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CBSE Model Paper no 1
Time allowed : 3 hours
Maximum Marks : 100
General Instructions :

(i) Question number 1 to 15 carry 2 marks each.
(ii) Question number 16 to 25 carry 4 marks each.
(iii) Question number 26 to 30 carry 6 marks each.
(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
 
1. 
Form a quadratic equation whose roots are 3 /2 and -5.
2. Find the median of the prime numbers between 16 to 54
3. evaluate:
sin² 20° +sin² 70° -tan²45° without using the trignometric tables
4. Show that
5. Given : ÐPQS = ÐPQR = 900 Show that
 QS2 + PR2 = PS2 + QR2
6. n the adjoining figure, O is the center of the circle. Find ÐDAC
7. The cost of an article is Rs. 856 and the rate of sales tax is 7%. If the customer pays
         only Rs. 856, inclusive of sales tax, find the reduction in the original price.
8. the mean of the following data is 14.5 Find the value of k.

      Marks obtained (x) 5 10 15 20 25
  Number of student (y) 3  6  4   k   3
9. Quadrilateral ABCD is a cyclic quadrilateral in which Ð A = 2ÐC. Find ÐA.
10. The sum of the numerator and denominator of a certain positive fraction is 11. If 1 is added to both numerator and denominator, the fraction is increased by 3/56. Find the fraction
11 If the area of a right-angled triangle is 300 square units and one side of the right angle is units, calculate the length of the other sides.
12. Find the GCD of x2 - 4x -12 ; x3 + 8
13. In the adjoining figure, EF is parallel to DC and DC is parallel to AB. Prove that
        AE/ED = BF/FC
14. In the adjoining figure DADC is an equilateral triangle . Find ÐBEC
15. If  a = c,  
    b     d        Prove that (2a+ 3b):(2c-3d)=(2a-3b)(2a+3d)    
16.  
17. Two years ago, a mans age was three times the square of his sons age. In three years time, his age will be four times his sons age. Find their present ages.
18. DrawÐABC = 40o. Take a point S in the interior of ÐABC. Draw a circle passing through the point S and touching sides of ÐABC.
19. Calculate the mean, correct to one decimal place for the following distribution:
Marks 0-10 10-20 20-30 30-40 40-50
No. of students 2 5 20 8 7
20. 25) Complete the following table and find the crude death rate from the table

Age Group

Population

Number of deaths

0 - 10

20,000

300

10 - 25

35,000

200

25 - 40

--

150

40 - 60

40,000

---

Above 60

10,000

350

 

1,20,000

1,200
21. 
The radius of a circle is less than twice the radius of the other by 1 cmThe sum of their areas is 34 p sq cm.
Find the radius of each circle.
22. 
Solve graphically 3x - y = .6, 2x + y = 4.
23 A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio of radius of cylinder to height of cylinder is 3 : 4.
24 In the adjoining figure two chordesAB andCD
of a circle  intersect each other at point P
outside the circle .If AB=5cm BP=3cm and PD=2 cm then find CD
25 The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?
26 deepak"s Annual Income is Rs. 74,600/- (excluding House Rent Allowance). His contribution to Provident Fund is Rs. 600 per month and he pays Rs. 2,600 as LIC premium during the year. Find the tax paid by him during the year

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
27 Use ruler and campass to construct   the tringle ABC in which BC=7cm and angle ABC =60  and AC-AB=1.5 cm .Construct a circle of radius 2cm to touch the angle ACB(6)
28 If x/a = y/b = z/c, prove that
       ax - by      +         by -cz      +       cz -ax          = 3.
   (a +b)(x -y)          (b +c)(y -z)        (c +a) (z -x)
29
Date Particulars Withdrawals
Rs. P.		 Deposits
Rs. P.		 Balance
Rs. P.
2000        
Jan 1 By balance – -- 1200.00
"  " 5 By cash – 500.00 1700.00
"  " 20 By cheque    - 700.00 2,400.00
Feb 15 To cash 500.00 1900.00
May  8 By cheque 1,000.00 2900.00
July12 By cheque 1500.00 4400.00
July20 To cheque 1000.00 3400.00
sep1 By cash – 1,200.00 4600.00
Oct5 To cheque 2000.00 2600.00
Dec15 By cheque 500.00 3,100.00

This is a page from pass book of Mr X"s saving Bank account in particular year is given above  .Assuming that  the intrest  rate is 5% p.a. and intrest is paid once in a year at the end of December . calculate the interest earned by Mr x at the end of the year
30 ABC is a tringle in  which AB=ACand Dis any point onBC .Prove that 
                           AB2 -AD2= BDxDC