HSC Science (Computer Science) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Select the correct answer from given alternative

If A = {a, b, c} The total no. of distinct relations in A × A is

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If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₁ = {(1, 4), (1, 5), (1, 6)}

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If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₂ = {(1, 5), (2, 4), (3, 6)}

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If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}

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If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)}

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Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}

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Determine the domain and range of the following relation.

R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}

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Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}

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Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}

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R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is reflexive

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R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is symmentric

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R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is transitive

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Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.

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Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.

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Show that the following is an equivalence relation

R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}

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Show that the following is an equivalence relation

R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}

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Show that the following is an equivalence relation

R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}

Evaluate the following limit:

`lim_(x -> 0)[(sqrt(6 + x + x^2) - sqrt(6))/x]`

Evaluate the following limit :

`lim_(x -> 3)[(sqrt(2x + 3) - sqrt(4x - 3))/(x^2 - 9)]`

Evaluate the following limit :

`lim_(y -> 0)[(sqrt(1 - y^2) - sqrt(1 + y^2))/y^2]`