Count the net number of odd days on the given date Step 2: Write:

Working Rules:

Step 1: Count the net number of odd days on the given date Step 2: Write:

For 0 odd days – Sunday For 1 odd day – Monday For 2 odd days – Tuesday

. . . .

For 6 odd days - Saturday

SOLVED EXAMPLES

1. If 11^th January 1997 was a Sunday then what day of the week was on 10^th January 2000?

Sol: Total number of days between 11^th January 1997 and 10^th January 2000 = (365 – 11) in 1997 + 365 in 1998 + 365 in 1999 + 10 days in 2000 = (50 weeks + 4 odd days) + (52 weeks + 1 odd day) +

(52 weeks + 1 odd day) + (1 week + 3 odd days)

Total number of odd days = 4 + 1 + 1 + 3 = 9 days = 1 week + 2 days

Hence, 10^th January, 2000 would be 2 days ahead of Sunday i.e. it was on Tuesday.

2. What day of the week was on 10^th June 2008?

Sol: 10^th June 2008 = 2007 years + First 5 months up to May 2008 + 10 days of June 2000 years have 0 odd days.

Remaining 7 years has 1 leap year and 6 ordinary years



2 + 6 = 8 odd days So, 2007 years have 8 odd days.

No. of odd days from 1^st January 2008 to 31^st May 2008 = 3+1+3+2+3 = 12 10 days of June has 3 odd days.

Total number of odd days = 8+12+3 = 23

23 odd days = 3 weeks + 2 odd days.

Hence, 10^th June, 2008 was Tuesday.

Brainstorming

1. The no. of odd days in 400 years is _______.

1. 1 2. 0 3. 3 4. 4

2. Smt. Indira Gandhi died on 31^st October, 1984. The day of the week is _____.

1. Monday 2. Tuesday 3. Wednesday 4. Friday

3. What will be the day of the week on April 29, 2005?

1. Friday 2. Tuesday 3. Saturday 4. Sunday

4. The first day of the year 1998 was Wednesday. If the birthday of Raju falls on 25^th June, then on which day of 1998 was his birthday?

