are from the ruling party and there are 245 members, how many members are from the ruling party?
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Solution
Members from ruling party = 30% of 245 = 0.3 * 245 = 73.5, rounded to 74.
Correct Answer: A — 70
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Q. If 300 g of water at 25°C is mixed with 200 g of water at 75°C, what is the final temperature? (Specific heat of water = 4.2 J/g°C)
A.
40°C
B.
50°C
C.
60°C
D.
70°C
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Solution
Using m1*T1 + m2*T2 = (m1 + m2)*Tf, we find Tf = (300*25 + 200*75) / (300 + 200) = 50°C.
Correct Answer: B — 50°C
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Q. If 3x = 12, what is the value of x? (2019)
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Q. If 3^(2x) = 81, what is the value of x?
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Solution
Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.
Correct Answer: A — 2
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Q. If 4 moles of aluminum react with 3 moles of oxygen, how many moles of aluminum oxide are formed?
A.
2 moles
B.
3 moles
C.
4 moles
D.
6 moles
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Solution
The balanced equation is 4Al + 3O2 → 2Al2O3, which shows that 4 moles of Al produce 2 moles of Al2O3.
Correct Answer: A — 2 moles
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Q. If 4 moles of solute are dissolved in 2 kg of solvent, what is the molality of the solution?
A.
2 m
B.
4 m
C.
1 m
D.
0.5 m
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Solution
Molality (m) = moles of solute / kg of solvent = 4 moles / 2 kg = 2 m.
Correct Answer: A — 2 m
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Q. If 40 students like Mathematics, 30 like Science, and 10 like both subjects, how many students like only Mathematics?
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Solution
The number of students who like only Mathematics is 40 - 10 = 30.
Correct Answer: B — 20
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Q. If 40 students play cricket, 30 play football, and 10 play both, how many students play only cricket?
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Solution
The number of students who play only cricket is 40 - 10 = 30.
Correct Answer: B — 20
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Q. If 40 students play cricket, 30 play football, and 10 play both, how many students play either cricket or football?
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Solution
Using inclusion-exclusion, the total is 40 + 30 - 10 = 60.
Correct Answer: A — 60
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Q. If 45% of people like tea, 35% like coffee, and 15% like both, what percentage of people like neither tea nor coffee?
A.
25%
B.
15%
C.
30%
D.
20%
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Solution
The percentage of people who like either tea or coffee is 45% + 35% - 15% = 65%. Therefore, those who like neither is 100% - 65% = 35%.
Correct Answer: A — 25%
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Q. If 4x ≡ 8 (mod 12), what is the smallest non-negative integer solution for x?
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Solution
Dividing both sides by 4 gives x ≡ 2 (mod 3), so the smallest non-negative solution is 2.
Correct Answer: C — 2
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Q. If 4z + 8 = 32, what is the value of z? (2023)
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Solution
4z + 8 = 32 => 4z = 24 => z = 6.
Correct Answer: B — 5
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Q. If 4^(x-1) = 64, what is the value of x?
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Solution
Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.
Correct Answer: B — 4
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Q. If 4^x = 64, what is the value of x?
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Solution
Since 64 = 4^3, we have x = 3.
Correct Answer: B — 3
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Q. If 5 cats can catch 5 mice in 5 minutes, how many cats are needed to catch 100 mice in 50 minutes? (2022)
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Solution
5 cats catch 5 mice in 5 minutes, so 1 cat catches 1 mouse in 5 minutes. To catch 100 mice in 50 minutes, we need 20 cats.
Correct Answer: C — 25
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