All India Institute of Medical Sciences 2007 A.M.I.E.T.E Electronics

Guess Paper – 2009

Subject – MATHEMATICS

FIRST


General Instructions:
1. All ques. are compulsory.
2. The ques. paper consists of 30 ques. divided into 4 parts – A, B, C and D. part A contains 10 ques. of one mark each, part B is of five ques. of two marks each, part C is of 10 ques. of three marks every and part D is of five ques. of six marks every.
3. In ques. on construction, the drawing should be neat and exactly as per the provided measurements.



part – A

1. Express sin A in terms of Cot A
2. In adjoining figure ?ABC ~ ?PQR, obtain y and z.
3. Express 7429 as a product of its prime factors
4. Find the number of integral zeros of x2 – 6x + 12.
5. Find the nature of the roots of the quadratic formula x2 - x + = 0.
6. Find the tenth term from end of the A.P. 4, 9, 14, …, 254.
7. The radii of 2 circles are three cm. and four cm. obtain the radius of a circle whose area is equal to the sum of the areas of 2 circles.
8. In adjoining figure, ?POB = 55o, obtain ?APB.
9. If the probability of winning a game is P and that of losing is 2P2, obtain the value of P.
10. The point of intersection of the Ogives (more than and less than type) is at a distance of 36cm from X-axis and 25cm from Y-axis. What is the Median?

part – B

11. For what value of k will the subsequent pair of linear formula has no solution:
ax + 3y = a – 3; 12x + ay = a.
12. In adjoining figure, prove that: .
13. The coordinates of A and B are (-3, 3) and (12, -7) respectively. P is a point which divides AB in the ratio AP : AB = 2:5, obtain the coordinates of P.
14. Evaluate :
15. A box contains cards bearing numbers six to 70. If 1 card is drawn at random from the box. obtain the probability that it bears:
(i) a 1 digit number, and
(ii) a number divisible by 5.

part – C

16. Physical teacher of a school decided to have maximum number of mixed parts for a team, every part has to accommodate equal number of boys player and equal number of girls player. What is the maximum number of such section, if there are 240 boys player and 228 girls player?

17. Find all the zeros of the polynomial , if the 2 of the zeros are three & -3.
18. Solve for x and y: ;
OR
The sum of the digits of a 2 digit number is 9. Also 9 times this number is twice the number found by reversing the order of the digits. obtain the number.
19. Find the sum of A.P.: , , , ………. to 11 terms.
20. In ?ABC, AB = 5cm, BC = 13cm, A = 90o, obtain the radius of the in-circle.
21. What kind of triangle is formed by joining the points (5, -2) (6, 4) and (7, -2)?
22. Find the value of k, if P (1, k), Q (4, -3) and R (-9, 7) are the vertices of a triangle whose area is 15 square units.
23. Prove that:
OR
If P, Q and R are the interior angle, of ?PQR, then prove that:
24. Construct a pair of tangents to a circle of radius five cm from an external point P, which are inclined to every other at an angle of 60o.
25. In adjoining figure, ABCD is a square of side 14 cm; obtain the area of shaded region.

part - D

26. The numerator of a fraction is 1 less than its denominator; if 3 is added to every of the numerator and denominator, the fraction increases by , obtain the fraction.
OR
Two pipes running together can fill a tank in minutes. If 1 pipe takes five minute more than the other to fill the tank, obtain the time in which every pipe would fill the tank.

27. The angle of elevation of the top of building from the foot of the tower is 30o and angle of elevation of the top of the tower from foot of the building is 60o. If the tower is 50 m high, obtain the height of the building.
OR
As observed from the top of a 75 m high light house from sea level, the angles of depression of the 2 ships are 30o and 45o. If 1 ship is exactly behind the other in the identical side of the light house obtain the distance of the 2 ships.

28. A metallic right circular cone 20 cm high and whose vertical angle is 60o is cut in to 2 parts at the middle of its height by a plane parallel to its base. If the frustum so found be drawn into wire of diameter cm, obtain the length of the wire
29. Find the mean, the mode and the median for the subsequent data:
Class Interval 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
Frequency 4 8 10 12 10 4 2

30. If In a triangle the square of 1 side is equal to the sum of the squares of the other 2 sides, then prove that the angle opposite to the 1st side is a right angle.
Use the above theorem to prove the following:
In figure O is a point inside ?PQR such that ?POR = 90o, OP = six cm, OR = eight cm. If PQ = 24 cm, QR = 26 cm, then
prove that PQR is a right angled triangle.












BISWAS TEST SERIES - 2009
Paper Submitted by:
DILIP BISWAS
Email dilipbiswas2006@gmail.com
Phone No. 09214927974

Earning:   Approval pending.