**SECTION “A” (COMPULSORY)(M.C.Q.S)**

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

(i) 12+ 12+ 12= ———-

* *3
** 10

* 11

* 100

(ii) The Cartesian product of A and B is written as:

* A.B

* *AxB*

* B.A

* BxA

(iii) The characteristic of log 8.368 is:

* 0

* *1*

* -1

* -2

(iv) The arithmetic mean of 2,3 and 4 is:

* 4.5

* *3*

* 3.5

* None of them

(v) It is called the multiplicative identity.

* 0

* -1

* 10

* *1*

(vii) The number repeated frequently in a given data is:

* Median

* Mean

* *Mode*

* None of these

(viii) If (x + 1, Y + 2) = (5 ,6) then the value of x is:

* 6

* 3

* 5

* *4*

(ix) (6x)°x 4x²= ———-

* *4x²*

* 24x²

* x³

* None of these

(x) An angle of less than 900 is called:

* Right angle

* *Acute angle
** Obtuse angle

* Vertical angle

(xi) 25+ 45= ———-

* *65*

* 85

* 25

* 115

(xii) If log3 N = 4 then value of N is:

* *81*

* 27

* 64

* none of these

(xiii) Is a set of points each of which is at the same distance from a fixed point.

* Chord

* Diameter

* Radius

* *Circle*

(xiv) Rate of zakat is = ——

* 5%

* *2-1/2%*

* 3-1/2%

* 10%

(xv) 2√9 x √9 = – – – – –

* 81

* *18*

* 36

* None of these

(xvi) Area of circle = ———

* πr

* πr/2

* 2πr

* *πr²*

(xvii) {1, 2, 3, ——- } is the set of:

* Integer

* Whole numbers

* *Natural number*

* even no.

(xviii) The multiplicative inverse of 1/x is:

* *x*

* x-1

* 1/x2″

* None of these

xix) 60 a²b²÷4ab = —–

* 12ab

* 12a²b

* *15ab*

* None of these

(xx) (x – 6) (x + 6) = ——–

* *X²-36 *

* X² + 36

* x – 6

* x + 6

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

Answer 10 questions from this section

**2. The sum of two numbers in Base five is 4315, One of the numbers is 2145, Find the other**

ANSWER

Sum of two numbers in Base 5 is 4315

One number is 2145

Other number = ?

Other Number 4315 – 2145

4315

2145

2125

**3. 90 worker men work in a factory. The scheme of their daily wages is given below. Find the A.M. of their wages.
**

**4. Divide: (x2- 5x + 6) -;-(x – 2)**

ANSWER:

**5. If A = 2p – 3q – 4r and B = -4q + 5p – 2r. Find the value of 3A – 4B.**

ANSWER

3A = 3 x (2p – 3q – 4r)

= 6p – 9q -12r

4B = 4x (-4q + 5p – 2r

= -16q + 20p – 8r

3A – 4B = 6p – 9q – 12r – (-16q + 20p – 8r)

= 6p – 9q – 12r +16q – 20p + 8r)

= -14p + 7q – 4r Ans.

**6. 15 spoons of sugar are required for 6 eggs cake. How many spoons of sugar will be required for 8 eggs cake?**

ANSWER:

ANSWER:

**8. Use an appropriate formula to Simplify 1025 x 975.**

ANSWER:

Using formula:

(a + b) (a – b) = a² – b²

1025 = 1000 + 25

975 = 1000 – 25

(1000 + 25) (1000 – 25)

= (1000)² – (25)²

= 1000000 – 625

= 999375 Ans.

**9. Annual savings of a person is 2,400 rupees. His wife has ornaments worth Rs.2050. What amount of Zakat is due to him?**

Saving of the person = Rs.2,400

Worth of ornaments = 2050

Total = 2400 + 2050 = 4450

Rate of Zakat = 5/2%

Amount of Zakat to be paid:

Rs. 111.25 Ans.

**10. If log10² = 0.3010, log10³ = 0.4771, and log105= 0.6990 find the value of log1030.**

ANSWER:

L0910 30 = 10910(2 x 3 x5)

L0910 30 = log102+ Iog103+ log105

Log10 30 = 0.3010 + 0.4771 + 0.6990

L0910 30 = 1.4771 Ans.

ANSWER:

**12. Define the following
**

**(i) Vertical angles(ii) Supplementary angle**

ANSWER:

**(i) Vertical angles:
**The angles whose arms form two pairs of opposite rays are called vertical angles.

**(ii) Supplementary angle
**If the sum of two angles is 180° they are called supplementary angles and each of the two angles is called supplement of the other. E.g. 60°, 120°

**13. A rectangular lawn whose length is 7.5m and breadth is 4m. Find the length of diagonal.**

**14. 8 masons can build a 10 meters long wall in 22 days. How many masons would be required to build a 165 meters long wall in 6 days.**

ANSWER:

**15. Convert 101110012 numbers into those of decimal system**

**16. If a diameter of a circle is perpendicular to a chord, it bisects the chord. Prove.**

**SECTION ‘C’ (DESCRIPTIVE-ANSWER QUESTIONS)**

Attempt 3 questions from this Section.

**Formula**

**18. A woman died. Her heirs were her husband, two daughters and a brother. A “Tarka” worth rupees 2,700 was distributed among her heirs in the ratio 1/4 , 2/3 and 1/12 Find the Share of each.**

ANSWER: Tarka = Rs.2,700

Ratio between

Husband : Two Daughter : Brother

1/4 : 2/3 : 1/12

Husband Share = 2700 x ¼ = 675

Two Daughters share = 2700 x 2/3 = 1800

Share of one daughter = 1800 x ½ = 900

Share of brother = 2700 x 1/12 = 225

**19.(a)Find the product: (2x – 3y) (4×2 + 9y2 + 6xy)**

ANSWER:

**(b) The A.M. of ten numbers is 32. Find the sum of numbers.**

= 320 Sum of Numbers = 320 Ans.

**20.(a)Factorize: (i) 3a4 – 48 (ii) ab + cd + be + ad**

ANSWER: (i)= 3(a4- 48)

= 3 [(a4_ 16]

= 3 (a2 + 4) (a2- 4)

= 3 (a2 + 4) (a)2 _ (2)2

= 3 (a2 + 4) (a + 2) (a – 2) Ans.

(ii) ab + cd + be + ad

Rearranging the terms

= ab + be + ad + cd

= a (a + c) +d (a + c) = (a + e) (a + d) Ans.

**(b) If x – y = 3 and xy = 10 then find the value of x3 – y3.**

ANSWER:

X-y = 3

XV = 10 x5 _ y3 = 7

(x _ y)³ = (3)3

x3 -y³ 3xy (x – y) = 27

x3 – y3 _ 3 x 10 x (3) = 27

x³ – y³ 90 = 27

x³ – y³ = 27 + 90

x³ -y³ = 117 Ans .

**21. Construct the triangle, the length of whose sides are 4cm, 3cm and 5cm. Draw a circle passing through its vertices.**