## Friday, 18 May 2012

### Summer holidays homework 2012 (Class X)

DAVCPS NARELA-2012-13
Holiday’s Homework
Class-X
Subject-science
·        Find out  ingredients of face powder,nail polish ,lipsticks,boot polish,Shampoo,hair cream,cold creamand perfumes.
·        Ammonia is used in a lot of chemicals in beauty parlours in many products like hair colour,bleach etc.
Find out their harmful effects on Skin/body/hair
Soap having pH equal to 7 is best for skin.Find out Dove Soap has Ph equal to 7 or more than 7.Compare it with other bathing soaps.
Talk to yours neighbours and find  out which which soap is popular and find      out its  pH.
Talk to dermatologist which soap is best for skin.
This should be done either by
“  power point presention”
Or
Graphical represention of “Soap vs pH”
Or
Bar chart of “pH vs Soap”

MATHS  :
Learn tables up to 25.
1.    Design a crossword puzzle with mathematical terms.
2.     Compare performance of two cricket teams in final IPL match.
3.    Do 20 MCQ each from squares & squares roots, cube & cube roots ,Algebraic identities.
4.    Revise above chapters for test.
5.    Write divisibility tests by 2,3,4,5,7,9,10,11.
6.    PROJECT: Life history of two Indian Mathematicians.
7.    Prepare a model on Algebraic Identities.
8.    Define following terms: Adjacent angles, Altitude ,Arc ,chord ,secant, median , complementary angles, supplementary angles, transversal,dividend,divisor,variable,centroid,orthocenter,intercept.

FUN TIME
1   Solve   :  USA +  USSR = PEACE  I .e .replace letters by digits so that this becomes  a true equation.
2  In a party everybody shakes hands with everybody else & there are 36 handshakes in all,how many persons are there in the party ?
3  Express all numbers from 1 to 50 as the sum of atmost 4 square numbers.
4  The smallest number which can be expressed as the sum of two cubes in two different ways is Ramanujan number 1729.Find 4 more numbers with same property.
5  If we replace A by C,B by D,…,X by Z, Y by A , Z by B,what will following become?
I LOVE MATHEMATICS.
MATHEMATICS IS FUN.

PROBLEM  SOLVING IS THE HEART OF MATHEMATICS.

ASSIGNMENT

Q. Find the least number which must be subtracted from the following numbers to make them a perfect square?

1.    2361                                                  ans. 57
2.    194491                                              ans. 10
Q. Find the least number which must be added to the following numbers to make them a perfect square?
1.    5607                                                  ans. 18
2.    37460                                                ans. 176
Q.  Find the greatest number of 5 digit which is a perfect sqare?
Ans. 99856
Q. Find the least number of 4 digit which is a perfect square?
Ans. 1024
Q. The cost of levelling and turfing a square lawn at Rs. 2.50 per m square is RS. 13322.50  .find the cost of fencing it at Rs. 5 per metre?
Ans. 1460
Q. Find the square root of of 12.0068 correct to four decimal places?
Ans. 3.4651
Q.Find the square of 11 correct to five decimal places?
Ans.3.31662
Q. The area of a square field is 325 m square. Find the approximate length of one side of the field?
Ans. 18.030
Q. Find the length of a side of a sqare, whose area is equal to the area of a rectangle with sides 240 m and 70 m?
Ans. 129.6
Q. Find the cubes of :
1.  -13/8                                               Ans. -2197/512
2.  0.08                                                Ans. 0.00512
Q. Find the cubes root of each of the following natural number :
1.  2744                                                Ans. 14
2.  35937                                              Ans. 33
Q. Three numbers are in ratio 1:2:3. The sum of their cubes is 98784 . find the numbers.
Ans. 14,28,42
Q.Find the cube root of each of the following rational numbers :
1.  -125/729                                          Ans.  -5/9
2.  10648/12167                                   Ans.  22/23
Q. The volume of a cubical box is 474.552 cubic metres . find the length of each sides of the box?
Ans. 7.8 m
Q. Use  diagonal method to find squares of 89, 68, 854.
Ans.7921,4624,729316.
Q. Find 10 rational numbers between 3/5 & 3/4.
Q . Divide sum of  - 13/5 &12/7 by product of -  31/7 & - 1/2
Ans -2/5
Q The  area of square field is  121/4 sq.m.Find length of side of square.
Ans. 11/2 m.
Q. The cost of 7/3 metres of cloth is Rs 301/4,Find cost of cloth per metre.
Ans.32.25
Q. Simplify
(a)   (5x + 3 ) (x – 1) (3x – 2)
(b)  ( x+ 2) (5x – 3) – (2x +5 ) (4x- 3)
(c) a (b- c) –b(c-a) –c (a-b)
Q.Evaluate using identities
(a) 102 X 106
(b) 34 X 36
(c) 103 X 96
(d) 9.8 X 10.2
Ans.10812,1224, 9888, 99.96.
Q. If 2x + 3 = 14 &   2x – 3y = 2, find xy.
Ans. 8
Q.   Find 3x(2x- 7) – 3(x – 4)- 63 for x = -2.
Ans.  21
Q. if x+1/x=12 find x-1/x
Ans.  Root  140
Q. if x+1/x =9 find x4 +1/x4
Ans. 6239
Q.factorise :
1. 7a(2x-3) +3b (2x-3)                                                       Ans. (7a+3b)(2x-3)
2. ax+bx+ay+by                                                                Ans. (a+b)(x+y)
3. x4-81y4                                                                           Ans. (x-3y)(x+3y)(x2+9y2)
4. a2+2ab+b2-16                                                                 Ans. (a+b+4)(a+b-4)
5. 6xy-4y+6-9x                                                                   Ans. (2y-3)(3x-2)
Q. write unit digit of cube of following numbers :
1. 3375                                                                                Ans. 5
2. 1728                                                                                Ans. 2
3. 729                                                                                  Ans. 9
4. 4913                                                                                Ans. 7
Q. find area of rectangular box whose length and breadth are 4ab and 5cd respectively
Ans. 20abcd