HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Answer the following:

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

Answer the following:

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

Answer the following:

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

Answer the following:

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

Answer the following:

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

Answer the following:

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.

Answer the following:

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}

Answer the following:

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}

Answer the following:

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]`

Evaluate the following limit :

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

Evaluate the following limit :

`lim_(x -> "a") [(sqrt("a" + 2x) - sqrt(3x))/(sqrt(3"a" + x) - 2sqrt(x))]`

Evaluate the following limit :

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

Evaluate the following limit :

`lim_(x -> 2)[(sqrt(1 + sqrt(2 + x)) - sqrt(3))/(x - 2)]`

Evaluate the following limit :

`lim_(y -> 0) [(sqrt("a" + y) - sqrt("a"))/(ysqrt("a" + y))]`

Evaluate the following limit :

`lim_(x -> 0)[(sqrt(x^2 + 9) - sqrt(2x^2 + 9))/(sqrt(3x^2 + 4) - sqrt(2x^2 + 4))]`

Evaluate the following limit :

`lim_(x -> 1) [(x^2 + xsqrt(x) - 2)/(x - 1)]`

Evaluate the Following limit :

`lim_(x -> 0) [(sqrt(1 + x^2) - sqrt(1 + x))/(sqrt(1 + x^3) - sqrt(1 - x))]`