Q. What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)
Solution
Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.
Correct Answer: A — 10
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Q. What is the value of the discriminant for the equation 3x² + 6x + 2 = 0? (2020)
Solution
The discriminant D = b² - 4ac = 6² - 4*3*2 = 36 - 24 = 12.
Correct Answer: B — 4
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Q. What is the value of the discriminant for the equation 3x² - 12x + 12 = 0? (2020)
Solution
The discriminant D = b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.
Correct Answer: A — 0
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Q. What is the value of the discriminant for the equation x² - 2x + 1 = 0? (2022)
Solution
The discriminant is b² - 4ac = (-2)² - 4*1*1 = 0.
Correct Answer: A — 0
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Q. What is the value of the discriminant for the equation x² - 4x + 4 = 0? (2022)
Solution
The discriminant is b² - 4ac = (-4)² - 4*1*4 = 0.
Correct Answer: A — 0
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Q. What is the value of the term containing x^4 in the expansion of (x + 1/2)^8? (2020)
Solution
The term containing x^4 is C(8,4) * (1/2)^4 = 70 * 1/16 = 4.375.
Correct Answer: A — 70
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Q. What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2020)
Solution
The term containing x^5 is C(8,5)(1/2)^3 = 56 * 1/8 = 7.
Correct Answer: B — 56
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Q. What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)
-
A.
112
-
B.
128
-
C.
256
-
D.
64
Solution
The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.
Correct Answer: B — 128
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Q. What is the value of x where f(x) = x^3 - 3x has a local maximum? (2022)
Solution
f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f(1) = -2.
Correct Answer: C — 1
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Q. What is the value of \( \begin{vmatrix} 2 & 1 \\ 3 & 4 \end{vmatrix} \)? (2022)
Solution
The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).
Correct Answer: A — 5
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Q. What is the value of \( |D| \) for the matrix \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \)? (2023)
Solution
The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).
Correct Answer: A — 1
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Q. What is the value of \( |H| \) for \( H = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \)? (2021)
Solution
The determinant of the identity matrix is always 1.
Correct Answer: B — 1
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Q. What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)
-
A.
(2, -1)
-
B.
(2, 1)
-
C.
(1, 2)
-
D.
(3, 0)
Solution
The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.
Correct Answer: A — (2, -1)
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Q. What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)
-
A.
(3, -1)
-
B.
(3, -5)
-
C.
(2, -4)
-
D.
(2, -2)
Solution
The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.
Correct Answer: A — (3, -1)
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Q. What is the voltage across a 10Ω resistor carrying a current of 3A? (2022)
-
A.
30V
-
B.
20V
-
C.
10V
-
D.
15V
Solution
Using Ohm's law, V = IR = 3A * 10Ω = 30V.
Correct Answer: A — 30V
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Q. What is the voltage across a 12Ω resistor carrying a current of 1.5A? (2023)
-
A.
18V
-
B.
12V
-
C.
6V
-
D.
24V
Solution
Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.
Correct Answer: A — 18V
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Q. What is the voltage across a 12Ω resistor carrying a current of 3A? (2023)
-
A.
36V
-
B.
24V
-
C.
12V
-
D.
18V
Solution
Using Ohm's law, V = IR = 3A * 12Ω = 36V.
Correct Answer: A — 36V
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Q. What is the voltage across a 5Ω resistor carrying a current of 3A? (2023)
-
A.
15V
-
B.
10V
-
C.
5V
-
D.
20V
Solution
Using Ohm's law, V = IR = 3A * 5Ω = 15V.
Correct Answer: A — 15V
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Q. What is the voltage across a 5Ω resistor if a current of 3A flows through it? (2020)
-
A.
15V
-
B.
10V
-
C.
5V
-
D.
20V
Solution
Using Ohm's law, V = IR = 3A * 5Ω = 15V.
Correct Answer: A — 15V
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Q. What is the volume of 0.2 M NaOH required to neutralize 0.1 M HCl in 250 mL? (2020)
-
A.
125 mL
-
B.
250 mL
-
C.
500 mL
-
D.
100 mL
Solution
Using the formula M1V1 = M2V2, (0.1 M)(0.25 L) = (0.2 M)(V2). V2 = 0.125 L = 125 mL.
Correct Answer: A — 125 mL
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Q. What is the volume of 1 M HCl solution needed to obtain 0.5 moles of HCl? (2022)
-
A.
0.5 L
-
B.
1 L
-
C.
2 L
-
D.
0.25 L
Solution
Volume = moles / molarity = 0.5 moles / 1 M = 0.5 L.
Correct Answer: A — 0.5 L
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Q. What is the volume of 1 mole of an ideal gas at STP? (2019) 2019
-
A.
22.4 L
-
B.
24 L
-
C.
1 L
-
D.
10 L
Solution
At STP, 1 mole of an ideal gas occupies 22.4 liters.
Correct Answer: A — 22.4 L
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Q. What is the volume of a 2 M NaOH solution needed to obtain 4 moles of NaOH? (2021) 2021
-
A.
2 L
-
B.
1 L
-
C.
0.5 L
-
D.
4 L
Solution
Volume (L) = moles / molarity = 4 moles / 2 M = 2 L.
Correct Answer: A — 2 L
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Q. What is the volume of a cube with side length 3 units? (2023)
Solution
Volume = side³ = 3³ = 27 cubic units.
Correct Answer: B — 27
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Q. What is the volume of a cube with side length 4 units? (2020)
Solution
Volume = side³ = 4³ = 64 cubic units.
Correct Answer: B — 64
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Q. What is the volume of a cylinder with radius 2 and height 5? (2023)
-
A.
20π
-
B.
10π
-
C.
15π
-
D.
25π
Solution
Volume = πr²h = π(2²)(5) = 20π cubic units.
Correct Answer: A — 20π
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Q. What is the volume of a cylinder with radius 3 units and height 5 units? (2021)
-
A.
45π
-
B.
30π
-
C.
15π
-
D.
9π
Solution
Volume = πr²h = π(3²)(5) = 45π cubic units.
Correct Answer: A — 45π
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Q. What is the volume of a sphere with radius 5 units? (2021)
-
A.
500/3π
-
B.
125/3π
-
C.
100/3π
-
D.
200/3π
Solution
Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3π cubic units.
Correct Answer: A — 500/3π
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Q. What is the work done by a force of 15 N acting at an angle of 60° while moving an object 4 m? (2021)
-
A.
30 J
-
B.
60 J
-
C.
45 J
-
D.
90 J
Solution
Work = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 × 4 × 0.5 = 30 J.
Correct Answer: C — 45 J
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Q. What is the work done by an ideal gas during an isobaric expansion if it expands from 2 L to 5 L at a pressure of 3 atm? (2022)
-
A.
9 J
-
B.
12 J
-
C.
15 J
-
D.
18 J
Solution
Work done (W) = P * ΔV = 3 atm * (5 L - 2 L) = 3 atm * 3 L = 9 atm·L = 15 J (1 atm·L = 101.325 J)
Correct Answer: C — 15 J
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