**SECTION ‘A’ MULTIPLE CHOICE QUESTION**

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

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

**(2) If U = {1,2,3,4,5,6, 7} , A = {1,3,5, 7} and B = {3,4,5,6}; Prove that A’ ∪ B’ = (A ∩ B)’**

**ANSWER:**

**(4) If a + b = 7 and ab = 11, find the value of (a – b).**

**ANSWER:**

**(6) Factors. r² (5 – t) + 5² (t – r) + t² (r – s)**

**ANSWER:**

**(7) Solve the following equations with the help of matrix:**

**(8) If one pair of opposite sides of a quadrilateral are congruent and parallel, it is a parallelogram. Prove it**

**(9) Solve the equation 2b² – 7b + 5 = 0 using quadratic formula.**

**(10) If a transversal intersects two coplanar lines, such that the pair of alternate angles are congruent, prove that the lines are parallel.**

**(13) For what value of a and b, X4 + 4×3 + 10×2 + ax + b is a perfect square?**

**(14) Eliminate x from the following equations**

**(15) Prove that the sum of the three angles of a triangle is equal to 180º**

**(16) Find the values of the trigonometric ratios of an angle of 30°.**

**SECTION ‘C’ (DETAILED – ANSWER QUESTION)**

**(17) Factorize the following:**

**(i) a³ – a² + 2 (ii) 8a³ + b³ + 27c³ – 18abc
(iii) 5x² – 13x – 6 (iv) x³ – 64y³**

**(18) Find the solution set of the following equations graphically: (Find four ordered pairs for each equation.)**

**x – 2y = -3
2x + y = 14**

**ANSWER:**

**(19) In any correspondence of two triangles, if one side and any two angles of_one .triangle are congruent to two corresponding’side and two angles of the other, the two triangles are congruent. Prove it.**

**(20) Find the variance from the following information**

**ANSWER:**

**(b) Factorize the following with the help of remainder theorem: x³ + 8x² + 19x + 12**

**ANSWER:**

**(21) Draw a circle of radius 2.5 cm. Take a point B at a distance of 6.5cm from the centre of the circle and draw two tangents to the circle passing through B. Find the lengths of the segments of the tangents by measuring them. Verify your measurement with the help of Pythagoras Theorem?**

**ANSWER:**