Q. If task D must be completed before task E and task F can only start after task D, which of the following is true?
A.
E can start before D.
B.
F can start before E.
C.
D must be completed before both E and F.
D.
E must be completed before D.
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Solution
D must be completed before both E and F, as per the given conditions.
Correct Answer: C — D must be completed before both E and F.
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Q. If task E cannot start until both tasks A and C are completed, which of the following statements is true?
A.
E can start before A
B.
E can start before C
C.
E can start after A and C
D.
E can start only after A or C
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Solution
E can only start after both A and C are completed, making the statement true.
Correct Answer: C — E can start after A and C
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Q. If task F can only begin after tasks G and H are completed, and task H can only begin after task I, which of the following is true?
A.
F can start before G.
B.
H can start before I.
C.
F can start after I.
D.
G can start after H.
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Solution
F can start after I because H must be completed after I, and G must be completed before F.
Correct Answer: C — F can start after I.
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Q. If task F cannot start until both tasks D and E are completed, which of the following is a correct statement?
A.
F can start before D
B.
F can start before E
C.
F can start after D and E
D.
F can start only after D or E
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Solution
F can only start after both D and E are completed, making the statement correct.
Correct Answer: C — F can start after D and E
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Q. If task F must be completed before task G, and task G must be completed before task H, which of the following is a valid sequence?
A.
H, G, F
B.
F, H, G
C.
F, G, H
D.
G, F, H
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Solution
The sequence F, G, H respects the order that F is before G and G is before H.
Correct Answer: C — F, G, H
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Q. If task J cannot start until task K is finished, and task K cannot start until task L is finished, which of the following is a correct inference?
A.
J can start before L.
B.
K can start before J.
C.
L must be completed before J.
D.
J can start at the same time as K.
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Solution
L must be completed before J can start, as J is dependent on K, which is dependent on L.
Correct Answer: C — L must be completed before J.
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Q. If task M can only start after task N and task O, which of the following is a correct implication?
A.
M can start before N.
B.
M can start before O.
C.
M can start only after both N and O.
D.
M can start at the same time as N.
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Solution
M can only start after both N and O are completed, as per the given condition.
Correct Answer: C — M can start only after both N and O.
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Q. If task M must be completed before task N, and task N must be completed before task O, which of the following is a valid sequence?
A.
O, N, M
B.
M, N, O
C.
N, O, M
D.
O, M, N
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Solution
The sequence M, N, O respects the order that M is before N and N is before O.
Correct Answer: B — M, N, O
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Q. If task M must be completed before task N, and task N must be completed before task O, which of the following is a valid inference?
A.
M can start after N
B.
O can start before M
C.
N can start before M
D.
M must be completed before O
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Solution
Since M must be completed before N, and N before O, M must indeed be completed before O.
Correct Answer: D — M must be completed before O
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Q. If task X is dependent on tasks Y and Z being completed first, which of the following statements is true?
A.
X can start before Y and Z
B.
Y and Z can start after X
C.
X can only start after Y and Z
D.
Y and Z are independent of X
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Solution
Task X can only start after both tasks Y and Z are completed, making this statement true.
Correct Answer: C — X can only start after Y and Z
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Q. If tasks A, B, and C are scheduled such that A must be completed before B, and B must be completed before C, which of the following sequences is valid?
A.
C, B, A
B.
A, C, B
C.
A, B, C
D.
B, A, C
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Solution
The sequence A, B, C respects the order that A is before B and B is before C.
Correct Answer: C — A, B, C
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Q. If tasks A, B, and C must be completed in that order, which of the following sequences is invalid?
A.
A, B, C
B.
B, A, C
C.
A, C, B
D.
C, A, B
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Solution
The sequence B, A, C is invalid as it does not respect the order of A before B.
Correct Answer: B — B, A, C
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Q. If tasks A, B, and C must be completed in that order, which of the following sequences is valid?
A.
C, B, A
B.
A, C, B
C.
B, A, C
D.
A, B, C
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Solution
The sequence A, B, C follows the required order.
Correct Answer: D — A, B, C
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Q. If tasks L, M, and N are to be completed with L before M and N, which of the following sequences is correct?
A.
M, L, N
B.
L, N, M
C.
