Question

Choose the correct alternative answer for each of the following questions.
(1) In ☐ PQRS, m∠ P = m∠ R = 108^ᴏ, m∠ Q = m∠ S =72^ᴏ. State which pair of sides of those given below is parallel.
(A) Side PQ and side QR
(B) Side PQ and side SR
(C) Side SR and side SP
(D) Side PS and side PQ
(2) Read the following statements and choose the correct alternative from those given below them.

(i) Diagonals of a rectangle are perpendicular bisectors of each other.
(ii) Diagonals of a rhombus are perpendicular bisectors of each other.
(iii) Diagonals of a parallelogram are perpendicular bisectors of each other.
(iv) Diagonals of a kite bisect each other.

(A) Statement (ii) and (iii) are true
(B) Only statement (ii) is true
(C) Statements (ii) and (iv) are true
(D) Statements (i), (iii) and (iv) are true.
(3) If 19³ = 6859, find $\sqrt[3]{0.006859}$.
(A) 1.9
(B) 19
(C) 0.019
(D) 0.19

Answer 1

(1) We have, in ☐ PQRS, m∠ P = m∠ R = 108^ᴏ, m∠ Q = m∠ S =72^ᴏ.

Since, both the pair of opposite angles of the quadrilateral are equal.

So, PQRS is a parallelogram.

$\Rightarrow$ Side PQ and side SR are parallel. (Opposite sides of parallelogram are equal.)

Hence, the correct answer is option (B).

Note: Since, side PQ and side QR; side SR and side SP; and side PS and PQ are pair of adjacent sides. So, side PQ and side QR; side SR and side SP; and side PS and PQ cannot be the pair of parallel sides. Thus, the only pair left side PQ and side SR are parallel.

(2) Since, the diagonals of rectangle and parallegram bisect each other but are not perpendicular and the one of the diagonal of kite bisect the other.

Also, the diagonals of a rhombus are perpendicular bisectors of each other.

Hence, the correct answer is option (B).

(3) We have, 19³ = 6859

$$\begin{gathered} \sqrt[3]{0.006859} \\ =\sqrt[3]{\frac{6859}{1000000}} \\ =\sqrt[3]{{\left(\frac{19}{100}\right)}^3} \\ =\frac{19}{100} \\ =0.19 \end{gathered}$$

Hence, the correct answer is option (D).