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Relations Test 2

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Relations Test 2
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  • Question 1
    1 / -0
    If X is brother of the son of Y's son. How is X related to Y?
    Solution
    Son of Y's Son- Grandson, Brother of Y's Grandson- Y's Grandson
    Option D is correct.
  • Question 2
    1 / -0
    If A={x:x23x+2=0}A=\left \{x:x^2-3x+2=0\right \} and B={x:x2+4x5=0}B=\left \{x:x^2+4x-5=0\right \} then the value of A-B is
    Solution
    A={x:x23x+2=0}A={1,2}A=\left \{x:x^2-3x+2=0\right \}\Rightarrow A=\left \{1, 2\right \}
    B={x:x2+4x5=0}A={1,5}B=\left \{x:x^2+4x-5=0\right \}\Rightarrow A=\left \{1, -5\right \}
    AB={2}\therefore A-B=\left \{2\right \}
  • Question 3
    1 / -0
    Suppose y is equal to the sum of two quantities of which one varies directly as x and the other inversely as x If y = 6 when x = 4 and y=103\displaystyle y=\frac{10}{3} when x = 3 then what is the relation between x and y?
    Solution
    (A)Ify=X+4x4+44=36=6y=X+\frac{4}{x}\Rightarrow 4+\frac{4}{4}=3 \neq 6=6
    (B)y+2x=4x6+2(4)=446+81y+2x=\frac{4}{x}\Rightarrow 6+2(4)=\frac{4}{4}\Rightarrow 6+8\neq 1
    (C)y=2x+8x6=2(4)+8468+2y=2x+\frac{8}{x}\Rightarrow 6=2(4)+\frac{8}{4}\Rightarrow 6\neq 8+2
    (D)y=2x8x6=2(4)84=82=6y=2x-\frac{8}{x}\Rightarrow 6=2(4)-\frac{8}{4}=8-2=6 If x=4 and y=6
    y=2x8x103=2×383103=103y=2x-\frac{8}{x}\Rightarrow \frac{10}{3}=2\times 3-\frac{8}{3}\Rightarrow \frac{10}{3}=\frac{10}{3} If x=3 and y=y=103y=\frac{10}{3}
    Then option (D)  Y=2x8xY=2x-\frac{8}{x}
  • Question 4
    1 / -0
    x varies directly as y and inversely as the square of z. When y = 4 and z is 14 x = 10. If y = 16 and z = 7 what is x?
    Solution
    Given x varies directly as y and inversely as the square of z. When y = 4 and z is 14 x = 10. If y = 16 and z = 7 
    Then x=kyz2x=k\frac{y}{z^{2}}
    10=k×414×14\Rightarrow 10=k\times \frac{4}{14\times14}
    k=490\Rightarrow k=490
    Thus x=490×167×7=160x=490\times \frac{16}{7\times 7}=160
  • Question 5
    1 / -0
    The number of reflexive relations of a set with four elements is equal to
    Solution
    Total number of reflexive relations in a set with n elements = 2n^n Therefore, total number of reflexive relations set with 4 elements = 24^4
  • Question 6
    1 / -0
    If R={(x,y)/3x+2y=15(x,y)/3x+2y=15 and x,y ϵ\displaystyle \epsilon N}, the range of the relation R is________
    Solution
    Given, 3x+2y=15 3x + 2y = 15

    =>y=153x2 => y = \dfrac {15-3x}{2}
    As both x,y x , y are natural numbers, we should find x x such that 153x 15-3x is divisible by 2 2

    We can see that when x=1 x =1  or 33 , we get y=6 y = 6  or  33

    Hence, the range is 3,6 {3,6}
  • Question 7
    1 / -0
    Let RR be the relation in the set NN given by R={(a,b):a=b2,b>6}R=\left\{(a, b): a=b-2, b>6\right\}. Choose the correct answer.
    Solution
    R={(a,b):a=b2,b>6}R=\left\{(a, b):a=b-2, b>6\right\}
    Now, since b>6,(2,4)Rb>6, (2, 4)\notin R
    Also, as 382,(3,8)R3\neq 8-2, (3, 8)\notin R
    And, as 8728\neq 7-2
    (8,7)R\therefore (8, 7)\notin R
    Now, consider (6,8)(6, 8).
    We have 8>68 > 6 and also, 6=826=8-2.
    (6,8)R\therefore (6, 8)\in R
    Hence the correct answer is C.
  • Question 8
    1 / -0
    If ordered pair (a,b)(a, b) is given as (2,0)(-2, 0), then a=a =
    Solution
    aa will be first entry in ordered pair (a,b).(a, b).
    So, option A is correct.
  • Question 9
    1 / -0
    If xx co-ordinate of a point is 22 and yy co-ordinate is 00, then ordered pair for its coordinate on XYXY plane is
    Solution
    Ordered pair for co-ordinate of a point in XYXY plane is written as (x,y).(x, y).
    So, option D is correct.
  • Question 10
    1 / -0
    What are the ways of representing a relation?
    Solution
    Relation can be represented in set builder form, roster form and Arrow diagram.
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