Q. What is the value of (4^2) * (4^3)?
-
A.
64
-
B.
128
-
C.
256
-
D.
1024
Solution
4^2 * 4^3 = 4^(2+3) = 4^5 = 1024
Correct Answer: C — 256
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Q. What is the value of (x^2)^3?
-
A.
x^5
-
B.
x^6
-
C.
x^7
-
D.
x^8
Solution
Using the power of a power property, (x^2)^3 = x^(2*3) = x^6.
Correct Answer: B — x^6
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Q. What is the value of 1 astronomical unit (AU) in meters?
-
A.
1.496 × 10^11 m
-
B.
1.496 × 10^9 m
-
C.
1.496 × 10^12 m
-
D.
1.496 × 10^10 m
Solution
1 astronomical unit (AU) is approximately equal to 1.496 × 10^11 meters, which is the average distance from the Earth to the Sun.
Correct Answer: A — 1.496 × 10^11 m
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Q. What is the value of 1 Joule in terms of base SI units?
-
A.
1 kg·m²/s²
-
B.
1 kg·m/s²
-
C.
1 m²/s²
-
D.
1 kg·s²/m
Solution
1 Joule is defined as 1 kg·m²/s², which is the product of mass, distance squared, and time squared.
Correct Answer: A — 1 kg·m²/s²
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Q. What is the value of 1 light year in meters?
-
A.
9.46 × 10^15 m
-
B.
3.00 × 10^8 m
-
C.
1.08 × 10^11 m
-
D.
6.37 × 10^6 m
Solution
1 light year is the distance light travels in one year, which is approximately 9.46 × 10^15 meters.
Correct Answer: A — 9.46 × 10^15 m
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Q. What is the value of 2sin(θ)cos(θ)?
-
A.
sin(2θ)
-
B.
cos(2θ)
-
C.
tan(θ)
-
D.
sec(θ)
Solution
By the double angle identity, 2sin(θ)cos(θ) = sin(2θ).
Correct Answer: A — sin(2θ)
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Q. What is the value of 2^(3x) * 2^(2x)?
-
A.
2^(5x)
-
B.
2^(6x)
-
C.
2^(x)
-
D.
2^(x+5)
Solution
Using the property of exponents, 2^(3x) * 2^(2x) = 2^(3x + 2x) = 2^(5x).
Correct Answer: A — 2^(5x)
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Q. What is the value of 2^5 × 2^3?
-
A.
2^8
-
B.
2^15
-
C.
2^2
-
D.
2^5
Solution
Using the property of exponents, a^m × a^n = a^(m+n), we get 2^(5+3) = 2^8.
Correct Answer: A — 2^8
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Q. What is the value of 2^5?
Q. What is the value of 3^(2x) if x = 1?
Solution
3^(2*1) = 3^2 = 9.
Correct Answer: C — 9
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Q. What is the value of 3^0?
-
A.
0
-
B.
1
-
C.
3
-
D.
undefined
Solution
Any non-zero number raised to the power of 0 is 1.
Correct Answer: B — 1
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Q. What is the value of 4^(x) if x = 3?
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
4^3 = (2^2)^3 = 2^6 = 64.
Correct Answer: C — 256
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Q. What is the value of 4^0?
-
A.
0
-
B.
1
-
C.
4
-
D.
undefined
Solution
Any non-zero number raised to the power of 0 is 1.
Correct Answer: B — 1
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Q. What is the value of 5C2?
Solution
5C2 = 5! / (2!(5-2)!) = 10.
Correct Answer: A — 10
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Q. What is the value of 5^2 * 5^3?
-
A.
5^5
-
B.
5^6
-
C.
5^7
-
D.
5^8
Solution
Using the property of exponents, 5^2 * 5^3 = 5^(2+3) = 5^5.
Correct Answer: A — 5^5
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Q. What is the value of 7^0?
-
A.
0
-
B.
1
-
C.
7
-
D.
undefined
Solution
Any non-zero number raised to the power of 0 is 1.
Correct Answer: B — 1
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Q. What is the value of 9^(1/2)?
Solution
9^(1/2) = √9 = 3.
Correct Answer: C — 3
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Q. What is the value of acceleration due to gravity at the surface of the Earth?
-
A.
9.8 m/s²
-
B.
10 m/s²
-
C.
9.81 m/s²
-
D.
9.6 m/s²
Solution
The standard value of acceleration due to gravity at the surface of the Earth is approximately 9.8 m/s².
Correct Answer: A — 9.8 m/s²
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Q. What is the value of cos(0°)?
-
A.
0
-
B.
1
-
C.
-1
-
D.
undefined
Q. What is the value of cos(180°)?
-
A.
0
-
B.
-1
-
C.
1
-
D.
Undefined
Solution
cos(180°) = -1.
Correct Answer: B — -1
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Q. What is the value of cos(2x) if sin x = 1/2?
Solution
Using the double angle formula cos(2x) = 1 - 2sin^2 x. Since sin x = 1/2, we have cos(2x) = 1 - 2*(1/2)^2 = 1 - 2*(1/4) = 1 - 1/2 = 1/2.
Correct Answer: A — 1/2
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Q. What is the value of cos(2θ) if sin θ = 1/2?
Solution
Using the double angle formula cos(2θ) = 1 - 2sin^2 θ. Here, sin θ = 1/2, so cos(2θ) = 1 - 2(1/2)^2 = 1 - 2(1/4) = 1 - 1/2 = 1/2.
Correct Answer: C — -1/2
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Q. What is the value of cos(60°)?
Solution
cos(60°) = 1/2.
Correct Answer: B — 1/2
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Q. What is the value of cos(90°)?
-
A.
0
-
B.
1
-
C.
-1
-
D.
undefined
Q. What is the value of cos(π/3)?
Solution
cos(π/3) = 1/2.
Correct Answer: B — 1/2
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Q. What is the value of cos^(-1)(-1)?
Solution
cos^(-1)(-1) = π, since cos(π) = -1.
Correct Answer: B — π
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Q. What is the value of cos^(-1)(0)?
Solution
cos^(-1)(0) corresponds to the angle where the cosine value is 0, which is π.
Correct Answer: C — π
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Q. What is the value of cot(cos^(-1)(1/2))?
Solution
cot(cos^(-1)(1/2)) = √3
Correct Answer: A — √3
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Q. What is the value of f(2) if f(x) = x^2 - 2x + 1?
Solution
f(2) = 2^2 - 2(2) + 1 = 4 - 4 + 1 = 1.
Correct Answer: A — 1
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Q. What is the value of gravitational acceleration (g) at the surface of the Earth?
-
A.
9.8 m/s²
-
B.
10 m/s²
-
C.
9.81 m/s²
-
D.
8.9 m/s²
Solution
The standard value of gravitational acceleration at the Earth's surface is approximately 9.81 m/s².
Correct Answer: C — 9.81 m/s²
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