Q. What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \)? (2023)
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Solution
The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)
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Solution
The determinant of the identity matrix is always 1.
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)? (2023)
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Solution
The determinant of this matrix is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)
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Solution
The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).
Correct Answer:
A
— 10
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Q. What is the diameter of a circle if its area is 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
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Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle if its area is 78.5 cm²? (2020)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
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Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the diameter of a circle with a radius of 9 cm? (2022)
A.
9 cm
B.
18 cm
C.
27 cm
D.
36 cm
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Solution
Diameter = 2 * radius = 2 * 9 cm = 18 cm.
Correct Answer:
B
— 18 cm
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Q. What is the diameter of a circle with an area of 50.24 cm²? (2019)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
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Solution
Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.
Correct Answer:
B
— 10 cm
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Q. What is the diameter of a circle with an area of 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle with an area of 78.5 cm²? (2018)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
Show solution
Solution
Area = πr²; 78.5 = πr²; r² = 78.5/π; d = 2√(78.5/π) ≈ 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the dielectric constant of a vacuum? (2023)
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Solution
The dielectric constant (κ) of a vacuum is defined as 1, which serves as the reference for other materials.
Correct Answer:
A
— 1
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Q. What is the dimension of energy? (2020)
A.
M^1L^2T^-2
B.
M^1L^1T^-1
C.
M^0L^2T^-2
D.
M^1L^0T^-1
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Solution
The dimension of energy is M^1L^2T^-2.
Correct Answer:
A
— M^1L^2T^-2
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Q. What is the dimension of force? (2019)
A.
M^1L^1T^-2
B.
M^1L^2T^-2
C.
M^1L^0T^-2
D.
M^0L^1T^-1
Show solution
Solution
The dimension of force is M^1L^1T^-2.
Correct Answer:
A
— M^1L^1T^-2
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Q. What is the dimension of velocity? (2022)
A.
M^1L^1T^-1
B.
M^0L^1T^-1
C.
M^1L^0T^-1
D.
M^1L^1T^0
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Solution
Velocity is defined as displacement per unit time, hence its dimension is M^0L^1T^-1.
Correct Answer:
B
— M^0L^1T^-1
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Q. What is the dimension of work? (2022)
A.
M^1L^2T^-2
B.
M^1L^1T^-2
C.
M^0L^2T^-2
D.
M^1L^0T^-1
Show solution
Solution
The dimension of work is M^1L^2T^-2.
Correct Answer:
A
— M^1L^2T^-2
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Q. What is the dimensional formula for force? (2022)
A.
[M^1 L^1 T^-2]
B.
[M^1 L^0 T^-2]
C.
[M^0 L^1 T^-1]
D.
[M^1 L^2 T^0]
Show solution
Solution
Force has the dimensional formula [M^1 L^1 T^-2].
Correct Answer:
A
— [M^1 L^1 T^-2]
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Q. What is the direction of conventional current? (2021)
A.
From negative to positive
B.
From positive to negative
C.
Random direction
D.
Depends on the circuit
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Solution
Conventional current is defined as the flow of positive charge, which is from positive to negative.
Correct Answer:
B
— From positive to negative
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Q. What is the direction of the magnetic field around a straight conductor carrying current? (2023)
A.
From north to south
B.
Clockwise
C.
Counterclockwise
D.
Radially outward
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Solution
The direction of the magnetic field around a straight conductor carrying current is counterclockwise when viewed from the positive end of the conductor.
Correct Answer:
C
— Counterclockwise
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Q. What is the direction of the magnetic field due to a current flowing in a circular loop when viewed from above? (2023)
A.
Out of the plane
B.
Into the plane
C.
Clockwise
D.
Counterclockwise
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Solution
Using the right-hand rule, if the current flows in a counterclockwise direction when viewed from above, the magnetic field direction is out of the plane.
Correct Answer:
A
— Out of the plane
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Q. What is the direction of the magnetic field inside a bar magnet? (2023)
A.
From south to north
B.
From north to south
C.
Circular
D.
Random
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Solution
The direction of the magnetic field inside a bar magnet is from the north pole to the south pole.
Correct Answer:
B
— From north to south
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Q. What is the direction of the magnetic field inside a current-carrying circular loop? (2019)
A.
Out of the plane
B.
Into the plane
C.
Clockwise
D.
Counterclockwise
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Solution
Using the right-hand rule, if the current flows in a counterclockwise direction, the magnetic field inside the loop points out of the plane.
Correct Answer:
A
— Out of the plane
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Q. What is the direction of the magnetic field inside a current-carrying solenoid? (2019)
A.
From south to north
B.
From north to south
C.
Perpendicular to the axis
D.
Radially outward
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Solution
The magnetic field inside a current-carrying solenoid is directed from the north pole to the south pole of the solenoid.
Correct Answer:
B
— From north to south
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Q. What is the direction of the magnetic field produced by a current-carrying wire when viewed from one end? (2023)
A.
Always towards the wire
B.
Always away from the wire
C.
Depends on the direction of current
D.
Always perpendicular to the wire
Show solution
Solution
The direction of the magnetic field produced by a current-carrying wire depends on the direction of the current, as determined by the right-hand rule.
Correct Answer:
C
— Depends on the direction of current
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Q. What is the discriminant of the equation 3x² - 12x + 12 = 0? (2023)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation 3x² - 12x + 9 = 0? (2023)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation 4x² - 12x + 9 = 0? (2019)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*4*9 = 144 - 144 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation x² + 6x + 9 = 0? (2020)
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Solution
The discriminant is b² - 4ac = 6² - 4*1*9 = 0.
Correct Answer:
A
— 0
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 12 cm? (2022)
A.
6 cm
B.
12 cm
C.
18 cm
D.
24 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 12 cm.
Correct Answer:
B
— 12 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 10 cm? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 10 cm.
Correct Answer:
B
— 10 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 15 cm? (2014)
A.
15 cm
B.
30 cm
C.
10 cm
D.
5 cm
Show solution
Solution
The distance from the center to any point on the circumference is always the radius, which is 15 cm.
Correct Answer:
A
— 15 cm
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