Q. What is the resistivity of a material if a wire of length 2 m and cross-sectional area 1 mm² has a resistance of 4 ohms?
A.
2 x 10^-6 Ω·m
B.
4 x 10^-6 Ω·m
C.
8 x 10^-6 Ω·m
D.
1 x 10^-6 Ω·m
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Solution
Resistivity (ρ) = R * (A / L) = 4 * (1 x 10^-6 / 2) = 4 x 10^-6 Ω·m.
Correct Answer:
B
— 4 x 10^-6 Ω·m
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Q. What is the resonant frequency of a series RLC circuit? (2020)
A.
f = 1/(2π√(LC))
B.
f = R/(2πL)
C.
f = 2π√(LC)
D.
f = 1/(2πR)
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Solution
The resonant frequency (f) of a series RLC circuit is given by the formula f = 1/(2π√(LC)).
Correct Answer:
A
— f = 1/(2π√(LC))
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Q. What is the resting membrane potential of a typical neuron? (2020)
A.
-70 mV
B.
-50 mV
C.
0 mV
D.
+30 mV
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Solution
The resting membrane potential of a typical neuron is approximately -70 mV.
Correct Answer:
A
— -70 mV
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Q. What is the result of (10 + 15) mod 7?
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Solution
(10 + 15) = 25; 25 mod 7 = 4.
Correct Answer:
B
— 2
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Q. What is the result of (15 + 10) mod 12?
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Solution
(15 + 10) = 25; 25 mod 12 = 1.
Correct Answer:
A
— 5
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Q. What is the result of (15 + 5) × 2? (2020)
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Solution
(15 + 5) = 20, then 20 × 2 = 40.
Correct Answer:
B
— 30
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Q. What is the result of (15 + 5) × 2? (2023) 2023
Show solution
Solution
(15 + 5) = 20, so 20 × 2 = 40.
Correct Answer:
A
— 30
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Q. What is the result of (15 ÷ 3) × 4? (2020)
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Solution
15 ÷ 3 = 5, then 5 × 4 = 20.
Correct Answer:
A
— 20
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Q. What is the result of (2x + 3)(2x - 3)?
A.
4x² - 9
B.
4x² + 9
C.
4x² - 6
D.
6x² - 9
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Solution
(2x + 3)(2x - 3) = 4x² - 9 by the difference of squares.
Correct Answer:
A
— 4x² - 9
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Q. What is the result of (2^3)^2?
A.
2^5
B.
2^6
C.
2^7
D.
2^8
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Solution
Using the power of a power property, (a^m)^n = a^(m*n), we have (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. What is the result of (3 * 4) mod 5?
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Solution
Calculating (3 * 4) = 12, and then 12 mod 5 = 2.
Correct Answer:
C
— 4
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Q. What is the result of (a - b)(a + b)?
A.
a² + b²
B.
a² - b²
C.
2ab
D.
ab
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Solution
(a - b)(a + b) = a² - b², which is the difference of squares.
Correct Answer:
B
— a² - b²
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Q. What is the result of (x + 1)² - (x - 1)²?
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Solution
(x + 1)² - (x - 1)² = [(x² + 2x + 1) - (x² - 2x + 1)] = 4x.
Correct Answer:
B
— 4
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Q. What is the result of (x + y + z)²?
A.
x² + y² + z² + 2(xy + xz + yz)
B.
x² + y² + z²
C.
x² + y² + z² + 3xyz
D.
x² + y² + z² - 2(xy + xz + yz)
Show solution
Solution
(x + y + z)² = x² + y² + z² + 2(xy + xz + yz) is the correct expansion.
Correct Answer:
A
— x² + y² + z² + 2(xy + xz + yz)
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Q. What is the result of (x + y)(x - y)?
A.
x² + y²
B.
x² - y²
C.
2xy
D.
xy
Show solution
Solution
(x + y)(x - y) = x² - y², which is the difference of squares.
Correct Answer:
B
— x² - y²
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Q. What is the result of (x - 4)(x + 4)?
A.
x² - 16
B.
x² + 16
C.
x² - 8
D.
x² + 8
Show solution
Solution
(x - 4)(x + 4) = x² - 16 using the difference of squares.
Correct Answer:
A
— x² - 16
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Q. What is the result of 10 mod 3?
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Solution
10 divided by 3 gives a remainder of 1, so 10 mod 3 = 1.
Correct Answer:
B
— 2
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Q. What is the result of 5.00 - 2.1, considering significant figures?
A.
2.90
B.
2.9
C.
2.8
D.
