Q. What is the range of the data set: 5, 7, 9, 12, 15?
Show solution
Solution
Range = Maximum - Minimum = 15 - 5 = 10.
Correct Answer:
A
— 10
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Q. What is the range of the data set: 8, 3, 5, 12, 7?
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Solution
Range = Maximum - Minimum = 12 - 3 = 9
Correct Answer:
B
— 9
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Q. What is the range of the following data set: 10, 20, 30, 40, 50?
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Solution
Range = Maximum - Minimum = 50 - 10 = 40.
Correct Answer:
A
— 30
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Q. What is the range of the following data set: 5, 10, 15, 20, 25?
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Solution
Range = Maximum - Minimum = 25 - 5 = 20.
Correct Answer:
A
— 15
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Q. What is the range of the function f(x) = -x^2 + 4?
A.
(-∞, 4]
B.
[0, 4]
C.
[4, ∞)
D.
(-∞, 0)
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Solution
The function is a downward-opening parabola with a maximum value of 4, so the range is (-∞, 4].
Correct Answer:
A
— (-∞, 4]
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Q. What is the range of the function f(x) = x^2?
A.
(-∞, ∞)
B.
[0, ∞)
C.
(-∞, 0)
D.
[0, 1]
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Solution
The function f(x) = x^2 has a minimum value of 0, so its range is [0, ∞).
Correct Answer:
B
— [0, ∞)
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Q. What is the range of the function sin^(-1)(x)?
A.
(-π/2, π/2)
B.
(-1, 1)
C.
(0, π)
D.
(0, 1)
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Solution
The range of sin^(-1)(x) is (-π/2, π/2).
Correct Answer:
A
— (-π/2, π/2)
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Q. What is the range of the function y = cos^(-1)(x)?
A.
[0, π]
B.
[0, 2π]
C.
[−π/2, π/2]
D.
[−1, 1]
Show solution
Solution
The range of y = cos^(-1)(x) is [0, π].
Correct Answer:
A
— [0, π]
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Q. What is the range of the function y = sin^(-1)(x)?
A.
[-π/2, π/2]
B.
[0, π]
C.
[-1, 1]
D.
[0, 1]
Show solution
Solution
The range of y = sin^(-1)(x) is [-π/2, π/2].
Correct Answer:
A
— [-π/2, π/2]
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Q. What is the range of the function y = tan^(-1)(x)?
A.
(-π/2, π/2)
B.
(0, π)
C.
(0, 1)
D.
(-1, 1)
Show solution
Solution
The range of the function y = tan^(-1)(x) is (-π/2, π/2).
Correct Answer:
A
— (-π/2, π/2)
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Q. What is the rank of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Solution
The rows of A are linearly dependent, hence the rank is 2.
Correct Answer:
B
— 2
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Q. What is the rank of the matrix B = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2019)
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Solution
The rows of B are linearly dependent, hence the rank of B is 2.
Correct Answer:
B
— 2
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Q. What is the rank of the matrix D = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2019)
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Solution
The rows of D are linearly dependent, hence the rank of D is 2.
Correct Answer:
B
— 2
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Q. What is the rank of the matrix E = [[1, 2, 3], [0, 0, 0], [4, 5, 6]]?
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Solution
The rank of a matrix is the maximum number of linearly independent row vectors. Here, the first and third rows are independent, while the second row is zero. Thus, the rank is 2.
Correct Answer:
B
— 2
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Q. What is the rank of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2023)
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Solution
The rank of E is 2 because the rows are linearly dependent (the third row is a linear combination of the first two).
Correct Answer:
B
— 2
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Q. What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Solution
The rank of the matrix is 2, as the rows are linearly dependent.
Correct Answer:
B
— 2
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Q. What is the rate constant of a first-order reaction if the half-life is 10 minutes? (2021)
A.
0.0693 min⁻¹
B.
0.1 min⁻¹
C.
0.693 min⁻¹
D.
0.5 min⁻¹
Show solution
Solution
For a first-order reaction, k = 0.693 / t₁/₂. Here, t₁/₂ = 10 min, so k = 0.693 / 10 = 0.0693 min⁻¹.
Correct Answer:
A
— 0.0693 min⁻¹
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Q. What is the rate law expression for a reaction that is first order with respect to A and second order with respect to B? (2022)
A.
