**SECTION “A” (COMPULSORY) (M.C.Q.S)**

**1. Choose the correct answer for each from the given options:**

(1) 32 out of 64 is:

* 16%

* *50%*

* 20%

* 80%

(ii) 9x²- 12xy + 4y² = ———

* *(3x – 2y)²*

* (3x + 2y)*²*

* (3x + 2y)³

* (x – 2y)*²*

(iii) √16 x√81 =—–

* *36*

* 9

* 4

* 72

(iv) If in a right angled triangle one angle is of 45°, the other angle will be of:

* 30°

* 60°

* 90°

* *45°*

(v) If a matrix has all of its elements zero, it is called:

* singular matrix

* equal matrix

* *Zero matrix*

* square matrix

(vii) Arithmatic mean of -16, -70, 16, 70 is:

* 9

* *0*

* -16

* -32

(viii) Union of Two non-collinear rays is called:

* *Angle*

* Opposite rays

* Straight line

* Rectangle

(ix) If the sum of two angles is 180°, it is called:

* *Supplementary angle*

* Complementary angle

* Acute angle

* Obtuse angle

(x) The straight line which touches the circle at one point is called:

* Secant

* *Tangent*

* Chord

* Diameter

(xi) (a + b)³= ———

* *a³ + b³ + 3ab (a + b)*

* a³ + b³ – 3ab (a – b)

* a²+ 2ab + b²

* a³ + b³ – 3ab

(xii) Area of Sector = π²

* 4

* 2

* 3

* *5*

(xiii) The mode of 7, 8, 9, 10, 12, 9, 16 is: ———-

* *9*

* 7

* 10

* 16

(xvii) If log2 64 = x, the value of x will be:

* *6*

* 16

* 8

* 12

(xix) The decimal system 101²= ——-

* 11

* 7

* 3

* *5*

(xx) {2,4,6, —–} is called the set of :

* *Even numbers*

* Odd numbers

* Natural numbers

* None of them

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

NOTE: Answer 10 questions from this section.

**4. If A = {1 , 2} and B = {4 , 6 , 8}, Find A x B and B x A.**

*ANSWER:*

A x B ={1,2} x {4,6,8}

A x B = {(1, 4), (1, 6), (1, 8), (2, 4), (2, 6), (2, 8)}

B x A = {4, 6, 8} x {1, 2}

B x A = {(4, 1), (4, 2), (6, 1), (6, 2), (8, 1), (8, 2)}

**6. Find the continued product of (x – y) (x + y) (x2 + y2) (x” + y4) with the help of formula.**

*ANSWER:*

(x – y) (x + y) (x² + y²) (x4 + y4)

Formula used

(a + b) (a – b) = a² _ b²

= (x² _ y²) (x² + y²) (x4 + 1)

= (x4 _ y4) (x4 + l)

= (X4)² _ (1)² = x8 -y8.

**7. Find the value of x3 + y3 when x + y = 5 and xy = 6**

*ANSWER:*

Given x + y = 5

And xy = 6

Formula:

(a + b)³ = a³ + b³ + 3ab (a + b)

Applying this formula in above x + y = 5

(x + y)³= (5)³

x³ + y³ + 3xy (x + y) = 125

Again putting the values of x + y and xy in L.H.S.

x³ + y³ + 3 x 6 (5) = 125

x³ + 1 + 90 = 125

x³ + y³ = 125 – 90

x³ + y³ = 35.

**13. Distribute Rs.9000 among Umar, Zaid and Bakr in the ratio of 2:3:4.**

*ANSWER:*

Given amount = Rs.9000

Ratio between Umer , Zaid and Bakr

2 : 3 : 4

Sum of terms of Ration = 2 + 3 + 4 = 9

Share of Umer = 9000 x 2/9 = 2000

Share of Zaid = 9000 x 3/9 = 3000

Share of Bakr = 9000 x 4/9 = 4000.

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

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

**18. A man died leaving behind Rs.15,000. He had a loan of Rs.3000. Divide rest of the amount among his wife, 2 sons and 4 daughters in such a way that the wife gets 1/8th of the whole amount and each son gets twice of the each daughter.**

*ANSWER:*

Amount of Tarka = 15000

Amount of debt = 3000

No. of sons = 2

No. of daughters = 4

No. of widows = 1

Each son gets twice that of a daughter

SOLUTION:

Amount left after paying the debt = 15000 – 3000 = 12000

Share of widow = 1/8 x 12000 = 1500

Suppose each daughter gets Re.1

Then each son gets Rs.2

4 daughters gets = 4 x 1 = 4 Rs.

2 sons get = 2 x 2 = 4 Rs.

Total amount = 4 + 4 = 8

Share of 4 daughters from Tarka = 418 x 10500 = 5250

(Amount left = 12000 -1500 = 10500)

Each daughter share = 5250 ÷ 4 = 1312.50

Share of 2 sons = 4/8 x 10500 = 5250

Each son gets = 5250 ÷ 2 = 2625.

**19.(b) Find the cube of 2a – 3b.**

*ANSWER:*

(2a – 3b)³

Formula

(a – b) = a³ – b³ – 3ab (a – b)

(2a – 3b)³

= (2a)³ – (3b)³ – 3(2a) (3b) (2a – 3b)

= 8a³ – 27b³ -18ab (2a – 3b)

= 8a³ _ 27b³ – 36a²b + 54ab².

**21.(a) A man saved Rs.20,000 in one year. The cost of the Jewellery of his wife is RS.15,000 .How much Zakat will he pay at the rate of 2.5%?**

*ANSWER:*

Saving = Rs.20000

Cost of Jewellery = Rs.15000

Total = 20000 + 15000 = 35000

Zakat Rate 2.5%

Amount of Zakat = 35000 x 2.5%

= 35000 x 2.5/100

= 875.

**21.(b) Find the product of: (a + b) (a2 – ab + b2 ) (a – b) (a2 + ab + b2 )**

*ANSWER:*

(a + b) (a² – ab + b²) (a – b) (a² + ab + b²)

By formula

a³ + b³ = (a + b) (a²- ab + b²) and

a³ – b³= (a – b) (a² + ab + b²) and

Given sentence becomes

= (a³+ b³) (a³ – b³) = (a³)2 – (b³)2

= a6 – b6.