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Relations And Functions

Question

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If dy/dx = y + 3 > 0 and y(0) = 2, then y(ln2) is equal to:

7

5

13

-2

Solution

A.

7

dy over dx space equals space straight y plus space 3 fraction numerator dy over denominator straight y space plus 3 end fraction space equals space dx l n left parenthesis straight y plus 3 right parenthesis space equals space straight x space plus straight c Given space at space straight x space equals space 0 comma space straight y space equals 2 l n space 5 space equals space straight c therefore space l n left parenthesis straight y plus 3 right parenthesis space space equals space space straight x space plus divided by straight n 5 l n open parentheses fraction numerator straight y plus 3 over denominator 5 end fraction close parentheses space equals space straight x straight y space plus space 3 space equals space 5 straight e to the power of straight x straight y space equals space 5 straight e to the power of straight x space minus space 3 therefore space straight y space left parenthesis l n 2 right parenthesis space equals space 5 straight e to the power of ln 2 end exponent minus 3 space equals 7

Some More Questions From Relations and Functions Chapter

If a matrix has 24 elements, what are the possible orders it can have ? Wh'at. if it has 13 elements ?

lf a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Give an example of a relation which is

(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L₁, L₂) : L₁ is perpendicular to L₂}. Show that R is symmetric but neither reflexive nor transitive.

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