**SECTION ·A’ MULTIPLE CHOICE QUESTION**

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

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

**2. If U = {x/x∈N . x ≤ 10}. A = (2, 4, 6, 8, 10} B = {3, 6, 9, 10} Prove that {A ∪ B} = A ∩ B**

**ANSWER:**

**6. Resolve into factors. r² (s – t) + s²(t² – r) + e (r – s)**

**ANSWER: Please see Q.no.6 of 2014.**

**7. The sum of three consecutive odd numbers is 909. Find the numbers**

The sum of these three odd no. will be

X + (x + 2) + (x + 4)

According to given condition

X + x + 2 + x + 4 = 909

3x + 6 = 909

3x = 909 – 6

3x = 903

x = 903/3

1st odd no. is x = 301

2nd no. is x + 2 = 301 + 2 = 303

Then the 3rd odd no.

X + 4 or 301 + 4 = 305

The three odd no. are 301, 303, 305

**9. By using Cramer’s rule, solve the**

**equation 2x + 5y = 9
4x – 2y = 1**

**ANSWER:**

**10. Find the solution set with the help of
quadratic equation. 2b² – 7b + 5 = 0**

**ANSWER: Please see Q.no.9of 2014.**

**11. Prove that the sum of the three angles of a triangle is equal to 180º.**

**ANSWER: Please see Q.no.15of 2014.**

**12. Find the relation independent of ‘t’ from the following equation **

**Similarly**

This is an equation independent of t

**13. If a transversal intersect two parallel lines, the alternate angles so formed are congruent. Prove it.**

**Prove that a = b = c**

**15. If two sides of a triangle are congruent, the angles opposite to them are also congruent. Prove it.**

**Proof:**

**16. Prove that cotβ + tanβ = cotβ sec² β.**

**SECTION’c’ (DETAILED- ANSWER QUESTION)**

**16. Find the Solution set of the following equations graphically. (Find four ordered pairs of each equation).
4x – y -10 = 0
3x + 5y -19 = 0
**

**19. In a correspondence of triangles if three sides of one triangle are congruent to the corresponding three sides of the other, the two triangles are congruent. Prove it.**

**Proof:**

**20.(a) Marks obtained by some students In computer science exam. are given below. Find Median of their numbers**

**ANSWER:**

**(b) Find the factors of X³ – X² – 14x + 24 with the help of remainder theorem.**

**21. Draw the transverse common tangents of the two circles with the radII 3cm and 2cm, when the distance b/e their centers
Is 6cm. Write down the steps of construction.**

Steps of Construction:

(1) Draw a straight line AB = 6cm

(2) With centre A draw a circle of radius 3 cm and with centre B draw a circle of radius 2 cm.

(3) With centre A draw a big circle of radius 3 + 2 = 5cm

(4) Bisect AB at 0 and with centre 0 and radius = mOA or m OB draw a 4th circle intersecting the big circle at Q and R.

(5) Join A to Q and R, intersecting the given circle at 5 & 5′

(6) Draw BT parallel to AQ and BT’ parallel to AR

(7) Join 5 and T and extend on either sides similarly join 5′ and T’ and extend on either sides. In this way 5T and SiT’ are the required transverse common tangents.