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Assignment 1

  Attempt all the questions 
  Part one is common for both ICSE and CBSE  but  choose your  board   for part  two
 
1. What number must be added to each of number of the numbers6,15,20,and 43 to make them propotional
2. A copper wire when bent in the form of a square enclose an area of 121square cm .If the same wire is bent in the form of a circle ,find the area of the circle.
3. Find the value of K so that the quadratic equation 4x2 - 2x + K = O has one root as the reciprocal of the other.
4. If the ratio of the roots of equation, lx2 + mx + m = 0, is p:q prove that:
5. A horse is placed far grazing inside a rectangular field with dimensions 70m by 52m and is tethered to one corner by a rope 21m. long. On how much area can it graze?
6. Prove that:
7. Without using trigonometric tables show that tan 5o tan 25o tan 65o tan 85o = 1.
8. Two poles of heights 6m and 11m stand vertically on a plane ground. If distance between their feet is 12m, determine the distance between their tops.
9. In the given figure find the value of p.
10.  AB is the diameter of the circle C (o, r). Chord CD is equal to radius OC, AC, BD produced intersect at P. Prove that ÐAPB = 60o which is constant.                                  
11. The size of 10 shirts in centimeters is given as 90, 95, 90, 105, 100, 95, 90, 95, 100, 90. Find the modal size (mode). If the size of one shirt is misread as 90 instead of 95. Find the correct modal size.
12. For the data:
1, 5, 7, x + 1, 9, x - 2, 3. If the mean is 4. Find the value of x. Using this value of s. Find median
13. David purchased a radiogram having a marked price of Rs, 6500 at 4% discount. If sales tax is charged at 7%. Find the amount David has to pay for purchasing the radiogram
14. The mean weight of 25 students of a class is 60 kg. If the mean weight of First 13 students of the class is 57 kg and that of the last 13 students is 63 kg. Find the weight of the 13th student.
15. Determine graphically the coordinates of the vertices of a triangle the equation of whose sides are y = x, 3y = x, x + y = 8.
16. The distance between Mumbai and Pune is 192 km. Travelling by Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speed of the two trains differ by 20 km/hr.
17. A cone of height 24 cm. has a curved surface are 550cm2. Find its volume.
18. If sec q + tan q =a. show that = sin q
19. If two sides of a cyclic quadrilateral are parallel prove that: (a) remaining two sides are equal and (b) both diagonals are equal.
20. 21. Construct a D ABC, in which BC = 6 cm, ÐA = 60o and median AD = 5cm. Also, construct another triangle, BPQ similar to triangle BAC such that the side BP = 3/2 BC.
21. Dinesh has his saving bank account in the state Bank of Patiala; His pass book entries are as follows:
Date
Particulars
Amount (Rs.)Withdrawn
Amount (Rs.)Deposited
Balance(Rs.)
1999
May, 9
By cash
-
1000.00
1000.00
May, 11
To cheque
350.00
-
650.00
July, 1
By cheque
-
1500.00
2150.00
July, 2
To cheque
500.00
-
1650.00
Aug, 4
To Ram Gopal
700.00
-
950.00
Sep, 20
To self
450.00
-
500.00

Rate of interest is 5% per annum compounded at the end of March and September. Calculate the interest due to him and balance on 1.10.99
22. Kalicharan has an annual income of Rs. 1,42,000 exclusive of HRA. He contributes Rs. 3000 per month in his Provident Fund A/c and pays an annual premium of Rs. 10,000 towards his LIC policy. He also donates Rs. 8000 to charitable trust (50% exemption). Calculate the income tax paid by him in the last month of the year, if his earler deduction for last 11 months for income tax were at the rate of Rs. 300 per month.


Assume the following for calculating the income tax.

(a) Standard Deduction
-
1/3rd of the total income subject to a max of Rs. 2,00,000. (Rs. 25, 000 if income is < Rs. 1,00,000
(b) Rate of Income Tax
Slab
Income Tax
(i) Upto Rs. 50000
-
No Tax
(ii) From Rs. 50001 to 60000
-
10% of the amount exceeding Rs. 50,000.
(iii) From Rs. 60001 to 1,50,000
-
Rs. 1000 + 20% of the amount exceeding Rs. 6,00,000.
(c) Rebate in tax
-
20% of the total saving subject to a maximum of Rs. 12,000.
(d) Surcharge
-
10% of the net tax payable.
23. Show that 3nx2 - 2mx + 3n = 0


24. A milk tanker cylindrical in shape having diameter 2 metres and length 4.2 metres supplies milk to the two booths in the ratio 3:2. One of the milk booths has rectangular vessel having base area 3.96 m2 and the other has a cylindrical vessel having diameter 2 metres. Find the level of milk in each of the two vessels.
25. From a window (h metres high above the ground) of a house in a street, the angle, of elevation and depression of the top and foot of another house on the opposite side of ht street are q and Æ respectively. Show that the height of the opposite house is h (1 + tan Æ cot q).
26. a) State that prove 'Basic Proportionality Theorem'.
(b) In the Figure if ÐADE = ÐB. Show that DADE ~ DABC. If AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm and BC = 4.2 cm. Find DE		                                 
27. a) Prove that if a chord is drawn through the point of contact of tangent to a circle, then the angles which this chord makes with the given tangent are equal respectively to the angles formed in the corresponding alternate segments.
(b) In a DABC, AB = AC and PAQ is a tangent to the circumc circle of DABC at the point A. Prove that PAQ is parallel to BC.		                         

Questions for ICSE's students

28.

B and C have coordinates (3, 2) and (0, 3). Find

  1. the image B' of B under reflection in the x axis

  2. the image C' of C under reflection in line BB'

  3. Calculate the length B' C

 

29. A sum of money is invested at interest compounded annually. The interest in two successive years was Rs. 450 and Rs. 480 respectively. Find the rate of interest.
30. A man invests Rs. 4000 in shares. He invests Rs. 800 in 7% shares at Rs. 80,
Rs. 1400 in 8% shares at Rs. 70 and the remainder in 9% shares. If all the shares have a face value of Rs. 100 each and his % return on investment is 10.25% at what price did he buy the 9% shares ? What was the yield from his investment in the 9% shares?
31.
  1. A function is defined as f(x) = x2 - 4, x Î R. Find the value of : f(4) - f(-4)/3.
  2. If f(x) = x2 + 2 where x is even,
              = x    2 - 2 where x is odd, and 2 £ x £ 5; x Î N,
    find the domain and range of this function and classify it.

 
32. The equation y = mx + c passes through the points
(1, 4) and (-2, -5). Determine the values of m and c

Questions for CBSE' students

28. Find the values of a and b for which the following system of equations has infinite number of solutions.

  x + 3y = 7
(a + b)x + (4a + b)y = 21
29. The gcd of two polynomials is (x - 1) and their lcm is (x6 - 1). If one of the polynomials is (x3 - 1). Find other.
30. Find the cost of living Index Number for the year 1998, using 1992 as base year, from the following data:
Commodity
quantity
in kg.
Rate per kg
(in 1992)
(in Rs.)
(in 1998)
A 15 10.00 15.00
B 20 7.00 8.00
C 24 5.00 6.50
D 05 16.00 16.00
E 09 40.00 60.00
31. Find the values of a and b for which the following system of equations has infinite number of solutions.

  x + 3y = 7
(a + b)x + (4a + b)y = 21
32. Prove: