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Assingment4
Attempt  all questions.
Part one is common for both ICSE and CBSE  but  choose your  board   for part  two
 
1. Evaluate (sec2A - 1)(1 - cosec2A ) 
2. Find the median of the following data:

46, 64, 87, 41, 58, 77, 35, 90, 55, 35, 96
If in the data, the observation 92 is replaced by 19, determine the new median
3. Evaluate without using trignometric table:

75o/sin 15o + sin 12o/cos 78o - cos 18o/sin 72o
4. The ages of two girls are in the ratio 5 : 7. Eight years ago their ages were in the ratio 7 : 13. Find their present ages. 
5. 
In Fig , OPQR is a rhombus, three of whose vertices 
.lie on a circle with centre

If the area of the rhombus is 323cm2   find the radius of the circle
6. 
Solve graphically the following system of linear equations:
            x + y = 3, 2x + 5y = 12 
7. A piece of cloth costs Rs. 200. If the piece were 5 m longer, and each metre of 
cloth costed Rs. 2 less, the cost of the piece would have remained unchanged.
How long is the piece and what is its original rate per metre             
8. Mrs Chatterjee opened a savings account in Canara Bank on 4th January, 2000, with Rs 2000. On 8th January, she deposited Rs 560 and on 10th January, she withdrew Rs 376·50 by a cheque. On 16th January she withdrew Rs 500 and on 23rd January she deposited Rs 235·45 by a cheque. She withdrew Rs 400 on 13th March. Write the entries in her passbook and find the interest due to her for the period ending 31st March at 5% p.a.
9. In Fig 2, ABCD is a parallelogram in which DC = 10 cm and BC = 43 cm
AP is perpendicular to DC. If  ADC = 60o, find the length of AP. 		           
10. A plane left 30 minutes late than the scheduled time and in order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hr from the usual speed. Find the usual time. 
11. 
Construct a ABC with AB = 4.4 cm, ACB = 65 and the median through C is of length 3.2 cm. Also,
            find the length of the altitude drawn from the vertex C on AB
12. The angle of elevation of a Jet plane from a point A on the ground is 60o. After a flight of 15 seconds  the angle of elevation changes to 30o  If the Jet plane is flying at a constant height 0f15003 m, find the speed of the Jet plane
13. 
The annual income of Rajesh(excluding HRA) is Rs. 1,65,000. He contributes Rs. 2000 per
  month in his Provident Fund and pays annual premium of R

s. 8,000 towards his Life Insurance
 Policy. Calculate the income tax paid by Rajesh in the last month of the year if his earlier
 deductions for 11 months for income tax were at the rate of Rs. 800 per month.

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
14. A trader takes a sample of 50 eggs and weighs them. The following table gives his findings :

Wt. in gms

Frequency

80-84
85-89
90-94
95-99
100-104
105-109
110-114

2
6
12
14
10
5
1

Calculate the mean weight to the nearest gm.
15. The diameter of a sphere is 18 cm. What is the length of the edge of a cube that has the same surface area as that of the sphere?
Give your answer correct to the nearest cm
16. 
The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire 
 of 28 cm diameter. Find the length of the wire.  (Marks 4)
17 
 Solve for x :
               4(x2 + 1/x2) + 8(x - 1/x) - 29 = 0 
18. In PQR, QS and RT are the altitudes on sides PR and PT, respectively. Prove that
QO OS = RO OT, where O is the point of intersection of the altitudes.
19. In the adjoining figure, O is the center of a circle. Ð OAB and Ð OCB are 30o and 40o respectively. Find Ð AOC. Show your steps of working. ima-circles22.gif (1255 bytes)
20. Sand is pouring from a pipe  at the rate of  18 cubic cm per sec . The falling sand forms a cone on the ground in such a way  that the hight of the cone ia always one sixth of the cone .Calculate the hight of the cone if pouring of sand is stopped after 110 seconds
21. If a : b = 1 : 4, find the value of (2a + b) : (3a + 5b)
22. In the adjoining figure, prove that :
  1. XY2 = YM . YZ
  2. XZ2 = MZ . YZ
23. Marks obtained by 70 students are given below:
Marks 20 70 50 60 75 90 40
No. of students 8 12 18 6 9 5 12

Find: (i) the median marks, (ii) the modal marks.

Questions for ICSE's students

24.  A  store has in stock 20 dozen shirts ,15 dozen trousers and 25 dozen pairs of sockc .If the selling price are Rs50 per shirt ,Rs90 per trouser  and Rs 12 per sock pair  .  Find the total amount the store owner will get after selling all the items in store ,  Use  matrix  method
25. Divide Rs. 12610 into 3 parts such that the amounts at 5% compound interest for 2, 3 and 4 years is the same
26. A man transfers his Rs. 100 shares from 10% at 75 to 16% at 80 and thereby increases his annual income by Rs. 2000. How many shares did he originally own?
27 Prove that x2 + 3x + 2 is one of the factors of f(x) = x3 + 2x2 - x - 2.
28 A and B are points in a plane at a distance of 10 cm from each other. Would it be possible for a point P to move in the plane such that the sum of the squares of the distances of P from A and B is a constant? If so, what is the possible locus of P, and what is the value of this constantge)
29. Given that (a, 2a) lie on the line y/2 = 3x - 6. Find the value of a 
 

Questions for CBSE' students

24 
Fill in the blanks in the following table and find the Crude Death Rate (CDR) for the data:  (Marks 2) 


  Age group(in years)              Population         Number of Deaths 


            0 - 15                            4,000                200 


            15 - 20                             -                       120

             25 - 40                           1,500                 100 


              40 - 50                           3,000                150 


             Above 50                          2,000                 - 


              Total                             13,000               700
25 
A part of monthly expenses of a family is constant and the remaining varies with the
 price of wheat. When the rate of wheat is Rs. 250 a quintal, the total monthly expenses
of the family are Rs. 1,000 and when it is Rs. 240 a quintal, the total monthly expenses
 of the family are Rs. 980. Find the total monthly expenses of the family when the cost of 
wheat is Rs 350 quintal
26 
Find the value of k for which the system of equations has no solution :
               3x - 4y + 7 = 0
               kx + 3y - 5 = 0  (Marks 2)
27. 
Find the values of k so that the quadratic equation
   2
x - 2x(1 +3k) + 7(3 + 2k) = 0
has equal roots
28 Find the G.C.D. and L.C.M. of the following polynomials: (2x2 – 8) and (x2 – 5x + 6).
 
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