APTITUDE TECHNIQUES FOR NUMBERS

1.  NUMBERS

    

IMPORTANT FACTS AND FORMULAE

I..Numeral : In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number.

 A group of digits, denoting a number is called a numeral.

 We represent a number, say 689745132 as shown below :

Ten Crores (108)	Crores(107)	Ten Lacs (Millions) (106)	Lacs(105)	Ten Thousands (104)	Thousands (103)	Hundreds (102)	Tens(101)	Units(100)
6	8	9	7	4	5	1	3	2

We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred and thirty-two'.

II  Place Value or Local Value of a Digit in a Numeral :

In the above numeral :

Place value of 2 is (2 x 1) = 2; Place value of 3 is (3 x 10) = 30;

Place value of 1 is (1 x 100) = 100 and so on.

Place value of 6 is 6 x 10⁸ = 600000000        

III.Face Value : The face value of a digit in a numeral is the value of the   digit itself at whatever place it may be. In the above numeral, the face value of 2 is 2; the face value of 3 is 3 and so on.

IV.TYPES OF NUMBERS

1.Natural Numbers : Counting numbers 1, 2, 3, 4, 5,..... are called natural

numbers.

2.Whole Numbers : All counting numbers together with zero form the set of whole
numbers. Thus,

        (i) 0 is the only whole number which is not a natural number.

        (ii) Every natural number is a whole number.

3.Integers : All natural numbers, 0 and negatives of counting numbers i.e.,
{…, -3,-2,-1, 0, 1, 2, 3,…..} together form the set of integers.

(i) Positive Integers : {1, 2, 3, 4, …..} is the set of all positive integers.

(ii) Negative Integers : {- 1, - 2, - 3,…..} is the set of all negative integers.

(iii) Non-Positive and Non-Negative Integers : 0 is neither positive nor

negative. So, {0, 1, 2, 3,….} represents the set of non-negative integers, while

{0, -1,-2,-3,…..} represents the set of non-positive integers.

4.  Even Numbers : A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc.

5.  Odd Numbers : A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc.

6.  Prime Numbers : A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.

Prime numbers upto 100 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

47,  53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Prime numbers Greater than 100 : Letp be a given number greater than 100. To find out whether it is prime or not, we use the following method :

Find a whole number nearly greater than the square root of p. Let k > *jp. Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime.

e.g,,We have to find whether 191 is a prime number or not. Now, 14 > V191.

Prime numbers less than 14 are 2, 3, 5, 7, 11, 13.

191 is not divisible by any of them. So, 191 is a prime number.

7.Composite Numbers : Numbers greater than 1 which are not prime, are known as composite numbers, e.g., 4, 6, 8, 9, 10, 12.

Note :    (i) 1 is neither prime nor composite.

(ii) 2 is the only even number which is prime.

(iii) There are 25 prime numbers between 1 and 100.

8.  Co-primes : Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes,

V.TESTS OF DIVISIBILITY

1.  Divisibility By 2 : A number is divisible by 2, if its unit's digit is any of 0, 2, 4, 6, 8.

Ex. 84932 is divisible by 2, while 65935 is not.

2.  Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3.

Ex.592482 is divisible by 3, since sum of its digits = (5 + 9 + 2 + 4 + 8 + 2) = 30, which is divisible by 3.

But, 864329 is not divisible by 3, since sum of its digits =(8 + 6 + 4 + 3 + 2 + 9) = 32, which is not divisible by 3.

3.  Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4.

Ex. 892648 is divisible by 4, since the number formed by the last two digits is

48,  which is divisible by 4.

But, 749282 is not divisible by 4, since the number formed by the last tv/o digits is 82, which is not divisible by 4.

4.  Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5. Thus, 20820 and 50345 are divisible by 5, while 30934 and 40946 are not.

5.  Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3. Ex. The number 35256 is clearly divisible by 2.

Sum of its digits = (3 + 5 + 2 + 5 + 6) = 21, which is divisible by 3. Thus, 35256 is divisible by 2 as well as 3. Hence, 35256 is divisible by 6.

6.   Divisibility By 8 : A number is divisible by 8, if the number formed by the last

three digits of the given number is divisible by 8.

Ex. 953360 is divisible by 8, since the number formed by last three digits is 360, which is divisible by 8.

But, 529418 is not divisible by 8, since the number formed by last three digits is 418, which is not divisible by 8.

7.   Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible

by 9.

Ex. 60732 is divisible by 9, since sum of digits * (6 + 0 + 7 + 3 + 2) = 18, which is divisible by 9.

But, 68956 is not divisible by 9, since sum of digits = (6 + 8 + 9 + 5 + 6) = 34, which is not divisible by 9.

8.   Divisibility By 10 : A number is divisible by 10, if it ends with 0.

Ex. 96410, 10480 are divisible by 10, while 96375 is not.