2.80
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Solution
When subtracting, the result should be rounded to the least number of decimal places. 5.00 has two decimal places and 2.1 has one, so the result should be rounded to one decimal place: 5.00 - 2.1 = 2.90 becomes 2.9.
Correct Answer:
B
— 2.9
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Q. What is the result of 5^2 * 5^(-3)? (2023)
A.
5^1
B.
5^(-1)
C.
5^0
D.
5^(-5)
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Solution
Using the property of exponents, we combine the exponents: 5^(2 + (-3)) = 5^(-1).
Correct Answer:
B
— 5^(-1)
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Q. What is the result of 6.022 x 10^23 rounded to 3 significant figures?
A.
6.02 x 10^23
B.
6.022 x 10^23
C.
6.0 x 10^23
D.
6.1 x 10^23
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Solution
6.022 rounded to 3 significant figures is 6.02.
Correct Answer:
A
— 6.02 x 10^23
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Q. What is the result of 6.022 × 10^23 rounded to three significant figures?
A.
6.02 × 10^23
B.
6.022 × 10^23
C.
6.0 × 10^23
D.
6.1 × 10^23
Show solution
Solution
6.022 rounded to three significant figures is 6.02 × 10^23.
Correct Answer:
A
— 6.02 × 10^23
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Q. What is the result of 60 ÷ 3 + 4 × 5?
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Solution
60 ÷ 3 = 20; 4 × 5 = 20; 20 + 20 = 40.
Correct Answer:
C
— 32
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Q. What is the result of adding 12.11 and 0.3 in terms of significant figures?
A.
12.41
B.
12.4
C.
12.5
D.
12.3
Show solution
Solution
The result should be rounded to one decimal place, giving 12.4.
Correct Answer:
B
— 12.4
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Q. What is the result of adding 12.11 and 0.3, considering significant figures?
A.
12.41
B.
12.4
C.
12.5
D.
12.3
Show solution
Solution
When adding, the result should be rounded to the least number of decimal places. 12.11 has two decimal places and 0.3 has one, so the result should be rounded to one decimal place: 12.41 becomes 12.4.
Correct Answer:
B
— 12.4
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Q. What is the result of adding the binary numbers 1011 and 1101?
A.
11000
B.
10100
C.
10010
D.
11110
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Solution
Adding 1011 and 1101 in binary results in 11110.
Correct Answer:
D
— 11110
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Q. What is the result of adding the polynomials (2x^2 + 3x + 4) and (3x^2 - x + 2)?
A.
5x^2 + 2x + 6
B.
5x^2 + 4x + 6
C.
5x^2 + 3x + 6
D.
5x^2 + 3x + 4
Show solution
Solution
When adding the polynomials, combine like terms: (2x^2 + 3x + 4) + (3x^2 - x + 2) = 5x^2 + 2x + 6.
Correct Answer:
B
— 5x^2 + 4x + 6
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Q. What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?
A.
3x^2 - 2x + 2
B.
3x^2 - 2x - 2
C.
x^2 - 2x + 2
D.
3x^2 + 2x + 2
Show solution
Solution
When adding the polynomials, combine like terms: (2x^2 + x^2) + (3x - 5x) + (-4 + 6) = 3x^2 - 2x + 2.
Correct Answer:
A
— 3x^2 - 2x + 2
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Q. What is the result of adding the polynomials (3x^2 + 2x + 1) and (4x^2 - x + 5)?
A.
7x^2 + x + 6
B.
7x^2 + 3x + 6
C.
x^2 + x + 6
D.
7x^2 + 2x + 5
Show solution
Solution
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - x) + (1 + 5) = 7x^2 + x + 6.
Correct Answer:
B
— 7x^2 + 3x + 6
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Q. What is the result of adding the polynomials (3x^2 + 2x - 1) and (4x^2 - 3x + 5)?
A.
7x^2 - x + 4
B.
7x^2 - x - 6
C.
x^2 - x + 4
D.
x^2 + 5
Show solution
Solution
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - 3x) + (-1 + 5) = 7x^2 - x + 4.
Correct Answer:
A
— 7x^2 - x + 4
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Q. What is the result of adding the polynomials 2x^2 + 3x + 4 and 4x^2 - x + 1?
A.
6x^2 + 2x + 5
B.
6x^2 + 4x + 5
C.
2x^2 + 4x + 5
D.
8x^2 + 2x + 5
Show solution
Solution
Adding the coefficients of like terms gives 6x^2 + 2x + 5.
Correct Answer:
B
— 6x^2 + 4x + 5
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