Let `R` be a relation defined on the set of natural numbers N as `R={(x , y): x , y in N ,2x+y=41}` Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.
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Find the common difference of an A.P if \( t_{18}-t_{14}=3 L \). If \( 3+k, 18-k, 5 k+1 \) are in A.P, then find \( k \). If \( p \) and \( q \) are positive integers, then we write \( p=a^{2} b^{3} \) and \( q=a^{3} b \) if \( a \), \( b \) are numbers, then verify that L.C.M of \( (p, q) \times \) H.C.F of \( (p, q)=p q \).
t18=t1+17×d t14=t1 +13×d solving the two equtaions, t18-t14= 4d subtisting 4d=32 = d=8
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A relation R is given by the set {(x,y)/y=x+3,xe{0,1,2,3,4,5}} Determine its domain and range.
x = {0, 1, 2, 3, 4, 5} y = x + 3 When x = 0 ⇒ y = 0 + 3 = 3 When x = 1 ⇒ y = 1...
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Let A={1,2 3,...,100} and R be therelation defined as ''is a cube number'' on A. write R as a subset of A×A. also, find the domain and range of.
A = {1,2,3,.....,100} R = {(a,b) ∈ A x A | b = a3} ∴ R = {(1,1),(2,8),(3,27),(4,64)} ∴ Domain of R is D = {1,2,3,4} & Range of R is RR = {1,8,27,64}
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Means of first 10 whole numbers and first 10 natural numbers is in the ratio of
Correct option is (A) 9: 11 Mean of first 10 whole numbers \(=\frac{0+1+2+....+9}{10}\) \(=\frac{9\times10}{20}=\frac92\) Mean of first 10 natural numbers \(=\frac{1+2+3+....+10}{10}\) \(=\frac{10\times11}{20}=\frac{11}2\) \(\therefore\) Their ratio \(=\cfrac{\frac92}{\frac{11}2}\) \(=\frac9{11}\) = 9 : 11
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The range of first 100 natural numbers is ……………
Correct option is B) 99
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If A={a,b,c,d}, then on A . (i) write the identity relation `I_(A)` . (ii) write a reflexive relation which is not the identity relation.
Correct Answer - (i) {(a,a),(b,b),(c,c),(d,d)} `" "` {(a,a),(b,b),(c,c),(d,d),(a,c),(b,d)}
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Let `N` be the set of all natural numbers and let `R` be a relation on `NxxN` , defined by `(a , b)R (c , d) a d=b c` for all `(a , b), (c , d) in Nxx
Correct Answer - (2,4) , (3,6)
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If Q is the set of rational numbers and a function `f:Q to Q ` is defined as `f(x)=5x-4, x in Q`, then show that f is one-one and onto. Also define `f
Correct Answer - `f^(-1):Q to Q , f^(-1)(y)=(y+4)/(5)`
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The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
Let the numbers be ‘a’ and ‘b’. Given, sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. ⇒ a + b = 8 ⇒ a...
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If the function f and g are given by `f={(1,2),(3,5),(4,1)} and g={(2,3),(5,1),(1,3)},` find range of f and g. Also write down `fog` and `gof"`as set
`f = {(1,2),(3,5),(4,1)}` and `g = {(2,3),(5,1),(1,3)}` `:.` Range of `f = {2,5,1}` `:.` Range of `g = {3,1}` Now, `fog(2) = f(g(2)) = f(3) = 5` `fog(5) = f(1) = 2` `fog(1) = f(3)...
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