Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Solution
The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
Solution
The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \)?
Solution
The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
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Q. What is the determinant of the matrix \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)?
Solution
The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix: | 1 2 3 | | 4 5 6 | | 7 8 10 |?
Solution
Calculating gives a determinant of -3.
Correct Answer:
A
— -3
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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
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
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
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
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
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
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)
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 difference between the amounts obtained by investing $1000 at 8% per annum for 2 years in simple interest and compound interest?
-
A.
$16
-
B.
$24
-
C.
$32
-
D.
$40
Solution
SI = 1000 * 8/100 * 2 = $160. CI = 1000(1 + 0.08)^2 = $1166.4. Difference = $1166.4 - $160 = $24.
Correct Answer:
B
— $24
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Q. What is the difference between the compound interest and simple interest on a principal of $1000 at 8% per annum after 2 years?
-
A.
$16
-
B.
$32
-
C.
$24
-
D.
$20
Solution
SI = 1000 × 0.08 × 2 = $160. CI = 1000(1 + 0.08)^2 - 1000 = 1000(1.1664) - 1000 = $166.40. Difference = $166.40 - $160 = $6.40.
Correct Answer:
B
— $32
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Q. What is the difference between the compound interest and simple interest on a sum of $1000 at 5% per annum after 2 years? (2023)
-
A.
$10
-
B.
$20
-
C.
$30
-
D.
$40
Solution
SI = 1000 * 5 * 2 / 100 = $100. CI = 1000[(1 + 0.05)^2 - 1] = $102.5. The difference is $2.5.
Correct Answer:
B
— $20
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Q. What is the difference in sales between Product A and Product C in Q2?
-
A.
$500
-
B.
$1000
-
C.
$1500
-
D.
$2000
Solution
Product A sold $2000 and Product C sold $3000 in Q2. The difference is $3000 - $2000 = $1000.
Correct Answer:
B
— $1000
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Q. What is the dimension of electric charge?
-
A.
[M^1 L^2 T^-3 I^1]
-
B.
[M^0 L^0 T^0 I^1]
-
C.
[M^1 L^1 T^-2 I^1]
-
D.
[M^0 L^1 T^-1 I^1]
Solution
The dimension of electric charge is [M^1 L^2 T^-3 I^1].
Correct Answer:
A
— [M^1 L^2 T^-3 I^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
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
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 frequency?
-
A.
M^0L^0T^-1
-
B.
M^1L^0T^-1
-
C.
M^0L^1T^-1
-
D.
M^0L^0T^0
Solution
Frequency is defined as the number of cycles per unit time, thus its dimension is [M^0L^0T^-1].
Correct Answer:
A
— M^0L^0T^-1
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Q. What is the dimension of the gravitational constant G?
-
A.
M^-1L^3T^-2
-
B.
M^1L^3T^-2
-
C.
M^1L^2T^-2
-
D.
M^0L^0T^0
Solution
The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
Correct Answer:
A
— M^-1L^3T^-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
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
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 acceleration?
-
A.
[M^0 L^1 T^-2]
-
B.
[M^0 L^0 T^-2]
-
C.
[M^1 L^1 T^-2]
-
D.
[M^1 L^0 T^-2]
Solution
The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.
Correct Answer:
A
— [M^0 L^1 T^-2]
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Q. What is the dimensional formula for electric charge?
-
A.
[M^1 L^2 T^-3 I^-1]
-
B.
[M^0 L^0 T^1 I^1]
-
C.
[M^0 L^1 T^-2 I^1]
-
D.
[M^1 L^1 T^-2 I^-1]
Solution
The dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1], derived from the definition of current (I = Q/t).
Correct Answer:
A
— [M^1 L^2 T^-3 I^-1]
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Q. What is the dimensional formula for energy?
-
A.
[M^1 L^2 T^-2]
-
B.
[M^1 L^1 T^-2]
-
C.
[M^1 L^2 T^0]
-
D.
[M^0 L^1 T^-2]
Solution
Energy has the dimensional formula [M^1 L^2 T^-2], as it is measured in Joules (1 J = 1 kg·m²/s²).
Correct Answer:
A
— [M^1 L^2 T^-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]
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 dimensional formula for frequency?
-
A.
[M^0 L^0 T^-1]
-
B.
[M^1 L^0 T^-1]
-
C.
[M^0 L^1 T^0]
-
D.
[M^0 L^0 T^1]
Solution
The dimensional formula for frequency is [M^0 L^0 T^-1], as it is defined as the number of cycles per unit time.
Correct Answer:
A
— [M^0 L^0 T^-1]
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Q. What is the dimensional formula for pressure?
-
A.
M¹L⁻¹T⁻²
-
B.
M¹L²T⁻²
-
C.
M⁰L⁰T⁰
-
D.
M¹L⁰T⁻²
Solution
Pressure is defined as force per unit area. The dimensional formula for force is M¹L¹T⁻², and for area is L², thus pressure = M¹L¹T⁻² / L² = M¹L⁻¹T⁻².
Correct Answer:
A
— M¹L⁻¹T⁻²
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Q. What is the dimensional formula for velocity?
-
A.
MLT⁻¹
-
B.
ML²T⁻²
-
C.
M⁰L⁰T⁻¹
-
D.
M⁰L¹T⁻²
Solution
Velocity is defined as displacement per unit time, which gives the dimensional formula of [MLT⁻¹].
Correct Answer:
A
— MLT⁻¹
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