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Questions and Answers
Which characteristics does relation R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} exhibit?
Which characteristics does relation R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} exhibit?
Which pair belongs to the relation R = {(a, b) : a = b - 2, b > 6}?
Which pair belongs to the relation R = {(a, b) : a = b - 2, b > 6}?
What type of function is defined by the relation R = {(x, x) : x ∈ ℝ}?
What type of function is defined by the relation R = {(x, x) : x ∈ ℝ}?
Which operation is NOT typically used for combining functions?
Which operation is NOT typically used for combining functions?
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Which of the following statements about relations is correct?
Which of the following statements about relations is correct?
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What is the principal value of $sin^{-1}(-\frac{1}{2})$?
What is the principal value of $sin^{-1}(-\frac{1}{2})$?
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What is the principal value of $cos^{-1}(\frac{\sqrt{3}}{2})$?
What is the principal value of $cos^{-1}(\frac{\sqrt{3}}{2})$?
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What is the principal value of $cosec^{-1}(2)$?
What is the principal value of $cosec^{-1}(2)$?
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What is the principal value of $tan^{-1}(-\sqrt{3})$?
What is the principal value of $tan^{-1}(-\sqrt{3})$?
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Which of the following statements describes the relation R = {(x, y): 3x - y = 0} in set A = {1, 2, 3,..., 14}?
Which of the following statements describes the relation R = {(x, y): 3x - y = 0} in set A = {1, 2, 3,..., 14}?
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For the relation R = {(x, y): y = x + 5 and x < 4} defined in the set of natural numbers, which is true?
For the relation R = {(x, y): y = x + 5 and x < 4} defined in the set of natural numbers, which is true?
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What classification does the relation R = {(a, b): a ≤ b²} in the set of real numbers fall into?
What classification does the relation R = {(a, b): a ≤ b²} in the set of real numbers fall into?
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The relation R = {(a, b): b = a + 1} defined in the set {1, 2, 3, 4, 5, 6} is classified as:
The relation R = {(a, b): b = a + 1} defined in the set {1, 2, 3, 4, 5, 6} is classified as:
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Which of these relations defined in set of integers is described as not symmetric?
Which of these relations defined in set of integers is described as not symmetric?
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Is the function $f: ext{R}^* \rightarrow \text{R}^*$ defined by $f(x) = \frac{1}{x}$ one-to-one?
Is the function $f: ext{R}^* \rightarrow \text{R}^*$ defined by $f(x) = \frac{1}{x}$ one-to-one?
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What happens to the injectivity of the function $f: ext{N} \rightarrow ext{N}$ defined by $f(x) = x^2$?
What happens to the injectivity of the function $f: ext{N} \rightarrow ext{N}$ defined by $f(x) = x^2$?
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Is the function $f: ext{R} \rightarrow ext{R}$ given by $f(x) = [x]$ onto?
Is the function $f: ext{R} \rightarrow ext{R}$ given by $f(x) = [x]$ onto?
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For the function $f: ext{Z} \rightarrow ext{Z}$ defined by $f(x) = x^2$, what can be said about its surjectivity?
For the function $f: ext{Z} \rightarrow ext{Z}$ defined by $f(x) = x^2$, what can be said about its surjectivity?
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What is true about the function $f: ext{N} \rightarrow ext{N}$ defined by $f(x) = x^3$?
What is true about the function $f: ext{N} \rightarrow ext{N}$ defined by $f(x) = x^3$?
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What is the characterization of the modulus function $f(x) = |x|$ in terms of injectivity and surjectivity?
What is the characterization of the modulus function $f(x) = |x|$ in terms of injectivity and surjectivity?
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Which statement about the signum function $f(x)$ is true?
Which statement about the signum function $f(x)$ is true?
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For the function $f: R
ightarrow R$ defined by $f(x) = 1 + x^2$, which property does it exhibit?
For the function $f: R ightarrow R$ defined by $f(x) = 1 + x^2$, which property does it exhibit?
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What is the range of y if sin⁻¹(x) = y?
What is the range of y if sin⁻¹(x) = y?
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Is the function $f: N
ightarrow N$ defined by $f(n) = rac{n+1}{2}$ if $n$ is odd and $f(n) = rac{n}{2}$ if $n$ is even a bijective function?
Is the function $f: N ightarrow N$ defined by $f(n) = rac{n+1}{2}$ if $n$ is odd and $f(n) = rac{n}{2}$ if $n$ is even a bijective function?
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What is the result of the expression tan⁻¹(√3) - sec⁻¹(-2)?
What is the result of the expression tan⁻¹(√3) - sec⁻¹(-2)?
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For the function $f: A
ightarrow B$ defined by $f(x) = \frac{x-3}{x-1}$ with $A = R - {3}$ and $B = R - {1}$, is it one-one and onto?
