sets relations and functions jee mains questions | JEE Main Mathematics Sets Relations And Functions

Q 31 :

If R is a relation defined by $a R b$ $i f f$ $a \leq b$ on $N \times N$ , then which of the following is correct?

R is not a symmetric relation
R is a symmetric relation
R is not a reflexive relation
R is a equivalence relation

(1)

Now

$\lim_{x \to 0} \frac{α (1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \dots) + β (1 - x + \frac{x^{2}}{2!} - \frac{x^{3}}{3!} + \dots) + γ (x - \frac{x^{3}}{3!} + \dots)}{x^{3}}$ $[∵ \sin x \leq x \forall x \in R]$

Constant terms should be zero $\Rightarrow α + β = 0$

Coefficient of $x$ should be zero $\Rightarrow α - β + γ = 0$

Coefficient of $x^{2}$ should be zero $\lim_{x \to 0} \frac{x^{3} (\frac{α}{3!} - \frac{β}{3!} - \frac{γ}{3!}) + x^{4} (\frac{α}{3!} - \frac{β}{3!} - \frac{γ}{3!})}{x^{3}} = \frac{2}{3}$

$\Rightarrow \frac{α}{2} + \frac{β}{2} = 0,$ Now $\Rightarrow \frac{α}{6} - \frac{β}{6} - \frac{γ}{6} = \frac{2}{3}$

$\Rightarrow α = 1, β = - 1, γ = - 2$

Q 32 :

The minimum number of elements that must be added to the relation $R = {(a, b), (b, c)}$ on the set ${a, b, c}$ so that it is an equivalence relation is _____

(7)

$R = {(a, b), (b, c), (a, a), (b, b), (c, c), (b, a), (c, b), (a, c), (c, a)}$

Topic Question Set

Q 31 :

If R is a relation defined by $a R b$ $i f f$ $a \leq b$ on $N \times N$ , then which of the following is correct?

Q 32 :

The minimum number of elements that must be added to the relation $R = {(a, b), (b, c)}$ on the set ${a, b, c}$ so that it is an equivalence relation is _____

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Topic Question Set

Q 31 : If R is a relation defined by aRb iff a≤b on N×N, then which of the following is correct?

Q 32 : The minimum number of elements that must be added to the relation R={(a,b),(b,c)} on the set {a,b,c} so that it is an equivalence relation is _____

Want Us to Email you About Special Offers & Updates?

Q 31 :

If R is a relation defined by $a R b$ $i f f$ $a \leq b$ on $N \times N$ , then which of the following is correct?

Q 32 :

The minimum number of elements that must be added to the relation $R = {(a, b), (b, c)}$ on the set ${a, b, c}$ so that it is an equivalence relation is _____