Relation Definition

Q. The relation $R$ defined on the set $A=\{1,2,3,4,5\}$ as $R=\left\{\right(a,b):|a^2-b^2|<16\}$ has cardinality equal to

Q.

The value of $\lambda$ for which the curve ${\left(7x+5\right)}^2+{\left(7y+3\right)}^2={\lambda }^2{(4x+3y-24)}^2$ represents a parabola is

1. $\pm \frac{6}{5}$

2. $\pm \frac{7}{5}$

3. $\pm \frac{1}{5}$

4. $\pm \frac{2}{5}$

Q. If $R=\left\{\right(x,y)|x,y\in Z,x^2+y^2\le 4\}$ is a relation in $Z$, then domain of $R$ is

1. $\{-2,-1,0,1,2\}$
2. $\{0,1,2\}$
3. $\{0,-1,-2\}$
4. $\{-2,-1,1,2\}$

Q.

If is the A.M. between a and b, then find the value of n.

Q. If $R=\{(x,y):x,y\in Z,x^2+3y^2\le 8\}$ is a relation on the set of integers $Z$, then the domain of ${\text{R}}^{-1}$ is:

1. $\{-1,0,1\}$
2. $\{-2,-1,1,2\}$
3. $\{0,1\}$
4. $\{-2,-1,0,1,2\}$

Q. Let the relation R be defined on N by aRb if 2a + 3b = 30. Then which of the following belong(s) to R?

1. (3, 8)
2. (2, 9)
3. (9, 4)
4. (5, 7)

Q. Let the relation R be defined on N by aRb if 2a + 3b = 30. Then which of the following belong(s) to R?

1. (3, 8)
2. (2, 9)
3. (9, 4)
4. (5, 7)

Q. Let $A=\{2,3,4,6\}$ and $R=\left\{\right(x,y):y=x^2-x;x,y\in A\}$ is a relation on $A$, then write $R$ as set of ordered pairs ?

Q. Let the relation R be defined on N by aRb if 2a + 3b = 30. Then which of the following belong(s) to R?

1. (3, 8)
2. (2, 9)
3. (9, 4)
4. (5, 7)

Q. If $X=\{1,2,3,4,5\},Y=\{1,3,5,7,9\},$ then which among the following is not a relation from $X$ to $Y$

1. $R_1=\left\{\right(x,y):y=x+2;x\in X,y\in Y\}$
2. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
3. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$
4. $R_4=\left\{\right(1,3),(2,1\left)\right(2,5),(3,7),(7,9\left)\right\}$

Q.

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12

Q. Let $R$ be a relation on $N$ defined by $R=\{(1+x,1+x^2):x\le 5,x\in N\}.$ Which of the following statements is FALSE?

1. $R=\left\{\right(2,2),(3,5),(4,10),(5,17),(6,26\left)\right\}$
2. Domain of $R$ is $\{2,3,4,5,6\}$
3. Range of $R$ is $\{2,5,10,17,26\}$
4. Range of $R^{-1}$ is $\{1,2,3,4,5\}$

Q. If $R=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$ is a relation on $Z$, then the domain of $R$ is

1. None of these
2. $\{0,-1,-2\}$
3. $\{-2,-1,0,1,2\}$
4. $\{0,1,2\}$

Q.

If a, b, c are in A.P, ; b, c, d are in G.P and are in A.P. prove that a, c, e are in G.P.

Q. If $R=\left\{\right(x,y)|x,y\in Z,x^2+y^2\le 4\}$ is a relation in $Z$, then domain of $R$ is

1. $\{0,1,2\}$
2. $\{0,-1,-2\}$
3. $\{-2,-1,0,1,2\}$
4. $\{-2,-1,1,2\}$

Q. If $X=\{1,2,3,4,5\},Y=\{1,3,5,7,9\},$ then which among the following is not a relation from $X$ to $Y$

1. $R_1=\left\{\right(x,y):y=x+2;x\in X,y\in Y\}$
2. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
3. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$
4. $R_4=\left\{\right(1,3),(2,1\left)\right(2,5),(3,7),(7,9\left)\right\}$

Q.

In triangle ABC which of the following is not true:

A.

B.

C.

D.

Q. The relation $R$ defined on the set $A=\{1,2,3,4,5\}$ as $R=\left\{\right(a,b):|a^2-b^2|<16\}$ has cardinality equal to

Q. Let the relation R be defined on N by aRb if 2a + 3b = 30. Then which of the following belong(s) to R?

1. (3, 8)
2. (2, 9)
3. (9, 4)
4. (5, 7)

Q. Find $S_{21}$ of an A.P. whose middle term is $20$.

Q. If $y=\sqrt{x+\sqrt{x+\sqrt{x+...\mathrm{to}\infty ,}}}$ prove that $\frac{dy}{dx}=\frac{1}{2y-1}$

Q. If $xy=1$, prove that $\frac{dy}{dx}+y^2=0$

Q. If the universal set $\{x\in W,3<x\le 12\},A=\{5,7,9\}$, then $A^{\prime }=$

1. $\{6,8,10,11,12\}$
2. None of the above
3. $\{3,6,8,10,11,12\}$
4. $\{4,6,8,10,11,12\}$