N, M, L
D.
L, M, N
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Solution
The sequence L, M, N is correct as it respects the order of L before both M and N.
Correct Answer: D — L, M, N
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Q. If tasks P, Q, R, and S are scheduled such that P must be completed before Q, and R must be completed before S, which of the following is a possible order?
A.
P, Q, R, S
B.
R, S, P, Q
C.
Q, P, S, R
D.
S, R, Q, P
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Solution
The order P, Q, R, S respects the constraints that P is before Q and R is before S.
Correct Answer: A — P, Q, R, S
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Q. If Team A wins 3 matches, loses 2, and draws 1 in a league of 6 teams, what is their total points assuming a win gives 3 points, a draw gives 1 point, and a loss gives 0 points?
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Solution
Points = (Wins * 3) + (Draws * 1) = (3 * 3) + (1 * 1) = 9 + 1 = 10.
Correct Answer: A — 10
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Q. If Team A wins 60% of its matches in a league of 10 teams, how many matches does Team A win if it plays 9 matches?
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Solution
If Team A wins 60% of its matches, then in 9 matches, it wins 0.6 * 9 = 5.4, which rounds to 6 matches.
Correct Answer: B — 6
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Q. If the 1st term of an arithmetic progression is 4 and the common difference is 3, what is the sum of the first 10 terms?
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Solution
The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_10 = 10/2 * (2*4 + 9*3) = 5 * (8 + 27) = 5 * 35 = 175.
Correct Answer: B — 80
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Q. If the 2nd term of a GP is 12 and the 4th term is 48, what is the common ratio?
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Solution
Let the first term be a and the common ratio be r. Then, 2nd term = ar = 12 and 4th term = ar^3 = 48. Dividing these gives r^2 = 4, so r = 2.
Correct Answer: A — 2
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Q. If the 2nd term of a GP is 8 and the 4th term is 32, what is the common ratio?
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Solution
Let the first term be a and the common ratio be r. Then, 2nd term = ar = 8 and 4th term = ar^3 = 32. Dividing gives r^2 = 4, so r = 2.
Correct Answer: A — 2
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Q. If the 2nd term of an arithmetic progression is 8 and the 4th term is 14, what is the 1st term?
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Solution
Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 3d = 14, we can find a = 6.
Correct Answer: A — 6
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Q. If the 2nd term of an arithmetic progression is 8 and the 5th term is 14, what is the 3rd term?
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Solution
Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 4d = 14, we can find the 3rd term a + 2d = 10.
Correct Answer: A — 10
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Q. If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?
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Solution
Let the first term be a. Then, the 3rd term is ar^2 = 27. Thus, a * 3^2 = 27, giving a = 3.
Correct Answer: B — 9
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Q. If the 3rd term of an arithmetic progression is 12 and the 7th term is 24, what is the common difference?
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Solution
Let the first term be a and the common difference be d. We have a + 2d = 12 and a + 6d = 24. Subtracting these gives 4d = 12, so d = 3.
Correct Answer: B — 4
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Q. If the 3rd term of an arithmetic progression is 15 and the 7th term is 27, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 6d = 27, solving gives d = 3.
Correct Answer: B — 4
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Q. If the 5th term of an arithmetic progression is 15 and the 10th term is 30, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 4d = 15 and a + 9d = 30, we can find d = 3.
Correct Answer: A — 3
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Q. If the 5th term of an arithmetic progression is 20 and the 10th term is 35, what is the first term?
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Solution
Let the first term be a and the common difference be d. From the equations a + 4d = 20 and a + 9d = 35, we can solve for a to find it is 10.
Correct Answer: B — 10
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Q. If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 5d = 30 and a + 8d = 45, we can find d = 5.
Correct Answer: A — 5
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Q. If the 7th term of an arithmetic progression is 50 and the common difference is 5, what is the first term?
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Solution
Using the formula for the nth term, a + 6d = 50. Substituting d = 5 gives a + 30 = 50, hence a = 20.
Correct Answer: B — 30
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Q. If the activation energy of a reaction is increased, what happens to the rate constant k?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
According to the Arrhenius equation, an increase in activation energy results in a decrease in the rate constant k.
Correct Answer: B — Decreases
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