Question
Construct a quadrilateral $\text{ABCD}\ ;$ if : $AB = 6 \ cm, CD = 4.5 \ cm, BC = AD = 5 \ cm$ and $\angle BCD = 60^\circ$ .
✓
Answer
The rough figure is as follow :
The Actual figure is constructed as follows.
Steps :
The Actual figure is constructed as follows.
Steps :
- Draw $BC = 5 \ cm$.
- Draw $\angle PCB = 60^\circ$ and cut $CD = 4.5 \ cm$.
- From $B$ and $D$, draw arcs of radii $6 \ cm$ and $5 \ cm$ respectively which intersect at $A$.
- Join $AB$ and $AD$.
Thus $\text{ABCD}$ is the required quadrilateral.
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→Consider the following sets :
$\begin{array}{l}
A=\{x: x \in N, x \text { is a factor of } 3\} \\
B=\{x: x \in N, x \text { is a factor of } 5\} \\
C=\{x: x \in N, x \text { is a factor of } 9\}
\end{array}$
1. $A \cap B=$ ?
(a) $\{x: x \in N, x$ is a factor of 3 or 5$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of both 3 and 5\}
(c) $\{x: x \in N, x$ is a factor of 15$\}$ $\quad$ (d) Both (b) and (c)
2. $A \cup B=$ ?
(a) $\{x: x \in N, x$ is a factor of either 3 or 5$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 3 or 5 or both $\}$
(c) $\{x: x \in N, x$ is a factor of 15$\}$ $\quad$ (d) $\{x: x \in N, x$ is a factor of both 3 and 5$\}$
3. $A \cup C=$ ?
(a) $\{x: x \in N, x$ is a factor of 3$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 9$\}$
(c) $\{x: x \in N, x$ is a factor of 27$\}$ $\quad$ (d) None of these
4. $A \cap C=$ ?
(a) $\{x: x \in N, x$ is a factor of 3$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 9$\}$
(c) $\{x: x \in N, x$ is a factor of 27\} $\quad$ (d) None of these
5. How many of the following statements are true:
I. $A \subset B$ II. $A \subseteq C$ III. $B \subseteq A$ IV. $C \subseteq A$
(a) Nil $\quad$ (b) One
(c) Two $\quad$ (d) All
→$\begin{array}{l}
A=\{x: x \in N, x \text { is a factor of } 3\} \\
B=\{x: x \in N, x \text { is a factor of } 5\} \\
C=\{x: x \in N, x \text { is a factor of } 9\}
\end{array}$
1. $A \cap B=$ ?
(a) $\{x: x \in N, x$ is a factor of 3 or 5$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of both 3 and 5\}
(c) $\{x: x \in N, x$ is a factor of 15$\}$ $\quad$ (d) Both (b) and (c)
2. $A \cup B=$ ?
(a) $\{x: x \in N, x$ is a factor of either 3 or 5$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 3 or 5 or both $\}$
(c) $\{x: x \in N, x$ is a factor of 15$\}$ $\quad$ (d) $\{x: x \in N, x$ is a factor of both 3 and 5$\}$
3. $A \cup C=$ ?
(a) $\{x: x \in N, x$ is a factor of 3$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 9$\}$
(c) $\{x: x \in N, x$ is a factor of 27$\}$ $\quad$ (d) None of these
4. $A \cap C=$ ?
(a) $\{x: x \in N, x$ is a factor of 3$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 9$\}$
(c) $\{x: x \in N, x$ is a factor of 27\} $\quad$ (d) None of these
5. How many of the following statements are true:
I. $A \subset B$ II. $A \subseteq C$ III. $B \subseteq A$ IV. $C \subseteq A$
(a) Nil $\quad$ (b) One
(c) Two $\quad$ (d) All
Divide the sum of $\frac{5}{8}$ and $\frac{-11}{12}$ by the difference of $\frac{3}{7}$ and $\frac{5}{14}$.
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