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Posted By: hima Member Level: Gold Posted Date: 27 May 2008
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2008 ICSE All India Institute of Medical Sciences sample paper University Question paper
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Sample Paper – 2008
Class – X
Subject - Mathematics
Set – 2
[Max. marks 80] [Time – Two hours and a half ]
Section – I (40 Marks)
Attempt all the questions from this section
Q.1. (a) When the rate of sales tax is decreased 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 2 equal instalments in two years. Find the value of each instalment. [4]
Q.2(a) If g(x) = (2x – 3) is a factor of f(x) = 2x3 – 9x2 + x + p, find the value of p. Hence, find all the factors. [3]
(b) Find 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 each 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 same wire is bent in the form of a circle, find 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. Find 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 – 3 < 5x + 3 < 2x + 3 [3]
(c) Given below 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
Calculate the mean weekly wage. [4]
Section – II (40 Marks)
Answer ANY FOUR questions from this section
Q.5(a) From a trapezium ABCD, in which AB ?? DC and ?BCD = 90º, quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2 cm. Calculate the remaining area. [3]
Fig
(b) If x cos? – y sin? = a and x sin? + y cos? = b, prove that x2 + y2 = a2 + b2. [3]
(c) The entries in a passbook of a Saving Bank Account are given below :
Date 2006 Particulars Withdrawals (in Rs.) Deposits (in Rs.) Balance (in Rs.)
Feb.2 By cash ------ 1000.00 1000.00
Feb.5 By salary ------ 20000.00 21000.00
Feb.8 To cheque 4000.00 -------- 17000.00
Feb.15 By cash --------- 6000.00 23000.00
Feb.25 To Neelu 2000.00 --------- 21000.00
Mar.2 By salary --------- 20000.00 41000.00
Mar.9 To cheque 10,000.00 ---------- 31000.00
Mar.21 To cheque 14000.00 ---------- 17000.00
Mar.27 To self 8000.00 ---------- 9000.00
Apr.1 By salary --------- 20000.00 29000.00
The account is closed on 16th April, 2006. Compute the interest if the rate of interest is 5% per annum. [Ans. Rs.108.30] [4]
Q.6.(a) In the given fig., prove that :
AP + BQ + CR = BP + CQ + AR [3]
Fig
(b) Find the equation of a line which is parallel to x – 2y + 8 = 0 and passes through the point (1,2). [Ans. x – 2y + 3 = 0] [3]
(c) Rachna purchased 3 shirts and 5 skirts. The cost of one shirt is Rs.150 and the cost of one skirt is Rs.350. Find the total cost of the clothes by matrix method.[Ans.Rs.2200][4]
Q.7.(a) The annual income of Ms. Manju is Rs.6,00,000 exclusive of HRA. She contributes Rs.7,500 per month to her provident fund and pays Rs.12,000 half yearly to the Life Insurance Policy. She has donated Rs.10,000 towards National Defence Fund (100% exemption) and Rs.4,000 towards Rajiv Gandhi Foundation (50% exemption). Find the income tax to be paid by her in the last month of the year , if she had been paying Rs.7,500 per month as income tax for the first 11 months of the financial year 2005 – 2006 . [Ans. Rs.12,258] [6]
(b) At a point on the level ground the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 m towards the tower tangent is found to be ¾. Find the height of the tower. [Ans. 180 m] [4]
Q.8. (a) In the given fig., AB is a common tangent to two circles intersecting at C and D. Write down the measure of ?ACB + ?ADB. Justify your answer. [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. 1 : 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, find 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 some water and is fully submerged. The diameter of the vessel is 7 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 following data by means of a histogram : [5]
Class interval 0 – 5 5 – 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 find 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 each row. If the number of rows is doubled and the number of seats in each row is reduced 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 = 2 4.(a) v3 (b) {x: x e R, – 2 < x < 0 } (c) Rs.145.
5. (a) 6.125 cm2 (c) Rs.108.30 6. (b) x – 2y + 3 = 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) 3 (b) x = – 6, 1
(c) 150 10. (b) 25/2 sq. units; 5v2 units 11. (c) 25.
Best of luck
M. P. Keshari [09434150289]
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