मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

If (x+13,y3-1)=(12,32), find x and y

Advertisements
Advertisements

प्रश्न

If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y

बेरीज
Advertisements

उत्तर

Since `(x + 1/3, y/3 - 1) = (1/2, 3/2)`

the corresponding elements are equal.

∴ `x + 1/3 = 1/2` and `y/3 - 1 = 3/2`

∴ `x = 1/2 - 1/3` and `y/3 = 3/2 + 1 = 5/2`

∴ x = `1/6` and y = `15/2`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Sets and Relations - Exercise 5.2 [पृष्ठ १०३]

APPEARS IN

संबंधित प्रश्‍न

Let A = {1, 2, 3, …, 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.


A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.


Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.

  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.

Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.


Let A = (3, 5) and B = (7, 11). Let R = {(ab) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.


Determine the domain and range of the relations:

(i) R = {(ab) : a ∈ N, a < 5, b = 4}


Let R be a relation on N × N defined by
(ab) R (cd) ⇔ a + d = b + c for all (ab), (cd) ∈ N × N
Show that:

(ii) (ab) R (cd) ⇒ (cd) R (ab) for all (ab), (cd) ∈ N × N

 

 


If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(xy) : xy ∈ A × B and x > y}


Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B


Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R−1 is


If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R is


Express {(x, y) / x2 + y2 = 100, where x, y ∈ W} as a set of ordered pairs


Let A = {6, 8} and B = {1, 3, 5}
Show that R1 = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R2 = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation


Write the relation in the Roster Form. State its domain and range

R7 = {(a, b)/a, b ∈ N, a + b = 6}


Write the relation in the Roster Form. State its domain and range

R8 = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}


Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) is


Select the correct answer from given alternative

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


Answer the following:

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)}


Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}


Answer the following:

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


Answer the following:

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


Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R1 = {(2, 1), (7, 1)}


Multiple Choice Question :

The range of the relation R = {(x, x2) | x is a prime number less than 13} is ________


Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”


Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it symmetric


Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence


Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it reflexive


On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is symmetric


On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is symmetric


Choose the correct alternative:

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is


Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.


If R2 = {(x, y) | x and y are integers and x2 + y2 = 64} is a relation. Then find R2.


If R3 = {(x, x) | x is a real number} is a relation. Then find domain and range of R3.


Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×