All India Institute of Medical Sciences 2008 - exam paper

Sample Paper – 2008
Class – X
Subject - Mathematics

Set – 2
[Max. marks 80] [Time – 2 hours and a half ]
part – I (40 Marks)
Attempt all the ques. from this part
Q.1. (a) When the rate of sales tax is reduced from 9% to 7% for a flat T V , Rajan has to pay Rs.632 less for it. What is the list price of the T V? [3]
(b) If a, b, c and d are in continued proportion, then prove that:
(a – b)3 : (b – c)3 = a : d [3]
(c) A sum of Rs.4,920 was borrowed at 5% p.a. compound interest. The loan was paid back in two equal instalments in 2 years. obtain the value of every instalment. [4]

Q.2(a) If g(x) = (2x – 3) is a factor of f(x) = 2x3 – 9x2 + x + p, obtain the value of p. Hence, obtain all the factors. [3]
(b) obtain lower quartile, upper quartile, interquartile range and semi-interquartile range of : 3, 6, 8, 13, 15, 5, 21, 23, 17, 10, 9, 1, 20, 21, 18, 12. [Ans. 6, 18, 12, 6] [4]
(c) Chords AB and CD of a circle intersect every other at right angle. Prove that the angle ACD and BDC are complementary. [3]

Q.3(a) Rachna saves Rs.40 every month and put it in a recurring deposit account. In order to have a total amount of Rs.6,500 nearly, how many instalments must she deposit? [3]
(b) A copper wire when bent into the form of a square encloses an area 121 sq. cm. If the identical wire is bent in the form of a circle, obtain the area of the circle. [3]
(c) A point P(a,b) becomes (3,c) after reflection in x – axis, and (d,6) after reflection in the origin. obtain the value of a, b, c, and d. [4]

Q.4(a) Without using trigonometric table, evaluate the following:
tan10º tan15º tan60º tan75º tan80º [3]
(b) Solve the inequation : 2x – three < 5x + three < 2x + three [3]
(c) provided beneath are the weekly wages of 200 workers in a small factory :
Weekly wages in Rs. 80 – 100 100 – 120 120 – 140 140 – 160 160 – 180
No. of workers 20 30 20 40 90
compute the mean weekly wage. [4]

Earning:   Approval pending.