PAPER - I
SECTION - A
ANSWER ALL QUESTION IN THIS SECTION
1. The C.I. and S.I. on a sum of money for 2 years is Rs. 210 and Rs. 200. If the rate of interest is the same, find the sum and the rate. [6]
2. Find the compound interest on Rs. 27000 for 9 years at 4% per annum. [6]
3. From the diagram given below calculate (i) AB (ii) AP (iii) DAPC : DABC
4. (i) Prove that Sin(90-q) Cos (90-q) = (1-sin2q} [3] tanq (ii) From the above diagram prove that BC2 + YX2 = BY2 + CX2 [3]
5. Construct a direct common tangent to two circles using ruler and compass. [8]
6. (i) Substitute a+3 = x and solve for x. using those values of x, find the values of a that satisfy the equation- 5(a+3)2 = 23(a+3)+10 [4]
(ii) Solve 4x2-12x+9 = 0 [4]
SECTION - (B)
ANSWER ONLY 4 QUESTIONS IN THIS SECTION ALL QUESTIONS CARRY EQUAL MARKS [10]
7. (i) Prove that (is parallel to) is an equivalence relation for a set of lines. (ii) A man on deck of a ship is 10m above water level. He observes that the angle of elevation of the top of a cliff is 42° and the angle of depression of the base is 20°. Calculate the distance of the cliff from the ship and the height of the cliff.
8. (a) If A = é 1 0 ù show that A2 ¹ A and A3 = A ë 0 -1û
(b) Given B = é 2 -3 ù and B2 = I find a, b if I is 2*2 identify matrix. ë a bû (c) Find the mean by direct method where x 2 4 6 8 10 f 3 5 6 4 2
9. (a) The linear equation y = x+1 is satisfied by the values of x and y, given , s, y, .å I Draw the graph. X = -1, 1, 2, 4, 5 Y = 0, 2, 3, 5, 6 (b) State the slope (m) and y - intercipt (c) of the line 2y = 4x-3
10. State the mean by `direct method' - X 4 8 12 16 20 Y 6 10 12 8 4
11. (a) Using ruler and compass only, construct a triangle ABC in which BC = 6 cm. Ðc = 60° and ÐB = 45°. Also construct a circle to touch the side BC at the point C and to pass through the vertex A. (b) Draw a histogram and estimate the mode from the following data:
Marks No. of pupils 0-5 4 5-10 6 10-15 12 15-20 8 20-25 2
12. (a) If a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is a cyclic quadrilateral. (b) The radius of a circle with centre P is 13. The length of the chord AB of this circle is 24. Determine the distance from P to the chord AB.
13. (a) A measuring jar of one litre of measuring milk is of right circular cylindrical shape. If the radius of the base is 5 cm. Find the height of jar [ P = 3.14] (b) Radius of larger circle is 18 and smaller is 5. Determine the ratio in which point P divides segAB.
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