Q. If h(x) = x^3 - 3x, what is the value of h(1)?
Solution
h(1) = 1^3 - 3*1 = 1 - 3 = -2.
Correct Answer: B — 0
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Q. If I = (1, 1, 1) and J = (2, 2, 2), what is the scalar product I · J?
Solution
I · J = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.
Correct Answer: D — 6
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Q. If I = (1, 2, 3) and J = (3, 2, 1), what is I · J?
Solution
I · J = 1*3 + 2*2 + 3*1 = 3 + 4 + 3 = 10.
Correct Answer: A — 10
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Q. If I = (1, 2, 3) and J = (4, 5, 6), calculate I · J.
Solution
I · J = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.
Correct Answer: B — 30
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Q. If I = (a, b, c) and J = (2, 2, 2) such that I · J = 12, what is the relationship between a, b, c?
-
A.
a + b + c = 6
-
B.
2a + 2b + 2c = 12
-
C.
a + b + c = 12
-
D.
2a + 2b + 2c = 6
Solution
I · J = 2a + 2b + 2c = 12 gives the equation 2a + 2b + 2c = 12.
Correct Answer: B — 2a + 2b + 2c = 12
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Q. If K = {a, b, c}, what is the number of subsets of K that do not contain the element 'a'?
Solution
If 'a' is excluded, we can form subsets from {b, c}, which has 2^2 = 4 subsets.
Correct Answer: C — 3
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Q. If log(x) + log(2) = 3, what is the value of x?
-
A.
1000
-
B.
2000
-
C.
500
-
D.
300
Solution
log(2x) = 3 => 2x = 10^3 => x = 1000.
Correct Answer: A — 1000
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Q. If log_10(2) = a, what is log_10(20) in terms of a?
-
A.
2a
-
B.
a + 1
-
C.
a + 2
-
D.
2 + a
Solution
log_10(20) = log_10(2 * 10) = log_10(2) + log_10(10) = a + 1.
Correct Answer: B — a + 1
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Q. If log_10(x) = 2, what is the value of x?
-
A.
100
-
B.
200
-
C.
300
-
D.
400
Solution
log_10(x) = 2 implies x = 10^2 = 100.
Correct Answer: A — 100
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Q. If log_2(x + 1) - log_2(x) = 1, what is the value of x?
Solution
log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.
Correct Answer: A — 1
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Q. If log_2(x + 1) = 3, what is the value of x?
Solution
log_2(x + 1) = 3 implies x + 1 = 2^3 = 8 => x = 7.
Correct Answer: A — 6
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Q. If log_2(x) + log_2(4) = 5, find x.
Solution
log_2(x) + 2 = 5 => log_2(x) = 3 => x = 2^3 = 8.
Correct Answer: B — 32
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Q. If log_2(x) + log_2(x - 3) = 3, what is the value of x?
Solution
log_2(x(x - 3)) = 3 => x(x - 3) = 2^3 = 8 => x^2 - 3x - 8 = 0. Solving gives x = 6.
Correct Answer: B — 6
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Q. If log_2(x) + log_2(x-1) = 3, what is the value of x?
Solution
log_2(x(x-1)) = 3 => x(x-1) = 2^3 = 8 => x^2 - x - 8 = 0. Solving gives x = 5.
Correct Answer: B — 5
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Q. If log_2(x) = 5, what is the value of x?
Solution
log_2(x) = 5 implies x = 2^5 = 32.
Correct Answer: C — 64
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Q. If log_3(9) + log_3(27) = x, what is the value of x?
Solution
log_3(9) = 2 and log_3(27) = 3, thus x = 2 + 3 = 5.
Correct Answer: C — 4
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Q. If log_3(9) = x, what is the value of x?
Solution
log_3(9) = log_3(3^2) = 2.
Correct Answer: B — 2
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Q. If log_3(x + 1) = 2, what is the value of x?
Solution
log_3(x + 1) = 2 implies x + 1 = 3^2 = 9 => x = 8.
Correct Answer: B — 8
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Q. If log_3(x) + log_3(4) = 2, find x.
Solution
log_3(4x) = 2 => 4x = 3^2 = 9 => x = 9/4 = 2.25.
Correct Answer: C — 9
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Q. If log_3(x) = 2, what is the value of x?
Solution
log_3(x) = 2 implies x = 3^2 = 9.
Correct Answer: B — 9
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Q. If log_4(64) = x, what is the value of x?
Solution
log_4(64) = log_4(4^3) = 3.
Correct Answer: B — 3
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Q. If log_4(x) = 1/2, what is the value of x?
Solution
log_4(x) = 1/2 implies x = 4^(1/2) = 2.
Correct Answer: A — 2
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Q. If log_4(x) = 2, what is the value of x?
Solution
log_4(x) = 2 implies x = 4^2 = 16.
Correct Answer: C — 16
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Q. If log_4(x) = 3, find x.
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
log_4(x) = 3 implies x = 4^3 = 64.
Correct Answer: B — 64
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Q. If log_4(x) = 3, what is the value of x?
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
log_4(x) = 3 implies x = 4^3 = 64.
Correct Answer: B — 64
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Q. If log_5(25) + log_5(5) = x, what is the value of x?
Solution
log_5(25) = 2 and log_5(5) = 1. Therefore, x = 2 + 1 = 3.
Correct Answer: C — 3
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Q. If log_5(25) = x, then what is the value of log_5(125) in terms of x?
-
A.
x + 1
-
B.
2x
-
C.
3x
-
D.
x - 1
Solution
log_5(125) = log_5(5^3) = 3. Since log_5(25) = 2, we have x = 2, thus log_5(125) = 3.
Correct Answer: C — 3x
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Q. If log_5(25) = x, what is the value of log_5(5^x)?
Q. If log_5(25) = x, what is the value of x?
Solution
log_5(25) = log_5(5^2) = 2.
Correct Answer: B — 2
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Q. If log_5(x) = 1/2, what is the value of x?
-
A.
5
-
B.
25
-
C.
sqrt(5)
-
D.
1/5
Solution
log_5(x) = 1/2 implies x = 5^(1/2) = sqrt(5).
Correct Answer: C — sqrt(5)
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