9.   Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.

Ex. The number 4832718 is divisible by 11, since :

(sum of digits at odd places) - (sum of digits at even places)

- (8 + 7 + 3 + 4) - (1 + 2 + 8) = 11, which is divisible by 11.

10.  Divisibility By 12 ; A number is divisible by 12, if it is divisible by both 4 and

3.

Ex. Consider the number 34632.

(i) The number formed by last two digits is 32, which is divisible by 4,

(ii) Sum of digits = (3 + 4 + 6 + 3 + 2) = 18, which is divisible by 3. Thus, 34632 is divisible by 4 as well as 3. Hence, 34632 is divisible by 12.

11.   Divisibility By 14 : A number is divisible by 14, if it is divisible by 2 as well as 7.

12.  Divisibility By 15 : A number is divisible by 15, if it is divisible by both 3 and 5.

13.  Divisibility By 16 : A number is divisible by 16, if the number formed by the last4  digits is divisible by 16.

Ex.7957536 is divisible by 16, since the number formed by the last four digits is 7536, which is divisible by 16.

14.  Divisibility By 24 : A given number is divisible by 24, if it is divisible by both3  and 8.

15.  Divisibility By 40 : A given number is divisible by 40, if it is divisible by both

5  and 8.

16.  Divisibility By 80 : A given number is divisible by 80, if it is divisible by both 5 and 16.

Note : If a number is divisible by p as well as q, where p and q are co-primes, then the given number is divisible by pq.

If p arid q are not co-primes, then the given number need not be divisible by pq,

even when it is divisible by both p and q.

Ex. 36 is divisible by both 4 and 6, but it is not divisible by (4x6) = 24, since

4  and 6 are not co-primes.

VI   MULTIPLICATION BY SHORT CUT METHODS

1.  Multiplication By Distributive Law :

(i) a x (b + c) = a x b + a x c    (ii) ax(b-c) = a x b-a x c.

Ex.   (i) 567958 x 99999 = 567958 x (100000 - 1)

= 567958 x 100000 - 567958 x 1 = (56795800000 - 567958) = 56795232042. (ii) 978 x 184 + 978 x 816 = 978 x (184 + 816) = 978 x 1000 = 978000.

2.  Multiplication of a Number By 5ⁿ :  Put n zeros to the right of the multiplicand and divide the number so formed by 2ⁿ

Ex. 975436 x 625 = 975436 x 5⁴= 9754360000 =   609647600

                                                            16

VII.   BASIC FORMULAE

1. (a + b)² = a² + b² + 2ab                      2. (a - b)² = a² + b² - 2ab

3. (a + b)² - (a - b)² = 4ab                       4. (a + b)² + (a - b)² = 2 (a² + b²)

5.  (a² - b²) = (a + b) (a - b)

6.  (a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)

7.  (a³ + b³) = (a +b) (a² - ab + b²)        8. (a³ - b³) = (a - b) (a² + ab + b²)

9. (a³ + b³ + c³ -3abc) = (a + b + c) (a² + b² + c² - ab - bc - ca)

10. If a + b + c = 0, then a³ + b³ + c³ = 3abc.

VIII.  DIVISION ALGORITHM OR EUCLIDEAN ALGORITHM

If we divide a given number by another number, then :

Dividend = (Divisor x Quotient) + Remainder

IX.     {i) (xⁿ - aⁿ ) is divisible by (x - a) for all values of n.

           (ii) (xⁿ - aⁿ) is divisible by (x + a) for all even values of n.

           (iii) (xⁿ + aⁿ) is divisible by (x + a) for all odd values of n.

X. PROGRESSION

A succession of numbers formed and arranged in a definite order according to certain definite rule, is called a progression.

1. Arithmetic Progression (A.P.) : If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P.

An A.P. with first term a and common difference d is given by a, (a + d), (a + 2d),(a + 3d),.....

The nth term of this A.P. is given by T_n =a (n - 1) d.

The sum of n terms of this A.P.

S_n = n/2 [2a + (n - 1) d] = n/2   (first term + last term).

SOME IMPORTANT RESULTS :

 (i) (1 + 2 + 3 +…. + n) =n(n+1)/2

(ii) (l² + 2² + 3² + ... + n²) = n (n+1)(2n+1)/6

(iii)  (1³ + 2³ + 3³ + ... + n³) =n²(n+1)²

2.   Geometrical Progression (G.P.) : A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression.

The constant ratio is called the common ratio of the G.P. A G.P. with first term a and common ratio r is :

a, ar, ar²,

In this G.P. T_n = ar^n-1

sum of the n terms, Sn=   a(1-rⁿ)

                                          (1-r)

SOLVED EXAMPLES

Ex. 1. Simplify :   (i) 8888 + 888 + 88 + 8   

                              (ii) 11992 - 7823 - 456  

Sol.   i )  8888                       ii) 11992 - 7823 - 456 = 11992 - (7823 + 456)

                888                                                            = 11992 - 8279 = 3713-

                  88                                  7823                         11992

         +         8                               +   456                      -   8279

               9872                                  8279                          3713

Ex. 2, What value will replace the question mark in each of the following equations ?

