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CBSE Model Paper No 3
Time allowed : 3 hours
Maximum Marks : 100
General Instructions :

(i) Question number 1 to 10 carry 3marks each.     (Section  A )
(ii) Question number 10 to 20carry 4 marks each. (Section   B)
(iii) Question number 21 to 25 carry 6 marks each.  (Section  C )
(iv) Write the serial number of the question before attempting it.
(v) Use of logarithmic and trignometric tables is permitted. Use of calculator is not permitted

 (Section  A )
1. Determine K so that the equation x2 + 4x – K = 0 has two equal roots.
2. A rectangular piece of paper is 44 cm long and 20 cm wide. A cylinder is formed    by rolling the paper along its length. Find the volume of the cylinder.
3.

 

 Calculate the mean and mode of 21, 16, 15, 14, 15, 18, 17, 22, 28, 15, 26, 15
                                                                     .OR

 State the mean by `direct method' -
        X   4  8  12 16 20
        Y   6 10 12  8   4
4 From the diagram given below calculate
    (i) AB
    (ii) AP
    (iii) DAPC : DABC
5 If the areas of three adjacent faces of cuboid are p, q and r and volume is v, prove
         that V2 = p q r
6 Prove that 
Sin(90-q) Cos (90-q) = (1-sin2q}                                                              
       tanq
7 If x3 + y3 / x3 - y3 = 91 / 37 . Show that x : y = 4 :3
8 
Aarti buys a saree costing Rs. 2500/- at Rs. 2700/- after paying sales tax.
Calculate the ratio of sales tax paid by her.
OR
Find side of square whose diagonal is 12 cm.
9 3x + 2y = 6 ;(k + 1 )x + 4y = (2k + 2) 
For what value of k, will the above system of equation have infinite solution.
10 The mean of 5 numbers is 15. If one number is excluded, the mean becomes 12.5, find the excluded number.

Section B
11. In figure ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC = 92o, FAE = 20o, find BCD.  
 
 
12. In a trapezium PQRS, PQ || SR and SR = 2 PQ. XY drawn parallel to PQ cuts PS in X and QR in Y such that . Diagonal QS intersects XY in Z. Prove that .
13.

 

Find the GCD of the polynomials 4(X-3)2 (X-1) (x+1)3 ; 6(X-1)2 (X+1)2 (X+7)
                                                                         OR

If Cos245 + Sin 30 = 2 Cos2A , Find Sec2A.
15. In the given figure DE || BC and AD : DB = 5 : 4
Find ( DFE)/( CFB)
16. Draw a cyclic quadrilateral ABCD in which BD = 4cm,A = 900, CD = 2.5cm and AB = 3cm
17. 
Calculate cost of living index from the following data :- 
    
Commodity
Quantity
Price in 1999
Price of 2000
P
5
4.20
6.00
R
4
5.00
8.50
A
3
8.00
10.50
G
7
9.00
11.50
S
8
12.50
16.00
18. An aeroplane takes 1 hour less for a journey of 1200 km. If its speed is increased by 100 km/hr, from its usual speed, find its usual speed.
19. The dimensions of a rectangular tank are 2 m, 7 m and 2 m. It is being filled with water using a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s. Calculate the time required to fill the tank.
20. 80% and 60% pure acid solutions are mixed to obtain 10 litres of 75% pure acid
         solution . Find the amount of each type of acid to be mixed to form the mixture.  

SectionC
21a

.

  b

 Draw graphically the following equations:
2y = x + 4
x + 2y = 4
A circle with centre O. AB and CD are two parallel chords on the same side of the centre. If the radius of the circle is 65 cm and the length of the chords are 112 cm and 126 cm respectively, find area of rectangle ABCD.
22a

.
22b

 Construct ABC such that AXB = 116o, AB = 7.8 cm, CF = 5 cm, CF AB.
X is the point of intersection of the altitudes AD and BE. Measure seg. AC
23  Page from a saving bank passbook for the year 2000 is given below. Calculate the interest at the end of the year at the rate of 5% p.a.
Date Particulars Amount withdrawn Rs. P. Amount deposited Rs. P. Balance
Rs. P.
          2000        
Jan 1 By balance – 1,120.00 1,120.00
11 By cash –    800.00 1,920.00
Feb 2 To cheque 300.00 – 1,620.00
Mar 10 By cash – 1,400.00 3,020.00
June 28 To cheque 500.00 – 2,520.00
Sept 5 By cash –    480.00 3,000.00
Dec 13 By cash – 1,200.00 4,200.00
24 Ramkumar has a total income of Rs. 95,000 excluding HRA. He pays a premium of
Rs. 2,000 half-yearly towards life insurance policy. Calculate the income tax he has to pay.
Assume the following rates:
Assume the following rates:
a) Standard deduction: 1/3rd of total income subject to a maximum of Rs. 20,000. (Rs. 25,000 if income is less than Rs. 1 lakh.)
b) Rate of tax
SLAB

i) Up to Rs. 50,000
ii) from Rs. 50,001 to Rs. 60,000
iii) from Rs. 60,001 to Rs. 1,50,000

iv) from Rs. 1,50,001 onwards
 
INCOME - TAX

Nil
(10% of the amount exceeding Rs. 50,000)
Rs. 1,000 + 20% of the amount exceeding Rs. 60,000
Rs. 19,000 + 30% of the amount exceeding Rs. 1,50,000
c) Rebate in tax 20% of the total savings subject to a maximum of Rs. 12,000
d) Surcharge 10% of the tax payable
25

 

 Solve for x :
4(x2 + 1/x2) + 8(x - 1/x) - 29 = 0 

                                                                     or

A tower in a city is 150 m high and a multistoried hotel at the city centre is 20 m high. The angle of elevation of the top of the tower at the top of the hotel is 5o. A building, h metres high, is situated on the straight road connecting the tower with the city centre at a distance of 1.2 km from the tower. Find the value of h if the top of the hotel, the top of the building and the top of the tower are in a straight line. Also find the distance of the tower from the city centre.
(Use tan 5o = 0.0875; tan 85o = 11.43

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