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Assignment no 2
      Attempt all the questions
      Part one is common for both ICSE and CBSE  but  choose your  board   for part  two
 
1. For the data 7, 10,14, x +2, 17,2-2, if the mean is 12, find the value of x. Using this find the mode of the data
2. Sarita buys goods worth Rs. 5,500. She gets a rebate of 5% on it. After getting the rebate of sales tax of 5% is charged, find the amount she will have to pay for the goods
3.  D and E are points on the sides AB and AC respectively of a D ABC such that AB= 8 cm, DB=12 cm, Ae=6cm, EC=9 cm. Prove that
BC= DE.
4. If Cosec A = Ö2, find the value of
5. In the fig. below, O is the circumcentre of D ABC, AB=BC. If ÐOBC
= 24o, find ÐBCA
6.  The circumference of the edge of a hemispherical bowl is 132 cm. Find the capacity of the bowl
7. Solve the equation graphically
x + 3y = 6
3x - 5y = 18
Hence, find the value of 'K' of 7x +3y = K.
8.  In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD2 = 7 AB2
9. 15 In the fig, PA & PB are tangents from P to the circle with centre O. M is the pt. on the circle. Prove that PL + LM = PN + NM               
10. .Prove

 (sin A +sec A)2 + ( cos A + cosecA)2 = (1+secA. cosec A)
11. The data given below gives the earnings of 350 workers in a cotton mill. Find the average earnings of the groups.
Weekly Wages
(Rs.)
No. of workers
160-180
40
180-200
54
200-220
60
220-240
72
240-260
45
260-280
32
280 - 300
28
300-320
15
320-340
4
12.
Date
1999
Particulars
Amt.
Withdrawn
(Rs.)
Amt.
depostied
(Rs.)
Balances
(Rs.)
Jan, 11 by cash
-
1000.00
1000.00
Jan, 30 to cheque
600.00
-
400.00
Feb, 10 by cash
-
2,500.00
2,900.00
Feb, 15 To cheque
500.00
-
2,400.00
Apr, 5 By cash
-
300.00
2,700.00
Apr, 30 To Ramesh
800.00
-
1,900.00
July, 14 To self
1000.00
-
900.00
Sept, 11 by cash
-
1,200.00
2,100.00

Calculate the amt. received by the person at the end of sept. If the rate of interest is 5% p.a.
13.  The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to base of its volume is th of the given cone, at what height above the base is the section made?
14. In the adjoining figure,
O is the center of the circle.
Ð AOE = 1500, Ð DAO = 510.
Calculate the sizes of
the angles CEB and CBE.		             
15.  The angles of elevation of the top of a hill at the city Centre of two towns on either side of the hill are observed to be 30o & 60o, If the distance uphill from the city centre is 12km. Fin kilometer the distance uphill from city centre correct upto two places of decimal
16.

Shyam Lal's monthly salary is Rs. 22,500(HRA not included). His monthly contribution to GPF = Rs. 5000. He pays Rs. 12,000as LIC premium & invests Rs. 3000 in NSC. He donates Rs. 10,000 towards PM relief fund (100% tax exemption) and Rs. 8000 to a charitable trust (50% tax exemption). Rs. 2500 are deducted each month from his salary as income tax fro 11 months. Calculate the income tax payable including surchage by him in the last month of the year.

Assume the foll. for calculating income tax

a) Standard deduction 1/3rd of the total amount of annual income subject to a max. of Rs. 20000 (Rs. 25,000 if income is less than Rs. 1 lakh
b) Rate of Income tax slab:
(i) upto Rs. 50,000 No tax
(ii) from Rs. 50,001 to Rs. 60,000 10% of the amt. exceeding Rs. 50,000
(iii) from Rs. 60,001 to Rs. 1,50,000 Rs. 1000 + 20% of the amt. exceeding Rs. 60,000
(iv) from 1,50,001 onwards Rs. 19,000 + 30% of the amt. exceeding Rs. 1,50,000
(c) Rebate in tax 20% of the total saving subject to a max. of Rs. 12,000.
(d) Surcharge 10% of the net tax payable
17. Solve for x:
  + 8 =29, x¹ 0
18.

 Construct a DABC in which BC = 6 cm. ÐA = 60o & median AD= 5 cm, Also construct DPQR similar to DBAC such that DP= BC. Also write the steps of construction
19. In the adjoining figure ABC is a triangle right angled at B. BC = 21 cm and AB = 28 cm. A semi-circle with AC as diameter and a quarter circle with BC as radius are drawn. Calculate the area of the shaded portion                     par2-cirumf19.gif (3568 bytes)
20. Solve for x : = 5
21. 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 .
22. Some students wished to find the height X of a building and the height Y of the flag pole on the building. They made the measurements as shown in the adjoining figure. Find X and Y. (Give your answer correct to the nearest metre).                 ima-height08.gif (1173 bytes)
 

Qestions for ICSE's students

23. A = { x : - 2 < x + 1 £ 5, x e R}
B = { x : - 3 < x £ 3, x e R}
Plot (a) A Ç B (a) A' Ç B on separate number lines
24 wpe8.gif (2636 bytes)
25 The points A(4, 3) and B(3, -1) are both reflected in the origin to A' and B' respectively. Find the coordinates of A' and B'. What type of figure is formed by ABA'B'? Would this type of figure be formed for any two point A and B reflected in the origin?
26. A sum of Rs. 16800 is borrowed @ 10% C.I. p.a. to be paid back in 2 equal instalments at the end of each year. Find the value of each instalment
27 Given f(x) = 3x2 - 4, x Î Z :
  1. Find the elements of the domain whose image is 239.
  2. Find x if f(x) = 44.
28 A person invested 20%, 30% an 25% of his savings in buying shares of three different companies A, B and C which declared dividends of 10%, 12% and 15% respectively. If his total annual income on account of dividends be Rs. 2337.50, find his savings and the amount which he invested buying shares of each company.
29 Using factor theorem find whether (x + 2) and (x - 3) are factors of the polynomial x3 - 3x2 - 4x + 12. If yes, factorise the given polynomial.
   

Questions for CBSE' students

23 For what values of p the quadratic polynomial px2 - 2x +2 can be factorized into real linear factors
24 Find the g.c.d of x3-y3 and x2y-y2
25  Reduce:in the lowest form.
26 the values of a and b for which the following system of equations has infinite number of solutions.
(a-b)x + ay=7
(a + b)x +2ay=a+11
27 Simplify:
28

Calculate the cost of living index number for the year 1994 taking 1990 as the base year from the foll. data:-

Commodity
Quantity
Price per
(in 1990)
Unit in Rs.
(In 1994)
A
80
10.00
14.00
B
20
6.50
10.00
C
10
6.00
8.00
D
25
42.00
50.00
E
40
20.00
25.00
F
25
18.00
20.00

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