Rate = k[A][B]^2
B.
Rate = k[A]^2[B]
C.
Rate = k[A]^2[B]^2
D.
Rate = k[A][B]
Show solution
Solution
The rate law for a reaction is determined by the order with respect to each reactant. For a first order with respect to A and second order with respect to B, the rate law is Rate = k[A][B]^2.
Correct Answer:
A
— Rate = k[A][B]^2
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Q. What is the rate law expression for a reaction that is first order with respect to reactant A? (2022)
A.
Rate = k[A]
B.
Rate = k[A]^2
C.
Rate = k[A]^0
D.
Rate = k[A]^[1/2]
Show solution
Solution
For a first order reaction, the rate law is directly proportional to the concentration of the reactant, hence Rate = k[A].
Correct Answer:
A
— Rate = k[A]
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Q. What is the rate law expression for a reaction that is second order with respect to reactant A? (2023)
A.
Rate = k[A]
B.
Rate = k[A]^2
C.
Rate = k[A]^2[B]
D.
Rate = k[A][B]
Show solution
Solution
For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.
Correct Answer:
B
— Rate = k[A]^2
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Q. What is the rate law expression for a reaction with the rate equation rate = k[A]^2[B]?
A.
rate = k[A][B]
B.
rate = k[A]^2
C.
rate = k[A]^2[B]
D.
rate = k[B]
Show solution
Solution
The rate law expression is derived directly from the rate equation, which is given as rate = k[A]^2[B].
Correct Answer:
C
— rate = k[A]^2[B]
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Q. What is the rate law for a reaction that is first order with respect to A and second order with respect to B? (2022) 2022
A.
Rate = k[A][B]^2
B.
Rate = k[A]^2[B]
C.
Rate = k[A]^2[B]^2
D.
Rate = k[A][B]
Show solution
Solution
The rate law is determined by the order of the reaction with respect to each reactant. For first order in A and second order in B, the rate law is Rate = k[A][B]^2.
Correct Answer:
A
— Rate = k[A][B]^2
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Q. What is the rate law for a reaction that is second order with respect to reactant A? (2023)
A.
Rate = k[A]
B.
Rate = k[A]^2
C.
Rate = k[A]^2[B]
D.
Rate = k[A][B]
Show solution
Solution
For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.
Correct Answer:
B
— Rate = k[A]^2
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Q. What is the ratio of sales of Product B to Product D in Q4?
A.
1:1
B.
2:1
C.
3:1
D.
4:1
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Solution
Product B sold $3000 and Product D sold $1500 in Q4, giving a ratio of 2:1.
Correct Answer:
B
— 2:1
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Q. What is the ratio of sales of Product C to Product D?
A.
1:2
B.
2:3
C.
3:4
D.
4:5
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Solution
Product C sold 300 units and Product D sold 450 units, giving a ratio of 300:450, which simplifies to 2:3.
Correct Answer:
B
— 2:3
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Q. What is the ratio of sales of Product D to Product C in the pie chart?
A.
1:1
B.
2:1
C.
3:1
D.
4:1
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Solution
The ratio of sales of Product D to Product C is 2:1 as per the pie chart.
Correct Answer:
B
— 2:1
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Q. What is the reactance of an inductor at a frequency of 50 Hz if the inductance is 0.1 H? (2023)
A.
31.4 Ω
B.
6.28 Ω
C.
157 Ω
D.
12.56 Ω
Show solution
Solution
Reactance (X_L) = 2πfL = 2π(50)(0.1) = 31.4 Ω.
Correct Answer:
A
— 31.4 Ω
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Q. What is the reactance of an inductor in an AC circuit with frequency f? (2023)
A.
2πfL
B.
1/(2πfL)
C.
L/(2πf)
D.
0
Show solution
Solution
The reactance of an inductor in an AC circuit is given by the formula X_L = 2πfL.
Correct Answer:
A
— 2πfL
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Q. What is the real part of the complex number 4 + 5i? (2023)
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Solution
The real part of the complex number 4 + 5i is 4.
Correct Answer:
A
— 4
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Q. What is the real part of the complex number 5 - 7i?
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Solution
The real part of 5 - 7i is 5.
Correct Answer:
A
— 5
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