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Assignment no 5
      Attept all the questions
      Part one is common for both ICSE and CBSE  but  choose your  board   for part  two
 
1. ABC ~ DEF. Area of ABC is 56 sq.cm. and area of DEF is 14 sq.cm. Find
2. Calculate the duplicate ratio of : :
3. Simplify : (1 + tan2 )(1 - sin )(1 + sin ) 
4. An electric pole and a telephone pole stand on the same ground.The electric pole is 6m. high and casts a shadow 8m.long.If the telephone pole casts a 10m. long shadow.Find it's height.
5. , ABCD is a rectangle with AD = 12 cm
and DC = 20 cm. Line segment DE
is drawn making an angle of 30with
 AD, intersecting AB in E.Find the
  lengths of DE and AE. 

 
6. Find the value of k such that sum of the roots of the quadratic equation

3x2 + (2k + 1)x - (k + 5) = 0 is equal to the product of its roots.
7. The following data has been arranged in ascending order: 12, 14, 17, 21, x, 26, 28, 32, 36. If the median of the data is 23, find x. If 32 is changed to 23, find the new median. (Marks 2)
8. If a cosq + b sinq = x, and b cosq - a sinq  = y,
show that a2 + b2 = x2 + y2.
9.  OABC is a rhombus whose three vertices A, B, and C lie on a circle
with centre O.f the  radius of the circle
 I is 10 cm, find the area of the rhombus.

 
10. sin (90° -) cos (90° - ) =   tan     
                                          1 +tan² 
11. Find the value of p for which 4x2 – 5x + p = 0, gives two equal roots.
12. Draw a line segment of length 10cm and determine the point that divides the given line segment internally in the ratio 5:4.
13. The mean weight of 25 students of a class is 60 kg. If the mean weight of the 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.
14.  The total salary of Manjeet Singh is Rs. 1,25,500 (excluding HRA) during a year. He pays a premium of Rs. 10,800 annually towards LIC and contributes Rs. 2,000 per month towards G.P.F. Rs. 250 are deducted each month from his salary as income tax. Calculate the income tax Manjeet Singh is to pay in the last month of the financial year.  

Assume the following for calculating income tax :

(a) Standard Deduction 1/3 of the total income subject to a maximum of Rs. 20,000
(Rs. 25,000 if income is less than Rs. 1 lac)
(b) Rates of Income tax

Slab

(i) Upto Rs. 50,000
(ii) From Rs. 50,001 to 60,000
(iii) From Rs. 60,001 to Rs. 1,50,000

  

Income Tax

No tax
10% of the amount exceeds Rs. 50,000
Rs. 1,000 + 20% of the amount exceeding Rs. 60,000
(c) Rebate in Tax 20% of the total savings subject to a maximum of Rs. 12,000
(d) Surcharge 10% of the tax payable
15. Sarla purchased an almirah, with a market price of Rs. 5600 at a discount of 5%. If the sales tax is charged at 10%, find the amount Sarla had to pay for purchasing the almirah
16. Determine graphically the co-ordinates of the vertices of the triangle, the equation of whose sides are:
y = x, 3y = x, x + y = 8. 
17. The sum of radius of base and the height of a solid cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, find the volume of the cylinder ( = 22/7). 
18. 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.
19. In fig BAC = 30o. Show that BC is equal to the radius of the circumcircle of ABC where centre is O.
20. A ladder 2 m long is placed against a vertical wall such that a man of 1.77 m height standing on the top rung just manages to look over the wall. Find the height of the wall if the ladder makes an angle of 600 with the ground. (Answer correct to two decimal places).
21. Draw a quadrilateral ABCD with AB = 5 cm, BC = DC = 6 cm, AD = 3 cm and internal ÐA = 600. Draw the bisectors of ÐA and ÐB and let them intersect at P.
  1. Measure and note the lengths of PA and PB
  2. Prove that P is equidistant from AD and BC.
22 The inner circumference of a circular jogging track is 1760 m. If the width of the track is 14 m find the outer circumference of the track.
23 A trader bought a number of articles for Rs 900. Five articles were damaged and he sold each of the rest at Rs 3 more than what he paid for it, thus getting a profit of Rs 150 on the whole transaction. Find the number of articles he bought.
24 DrawÐABC = 40o. Take a point S in the interior of ÐABC. Draw a circle passing through the point S and touching sides of ÐABC.
25

A page from the pass book of Ram Lal's Saving Bank Account in a particular year is given below :-

Date Particulars Amt. Withdrawn
Rs.  P.		 Amt. Deposited
Rs.  P.		 Balance
Rs.  P.
Jan. 1 By Balance 1200.00
Jan. 5 By Cash 500.00 1700.00
Feb. 20 By Cash 700.00 2400.00
Feb. 25 To Cheque 500.00 1900.00
May, 8 By Cash 1000.00 2900.00
July, 12 By Cash 1500.00 4400.00
July, 20 To Cheque 1000.00 3400.00
Sept. 1 By Cash 1200.00 4600.00
Oct. 5 To Cheque 2000.00 2600.00
Dec. 15 By Cash 500.00 3100.00

Assuming the rate of interest is 5% p.a. and interest is paid once in a year, at the end of December, calculate the interest earned by Ram Lal at the end of the year.
26 Find the mean for the following frequency distribution :

Marks

Number of students

  

Marks

Number of students

0 - 9
10 - 19
20 - 29
30 - 39
40 - 49

2
5
7
8
11

  

50 - 59
60 - 69
70 - 79
80 - 89
90 - 99

12
9
7
5
4

Questions for ICSE students

27  The following arrow diagram represents a relation R. Represent the relation R in
(i) roster from   (ii) builder form.
28 The points A(2, -3), B(3, 4) and C(7, 5) are the vertices of DABC.
(i) Write the co-ordinates of A1, B1, C1 where DABC is reflected in the x-axis to DA1B1C1
(ii) Write the co-ordinates of A2, B2, C2 when DA1B1C1 is reflected in the y-axis to DA2B2C2.
(iii) Write the co-ordinates of A3, B3, C3 when DA2B2C2 is reflected in the origin to DA3B3C3.
29       i   Find  the order of  A
ii   Find aij  = 7/2 
iii  Find the elements  a21 a31
30 A man borrows Rs. 8000 at 5% p.a. C. I. and repays Rs. 400 at the end of each year. Find the amount of loan outstanding at the end of the second year
31 Mr. Mehta invests Rs. 30000 in shares paying 6% and sells all of them at Rs. 110 each. He re-invests his sale proceeds partly in 6% shares at Rs. 120 and balance in 9% shares at Rs. 90, and his income increases by Rs. 750. How much does he invest in each?
   


 
27 Solve for x:
54x - 3 x 52x + 1 = 250 
28 Find the G.C.D. of the following polynomials:
(8x3 – 8x2 + 8x) and (28x3 + 28)
29 State and prove Pythagoras theorem
31. Show that : - a2(b + c) + b2 (c + a) + c2 (a + b) +3abc = (a+b+c)(ab + bc + ca).
32.