**SECTION “B” (SHORT-ANSWER QUESTIONS)**

NOTE: Answer 10 questions from this section.

**2. If A = {2, 4, 6} and B = {x, y} find A x B.**

*ANSWER:*

A = {2, 4, 6} B = {x, y}

A x B = {2, 4, 6} x {x, y}

A x B = {(2, x), (2, y), (4, x), (4, y), (6, x), (6, y)} Ans.

**4. Divide 450 rupees among Ahmed, Bashir & Jamil in the ratio of 2, 3 and 4 respectively.**

*ANSWER:*

Rate of the shares 2 : 3 : 4

Sum of the ratios 2 + 3 + 4 = 9

Amount to be distributed = 450

Share of Ahmed = 450 x 2/9 = 100

Share of Bashir = 450 x 3/9 = 150

Share of Jamil = 450 x 4/9 = 200.

**6. Factorize the following:
**

**(i) ax + ay – 4x – 4y (ii) X² – 10x + 21**

*ANSWER:*

(i) ax + ay – 4x – 4y

= a (x + y) -4 (x + y)

= (x + y)(a – 4)

(ii) X**² **– 10x + 21

= X**²** – 7x – 3x + 21

= x (x – 7) -3 (x – 7)

= (x – 7) (x – 3)

**7. The length of the arc of the sector of a circle is 42 meters and diameter of the circle is 60 meters. Find the area of the sector.**

*ANSWER:*

Length of the arc = 42 metre

Diameter of circle = 60 metre

Area of the sector = ?

Formula:

Area of sector = ½ (length x Breadth) = ½ (length of sector x Radius of circle)

Radius = D/2 = 60/2 = 30 metre

:. area = ½ x 42 x 30 = 630 metre Ans.

**11. The number of attendance of a student in 6 months is 36, 46, 48, 20, 47, 45 respectively. Find the median of attendance.**

*ANSWER:*

Attendance is

20,36,45, 46,47,48

There is no number in between

Median will be

45+46

2

= 45.5 Ans.

**12. Convert 11102 into decimal system.**

*ANSWER:*

1110² = (1 X 2³) + (1 X 2²) + (1 X 2¹) + (0 x 2°)

= (1 x 8) + (1 x 4) + (1 x 2) + (0 x 1)

= 8 + 4 + 2 + 0

= 14

= 14¹° Ans.

**16. Find the continued product with the help of formula: (2 – x)(2 + x)(4 + x²)**

ANSWER:

(2 – x){2 + x)(4 + x²)

Let 2 = a

X=b

Now (a – b) (a + b) = a² – b²

= (2 – x) (2 + x) (4 + x2)

= (2)² – (x)² (4 + x²)

= (4 – x²) (4 + x²)

= (4)² _ (x²)²

= 16 – x4.

**SECTION C (DETAILED-ANSWER QUESTIONS)**

NOTE: Answer any 3 questions from this Section. Question No. 19 is compulsory.

**18. A person dies leaving behind him a ‘Tarka’ worth Rs.30,000. Distribute the Tarka among 4 sons and 3 daughters. So that each Daughter gets half of what a son gets. Find the share of each when a debt of Rs.8,000 is also paid from Tarka.**

*ANSWER:*

Amount of Tarka = 30,000

Amount of Debt = 8,000

Number of sons = 4

Number of daughter = 3

Each son gets twice that of a daughter.

**SOLUTION:
**Amount left after paying back debt = 30,000 – 8,000 = 22,000

Suppose each daughter gets Re.1

Suppose each son gets Rs.2

3 daughters get 3 x 1 = 3 Rs.

4 sons get 4 x 2 = 8 Rs.

Total amount = 3 + 8 = 11

Share of 3 daughters = 22,000 x 3111 = 6,000

So each daughter gets = 6.000/3 = Rs.2,000

Share of 4 sons = 22,000 x 8/11= 16,000

Share of each son = 16,000/4 = Rs.4,000

Hence,

Share of each daughter = Rs.2,000

Share of each son = Rs.4,000.