1. Friday 2. Tuesday 3. Wednesday 4. Sunday

5. If you are born on 13^th April, 1992 which is a Saturday, then which day of the week is your birthday in 1993?

1. Sunday 2. Monday 3. Tuesday 4. Wednesday 6. Find the day of the week on 15^th July, 1776?

1. Sunday 2. Monday 3. Tuesday 4. Wednesday

7. How many odd days are there in 352 days?

1. 1 2. 2 3. 3 4. 4

8. If 9^th March, 1988 is Tuesday, on what day of the week will 9^th March, 1989 falls?

1. Sunday 2. Monday 3. Tuesday 4. Wednesday

9. What will be the day of the week on April 29, 2005?

1. Saturday 2. Monday 3. Tuesday 4. Friday

10. On which day of the week does 5^th June, 2001 fall?

1. Thursday 2. Monday 3. Tuesday 4. Wednesday

11. If Ram was born on 29^th June, 1988 which is Monday, on what day was your birthday in 1989?

1. Friday 2. Monday 3. Tuesday 4. Wednesday

12. Find the day of the week of April 16^th, 1976, if April 16^th 1974 was Tuesday?

1. Friday 2. Monday 3. Tuesday 4. Saturday

13. Find the day of the week on 15^th January, 1979?

1. Sunday 2. Monday 3. Friday 4. Wednesday

14. If 23^rd May, 2003 is a Friday, what day of the week will be 23^rd December?

1. Tuesday 2. Monday 3. Tuesday 4. Friday

15. January 3^rd, 1992 was a Friday. What day of the week was January 3^rd, 1993?

1. Sunday 2. Thursday 3. Friday 4. Saturday

16. On which day of the week does 28^th May, 2003 fall?

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

17. If your birthday is on 28^th May, 1991, then what was the day it was?

1. Tuesday 2. Wednesday 3. Friday 4. Sunday

18. What day of the week is 1^st March, 1990?

1. Sunday 2. Thursday 3. Tuesday 4. Friday

19. Which year will have the same calendar that of 2007?

1. 2008 2. 2013 3. 2010 4. 2018

20. Which year will have same calendar that of 2001?

1. 2002 2. 2005 3. 2006 4. 2007

21. You entered the college first time on 4^th June, 2001. What was the day?

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

22. The no. of odd days in an ordinary year is _______.

1. 1 2. 2 3. 3 4. 4

23. If 3^rd April, 2003 was Thursday then which day of the week is 28^th December of the same year?

1. Sunday 2. Monday 3. Tuesday 4. Wednesday

24. Which among the following is a leap year?

1. 2600 2. 2700 3. 2800 4. 3000

25. What day of the week was 25^th April, 1901?

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

26. Raju‟s brother was born on 7^th November, 1984. The day of the week was _____.

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

27. What was the day of the week on 23^rd July, 1970?

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

28. If today is Monday, then what day of the week will be 427^th day from today?

1. Sunday 2. Monday 3. Tuesday 4. Wednesday

29. Which day of the week was January 29^th, 1601?

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

30. If Sundays are holidays, and in a particular year 2^nd April is Sunday. Is 30^th September in that year a holiday?

1. Yes 2. No 3. Insufficient Data 4. None

31. On what dates of September 1972 did Wednesday

1. 6, 13, 20, 27 2. 4, 11, 18, 25 3. 5, 12, 19, 26 4. 3, 10, 17, 24 32. If 15^th February, 1995 was a Wednesday then 15^th February, 1994 was on which day?

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

33. Today is Saturday. After 100 days it will be _______.

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

34. On which day this year (2008) you celebrated the Independence Day?

1. Monday 2. Friday 3. Wednesday 4. Thursday

35. 4^th April, 2002 was Thursday. The day of the week on 4^th April, 2003 was ______.

1. Monday 2. Friday 3. Wednesday 4. Thursday

36. 31^st March, 2003 was Monday. The day of the week on 31^st March, 2004 was _____.

1. Monday 2. Friday 3. Wednesday 4. Thursday

37. 15^th August, 1947 was Friday. Find the day of the week on 15^th August, 1960.

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

38. 17^th May, 1989 was Wednesday. The day of the week on 9^th November, 1989 was _______.

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

39. 27^th October, 1992 was Tuesday. The day of the week on 29^th March, 1993 was ________.

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

40. The day of your birthday was __________

20. MENSURATION: 2D

Types of Plane Figures

1. Triangle 2. Quadrilateral 3. Polygon 4. Circle 5. Sector of a circle 6. Rectangular Paths 7. Circular paths

I. Triangle

(a). Any triangle

a, b and c are three sides of the triangle; h is the altitude and AC is the base.

Perimeter (P) : P = a + b + c = 2s

Area (A) : A =  2

1 base  altitude = 2

1  any side  length of r dropped on that side =

) c s ( ) b s ( ) a s (

s   

(b). Equilateral

a is the length of each side Perimeter (P) : P = 3a

Area (A) : A = 4

3 a²

(c). Right-angled

b, c are the lengths of the two legs Perimeter (P) : P = a + b + c = 2s

Area (A) : A =  2

1 product of two legs

(d). Isosceles

a is the length of two equal sides b is the base

BD is the perpendicular dropped on base such that it divides the base equally AD = CD =

2 b

Perimeter (P) : P = 2a+b

Area (A) : A = 4a² b² 4

b 

(e). Right-angled Isosceles

Perimeter (P) : P = 2  a  ( 2 +1)

A C

a a

A C

b c

90o

A C

D a

b/2 b/2

A C

c h

Hypotenuse - h a

Area (A) : A =  2

1 (a)²

II. Quadrilateral

(a). Any Quadrilateral

AC is the diagonal = d, DE and BF are two

perpendicular drawn on the diagonal (AC) P₁, and P₂ are the lengths of the two perpendiculars

Perimeter (P) : P = sum of the four sides. 2(b+Error! Objects cannot be created from editing field codes.) = 2 d²2A

Area (A): A = lb = l  d²l² = bError!

Objects cannot be created from editing field codes., when p and A are known and l and b are unknown.

Area (A) : A = 

a and b are two parallel sides, h is the height

Area (A) : A = 2

1 (a + b)  h = 2

1 (sum of parallel sides)

 (perpendicular distance between parallel sides)

(f). Parallelogram

b is the base

h is the perpendicular distance between the base and its opposite side

Area (A) : A = b  h = base  (perpendicular distance between the base and its opposite sides)

= 2  area of Δ ABD (or Δ BCD)

III. Polygon

Polygon is a n-sided closed figure bounded only by line segments.

In a polygon if the internal angle at each vertex is less than 180^o then the polygon is a convex polygon, else a concave polygon.

In document Arithmetic Material (Page 143-148)