All India Institute of Medical Sciences 2008 - exam paper

(b) At a point on the level ground the angle of elevation of a vertical tower is obtained to be such that its tangent is 5/12. On walking 192 m towards the tower tangent is obtained to be ¾. obtain the height of the tower. [Ans. 180 m] [4]

Q.8. (a) In the provided fig., AB is a common tangent to 2 circles intersecting at C and D. Write down the measure of ?ACB + ?ADB. Justify your ans. [Ans. 180º] [3]
(b) In what ratio is the line segment joining the points (– 3, – 2) and (6,1) divided by the y – axis ? [Ans. one : 2] [3]
(c) Azam sold 400 (Rs.20) shares paying 5% at Rs.18 and invested the proceeds in (Rs.10) shares, paying 7% at Rs.12. How many (Rs.10) shares did he buy and what was the change of his income ? [Ans. 600, Rs.20] [4]

Q.9. (a) If f(x) = (x + 1)/x, obtain the value of
(i) f(1) (ii) f(– 1) (iii) f(1/2) [Ans. (i) 2, (ii) 0, (iii) 3] [3]
(b) Solve for x :
(x + 1)(x + 2)(x + 3)(x + 4) = 120. [Ans. x = – 6, 1] [3]
(c) Spherical marbles of diameter 1.4 cm are dropped into cylindrical vessel containing a few water and is fully submerged. The diameter of the vessel is seven cm. How many marbles have been dropped in it if the water rises by 5.6 cm? [Ans. 150] [4]

Q.10. (a) Represent the subsequent data by means of a histogram : [5]
Class interval 0 – five five – 10 10 – 20 20 – 30 30 – 50 50 – 70
Frequency 5 10 15 20 25 30
(b) Prove that (2 ,– 2), (– 2,1) and (5,2) are the vertices of a right angled triangle. Also obtain the area of the triangle and the length of the hypotenuse. [5]
[Ans. 25/2 sq. units, 5v2 units]

Q.11. (a) D is a point on the side BC of a triangle ABC such that ?ADC = ?BAC. Prove that : CA/CD = CB/CA. [3]
(b) Construct a cyclic quadrilateral ABCD where AB = 3.1 cm, BC = 6.3 cm, AC = 4.2 cm and AD = 2.4 cm. [3]
(c) In a picture hall, the number of rows was equal to the number of seats in every row. If the number of rows is doubled and the number of seats in every row is decreased by 5, then the total number of seats is increased by 375. How many rows were there. [4]
[Ans. 25]

ANSWERS

1.(a) Rs.31,600 (c) Rs.2,646 2.(a) p = 12; (x + 1)(x – 4)(2x + 3) 3.(a) 96 (b) 154 sq. cm (c) a = 3, b = – 6, c = 6, d = two 4.(a) v3 (b) {x: x e R, – two < x < 0 } (c) Rs.145.
5. (a) 6.125 cm2 (c) Rs.108.30 6. (b) x – 2y + three = 0 (c) Rs.2200 7. (a) Rs.12,258
(b) 180 m 8. (a) 180º (b) 1:2 (c) 600; Rs.20 9. (a)(i) 2, (ii) 0, (iii) three (b) x = – 6, 1
(c) 150 10. (b) 25/2 sq. units; 5v2 units 11. (c) 25.
Best of luck
M. P. Keshari [09434150289]

Earning:   Approval pending.