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

NOTE: Answer any Ten questions from this section.

**2. If A = (0, 1) , B = {1, 2, 3), find A x B**

*ANSWER:*

Given: A = {0, 1} B = {1, 2, 3}

A xB = {0, 1} x {1, 2, 3}

A x B = ({0,1), (0,2), (0,3), (1,1), (1,2), (1,3)} ans.

**4. Find the cube of the following: (2x + 5y)**

*ANSWER:*

(2x + 5y)

Formula used

(a + b)3 = a3 + b³ + 3ab (a + b)

2x + 5y)³ = (2x)³+ (5y) + 3(2x) (5y) (2x + 5y)

= 8x³ + 125y³ + 30xy. (2x + 5y)

= 8x³ + 125y³ + 60x y + 150x²

or 8x³ + 60x²y + 150xy² + 125y³.

**7. If p (x) = 2x + 3×3 – X2 – 5, find the value of p (-2)**

*ANSWER:*

P (-2) = 2 (-2) + 3 (-2)3- (-2)²- 5

= (2 x -2) + (3 x -2 x -2 x -2) – (-2) x (-2) -5

= -4 – 24-4- 5

= -37 Ans.

**12. Prove that central angle of minor arc of a circle is double (in measure) of me inscribed angle of the corresponding major arc.**

*ANSWER:*

**14. Find the value of A + B + C when:
**

**A = 2x³ – 4x² – 5**

**B = 4x³ – 9x + 8x² – 3**

**C = -6x³ -3x³ + 2 – 5x**

ANSWER:

Adding the expressions of A, Band C

A+B+C = (2x³ – 4x²- 5)+(4x³ – 9x + 8x² – 3)+(-6x² – 3x³ + 2 – 5x)

= 2x³ – 4x²- 5 + 4x³ – 9x + 8x² – 3 – 6x² – 3x³ + 2 – 5x

= 2x³ + 4x³ – 3x³ – 4x²+ 8x² – 6×2 – 9x – 5x – 5 – 3 + 2

= 3x³ -2x²-14x-6 Ans.

**17. A man left behind him an inheritance (Tarka) worth Rs.30,000. Distribute the Tarka among his four sons and three daughter. such that each son gets twice as much as a daughter. The deceased left behind him a debt of Rs.8,000.**

*ANSWER:*

**Please see Q.no. 18 of 2012**

**19. Factorize the following:
(i) x² – xy – 3x + 3y
(ii) 4x² + 4xy + y²
(iii) a²x² – 4
(iv) x² + 7x + 12**

*ANSWER:*

(i) x**² **–** **ay – 3x + 3y

= x (x – y) -3 (x – y)

= (x – y) (x – 3)

(ii) 4x**²**+ 4xy + y**²**

Using formula a**²** + 2ab + y = (a + b)**²**

Writing in the farm of formula

= (2x)**²**+ 2 (2x) (y) + (y)**²**

= (2x + y)**²** Ans.

(iii) a²x² – 4

Using the formula a**²**– b**²** = (a + b) (a – b)

A**²**x**² **– 4 = (ax)**²** – (2)**²**

= (ax + 2) (ax – 2) Ans.

(iv) x² + 7x + 12

= x²+ 4x + 3x + 12

= x (x + 4) + 3(x + 4)

= (x + 4) (x + 3).

**20.(a) Find the continued product with the help of formula:
(x + y) (x² + y²)(X – y)**

*ANSWER:*

(x + y) (x – y) (x**²** + Y**²**)

= (x**²** – y**²**) (x**²** + y**²**)

= (x**²**)**² **– (y**²**)**²**

= x4 – y4

**21. Draw a circle of radius 3cm and take a point P at a distance of 10cm from the centre. Draw the tangent from the external point P . Write the steps of construction.**

*ANSWER:*

**Steps of Construction:
**(1) Draw a circle of radius = 3 cm

(2) From its centre 0 take a point at a distance of 10 cm and give name P

(3) Join OP and bisect it with compasses. Let the mid point of OP be Q

**.**

(4) With centre Q and radius = QO draw another circle to cut the first circle at T. Join point P to T. Then PT is the required tangent.