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SECTION – A Question numbers 1 to 4 carry 1 mark each. 1 Find the product 3 2 . 4 2 . 12 32 . 2 Find one factor of (9x 1) (13x) . 1 3 An exterior angle of a triangle measures 140. If the interior opposite angles are in the ratio 3 : 1 1 2 1 2 then find the angles of the triangle. 4 What is the x-co odinate of any point on the y-axis ? 1 SECTION – B Question numbers 5 to 10 carry 2 marks each. 3 5 and . 5 7 5 Insert three rational numbers between 2 6 For what value of k is the polynomial p(x)2x3kx23x10 exactly divisible by (x2) ? 2 7 In figure C is the mid-point of AB and D is the midpoint of AC. Prove that 2 1 AD AB. 4 8 In figure, if lines PQ and RS intersect at point T, such that PRT50, TSQ60 and RPT100, find SQT. Page 1 of 4 2 9 If a point P(2, 3) lies in first quadrant, then what will be the co-ordinates of a point Q opposite to it in 2 fourth quadrant having equal distance from x-axis ? 10 The semi-perimeter of a triangle is 132 cm. The product of the difference of 2 3 semi-perimeter and its respective sides is 13200 cm . Find the area of the triangle. SECTION – C Question numbers 11 to 20 carry 3 marks each. 11 12 If 1 2 1 2 a b 2 , then find a and b . 1 2 1 2 Find the value of a and b if 5 3 ab 3 . 7 4 3 3 3 13 If ab7 and a2b285, find a3b3. 3 14 If xa is a factor of x4a2x23xa, then find the value of a. 3 15 ABCD is a square. X and Y are points on the sides AD and BC such that AY= BX. Prove that 3 XAY=YBX 16 In the given figure ABC and DBC are two triangles on the same base BC and vertices A and D are on the same side of BC, AD is extended to intersect BC at P. Show that : (i) Page 2 of 4 ABD ACD (ii) ABP ACP 3 17 If a transversal intersects two parallel lines, then prove that bisectors of alternate interior angles 3 are parallel. 18 In figure two sides AB and BC and median AM of ABC are respectively equal to sides DE and 3 DF and the median DN of DEF. Prove that ABCDEF. 19 Find the area of the trapezium in which parallel sides are 25 cm and 10 cm and non-parallel sides 3 are 14 cm and 13 cm. 20 The adjacent sides of a parallelogram ABCD are AB 34 cm, BC20 cm and diagonal AC = 42 3 cm. Find the area of the parallelogram. SECTION – D Question numbers 21 to 31 carry 4 marks each. 21 Varun was facing some difficulty in simplyfying 1 . His classmate Priya gave him a clue to 7 3 rationalise the denominator for simplification. Varun simplified the expression and thanked Page 3 of 4 4 Priya for this goodwill. How Varun simplified 1 1 2 22 Prove that : 23 a2b2 Simplify 3 1 ? What value does it indicate ? 7 3 1 1 1 .......... 2 2 3 3 4 8 3 b2c2 3 c2a 2 4 3 4 ab3 bc3 ca3 4 3 2 2 24 Without actual division prove that x 2x 2x 2x3 is exactly divisible by x 2x3. 4 25 Show by long division that 2x3 is a factor of p(x)4x48x35x2x3. 4 26 Find the value of k, if (x3) is a factor of p(x)2x35x23xk. 4 27 Show that the perimeter of a is greater than the sum of its three medians. 4 28 Prove that the sum of three angles of a triangle is 180. Using this result, find the value of x and 4 all three angles of a triangle if the angles are (2x7), (x25) and (3x12). 29 Prove that the angles opposite to equal sides of a triangle are equal. 4 30 In the given figure AB is a line segment and p is its mid-point. D and E are points on the same 4 side of AB such that BADABE and EPADPB. Show that : (i) 31 DAP EBP , (ii) ADBE If two lines intersect each other, then prove that the vertically opposite angles are equal. Page 4 of 4 4