For the function $f: A ightarrow B$ defined by $f(x) = \frac{x-3}{x-1}$ with $A = R - {3}$ and $B = R - {1}$, is it one-one and onto?
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What is the value of cos⁻¹(1/√2)?
What is the value of cos⁻¹(1/√2)?
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What is the result of the expression cot⁻¹(√3)?
What is the result of the expression cot⁻¹(√3)?
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How can you express the sum cos⁻¹(1/2) + 2 sin⁻¹(1/2)?
How can you express the sum cos⁻¹(1/2) + 2 sin⁻¹(1/2)?
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What is the simplest form of $\tan^{-1} \frac{\cos x - \sin x}{\cos x + \sin x}$?
What is the simplest form of $\tan^{-1} \frac{\cos x - \sin x}{\cos x + \sin x}$?
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For $\tan^{-1} \frac{x}{\sqrt{a^2 - x^2}}$, what is the simplest interpretation when $0 < x < a$?
For $\tan^{-1} \frac{x}{\sqrt{a^2 - x^2}}$, what is the simplest interpretation when $0 < x < a$?
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What is the correct relation for $\tan^{-1}(\frac{1 - \cos x}{1 + \cos x})$ for $0 < x < \pi$?
What is the correct relation for $\tan^{-1}(\frac{1 - \cos x}{1 + \cos x})$ for $0 < x < \pi$?
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What does $3 \sin x = \sin^{-1} (3x - 4x^3)$ imply about the domain of $x$?
What does $3 \sin x = \sin^{-1} (3x - 4x^3)$ imply about the domain of $x$?
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What is the result of $\tan^{-1}(\frac{2\sin^{-1} x}{1 + x^2})$ for $|x| < 1$?
What is the result of $\tan^{-1}(\frac{2\sin^{-1} x}{1 + x^2})$ for $|x| < 1$?
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What is the total number of elements in matrix A?
What is the total number of elements in matrix A?
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Which of the following pairs of indices corresponds to the element -5 in matrix A?
Which of the following pairs of indices corresponds to the element -5 in matrix A?
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If a matrix has 24 elements, which of the following is NOT a possible order for this matrix?
If a matrix has 24 elements, which of the following is NOT a possible order for this matrix?
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What is the value of a23 in matrix A?
What is the value of a23 in matrix A?
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Which equation can be used to represent the element at position (i, j) in a 2 x 2 matrix where aij = (i + j)² / 2?
Which equation can be used to represent the element at position (i, j) in a 2 x 2 matrix where aij = (i + j)² / 2?
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Which properties does the relation R = {(1, 2), (2, 1)} exhibit?
Which properties does the relation R = {(1, 2), (2, 1)} exhibit?
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In which of the following relations is R = {(x, y): x and y have the same number of pages} not an equivalence relation?
In which of the following relations is R = {(x, y): x and y have the same number of pages} not an equivalence relation?
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Which set exhibits an equivalence relation with the property R = {(a, b): |a - b| is even}?
Which set exhibits an equivalence relation with the property R = {(a, b): |a - b| is even}?
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Which relation is NOT an equivalence relation?
Which relation is NOT an equivalence relation?
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In the relation R = {(P, Q): distance of point P from the origin is same as point Q from the origin}, what shape is formed by all related points?
In the relation R = {(P, Q): distance of point P from the origin is same as point Q from the origin}, what shape is formed by all related points?
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Which of the following triangles are similar among T₁ (3, 4, 5), T₂ (5, 12, 13), and T₃ (6, 8, 10)?
Which of the following triangles are similar among T₁ (3, 4, 5), T₂ (5, 12, 13), and T₃ (6, 8, 10)?
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What type of relation is represented by R = {(L₁, L₂): L₁ is parallel to L₂}?
What type of relation is represented by R = {(L₁, L₂): L₁ is parallel to L₂}?
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Which example is reflexive and symmetric but not transitive?
Which example is reflexive and symmetric but not transitive?
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Which relation is an example of being transitive but neither reflexive nor symmetric?
Which relation is an example of being transitive but neither reflexive nor symmetric?
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What is the value of $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$?
What is the value of $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$?
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Which expression represents $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$ correctly?
Which expression represents $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$ correctly?
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What is the principal value of $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$ when $ rac{3 heta}{4}$ exceeds the principal range?
What is the principal value of $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$ when $ rac{3 heta}{4}$ exceeds the principal range?
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The expression $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$ relates to which trigonometric property?
The expression $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$ relates to which trigonometric property?
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Evaluate the expression $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$. If this angle is negatively expressed, what will be the adequate answer?
Evaluate the expression $ an^{-1}ig( anig( rac{3 heta}{4}ig)ig)$. If this angle is negatively expressed, what will be the adequate answer?
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