Write true (T) or false (F):

(i) In an improper fraction, the numerator is always greater than the denominator.

(ii) The product of two proper fractions can be an improper fraction.

(iii) Any improper fraction is always greater than any proper fraction.

(iv) Every unit fraction is equal to 1.

(v) The reciprocal of a proper fraction is an improper fraction.

(vi) The product of two proper fractions is always greater than each of the two proper fractions.

(vii) There exists a fraction whose multiplicative inverse is equal to the fraction itself.

(viii) The product of a proper fraction and and an improper fraction is always less than the improper fraction.

When Prabhu Dayal died, he left all his money for his grand-children, 3 of whom were boys and 5 were girls. In his will he insisted that each grand-child must get equal share of the total amount of ₹56,00,000.

(1) What was the share of each child ?

1. ₹8,00,000

2. ₹11,20,000

3. ₹6,40,000

4. ₹7,00,000

(2) What fraction of the money did the girls receive ?

1. $\dfrac{5}{3}$

2. $\dfrac{3}{5}$

3. $\dfrac{5}{8}$

4. $\dfrac{3}{8}$

(3) How much did the boys receive in total ?

1. ₹21,00,000

2. ₹24,00,000

3. ₹35,00,000

4. ₹40,00,000

(4) If one of the girls did not take her share and the money is divided among the remaining grand-children, the fraction of the money received by the boys is :

1. $\dfrac{3}{5}$

2. $\dfrac{2}{5}$

3. $\dfrac{4}{7}$

4. $\dfrac{3}{7}$

Amar is an electrician. He bought $7\dfrac{1}{2}$ bundles of an electric cable where each bundle had $202\dfrac{4}{5}$ m of cable.

(1) Find the total length of the cable purchased by Amar.

1. 1427 m
2. 1521 m
3. 1605 m
4. 1717 m

(2) If the cost of cable is ₹$6\dfrac{2}{3}$ per metre, find the amount paid by Amar.

1. ₹8830
2. ₹9520
3. ₹10140
4. ₹11280

(3) Amar used $2\dfrac{1}{2}$ bundles of cable for electric connections in the top floor of the building. What length of cable was used for the top floor ?

1. 476 m
2. 507 m
3. 625 m
4. 712 m

(4) Amar cut a length of $13\dfrac{4}{5}$m from a bundle and divided the remaining cable of this bundle into pieces of 21 m, length each. How many pieces of 21 m did he get from this bundle ?

1. 9
2. 10
3. 11
4. 12

Assertion: The product of two proper fractions is less than each of the fractions.

Reason: For any two fractions $\dfrac{a}{b}$ and $\dfrac{c}{b}$, we have, $\dfrac{a}{b} \times \dfrac{c}{b} = \dfrac{ac}{b}$.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.