(i) ? - 1936248 = 1635773            (ii) 8597 - ? = 7429 - 4358

Sol.  (i) Let x  - 1936248=1635773.Then, x = 1635773 + 1936248=3572021.                 (ii) Let 8597 - x = 7429 - 4358.

Then, x = (8597 + 4358) - 7429 = 12955 - 7429 = 5526.

 Ex. 3. What could be the maximum value of Q in the following equation?          5P9 + 3R7 + 2Q8 = 1114                     

Sol. We may analyse the given equation as shown :                     1   2     

Clearly, 2 + P + R + Q = ll.                                                           5   P  9

So, the maximum value of Q can be                                                3   R  7

(11 - 2) i.e., 9 (when P = 0, R = 0);                                               2   Q  8

                                                                                                      11  1   4

Ex. 4. Simplify : (i) 5793405 x 9999  (ii) 839478 x 625

Sol.

i)5793405x9999=5793405(10000-1)=57934050000-5793405=57928256595.b

ii) 839478 x 625 = 839478 x 5⁴ = 8394780000 = 524673750.

                                                            16

Ex. 5. Evaluate : (i) 986 x 237 + 986 x 863    (ii) 983 x 207 - 983 x 107

Sol.

(i) 986 x 137 + 986 x 863 = 986 x (137 + 863) = 986 x 1000 = 986000.

(ii) 983 x 207 - 983 x 107 = 983 x (207 - 107) = 983 x 100 = 98300.

Ex. 6. Simplify : (i) 1605 x 1605    ii) 1398 x 1398

Sol.

i) 1605 x 1605 = (1605)² = (1600 + 5)² = (1600)² + (5)² + 2 x 1600 x 5

                                                               = 2560000 + 25 + 16000 = 2576025.

(ii) 1398 x 1398 - (1398)² = (1400 - 2)²= (1400)² + (2)² - 2 x 1400 x 2

                                                         =1960000 + 4 - 5600 = 1954404.

Ex. 7. Evaluate : (313 x 313 + 287 x 287).

Sol.

 (a² + b²) = 1/2 [(a + b)² + (a- b)²]

(313)² + (287)² = 1/2 [(313 + 287)² + (313 - 287)²] = ½[(600)² + (26)²]

= 1/2 (360000 + 676) = 180338.

Ex. 8. Which of the following are prime numbers ?

(i) 241           (ii) 337         (Hi) 391           (iv) 571

Sol.                             

(i)         Clearly, 16 > Ö241. Prime numbers less than 16 are 2, 3, 5, 7, 11, 13.

             241 is not divisible by any one of them.

         241 is a prime number.

                                   

(ii)        Clearly, 19>Ö337. Prime numbers less than 19 are 2, 3, 5, 7, 11,13,17.          

             337 is not divisible by any one of them.

          337 is a prime number.

(iii)       Clearly, 20 > Ö39l". Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19.

           We find that 391 is divisible by 17.

          391 is not prime.

(iv)       Clearly, 24 > Ö57T. Prime numbers less than 24 are 2, 3, 5, 7, 11, 13, 17, 19, 23.

            571 is not divisible by any one of them.

         571 is a prime number.

 Ex. 9. Find the unit's digit in the product (2467)163 x (341)72.

Sol. Clearly, unit's digit in the given product = unit's digit in 7¹⁵³ x 1⁷².                                 

       Now, 74 gives unit digit 1.

       7¹⁵²  gives unit digit 1,

  \ 7¹⁵³  gives unit digit (l x 7) = 7. Also, 1⁷² gives unit digit 1.

       Hence, unit's digit in the product = (7 x 1) = 7.

Ex. 10. Find the unit's digit in (264)¹⁰² + (264)¹⁰³

Sol. Required unit's digit = unit's digit in (4)¹⁰² + (4)^103.

       Now, 4²  gives unit digit 6.

   \(4)¹⁰² gives unjt digit 6.

   \(4)103 gives unit digit of the product (6 x 4) i.e., 4.

       Hence, unit's digit in (264)m + (264)103 = unit's digit in (6 + 4) = 0.

 Ex. 11. Find the total number of prime factors in the expression (4)¹¹ x (7)⁵ x (11)².

Sol. (4)¹¹x (7)⁵ x (11)² = (2 x 2)¹¹ x (7)⁵ x (11)² = 2¹¹ x 2¹¹ x7⁵x 11² = 2²² x 7⁵ x11²

       Total number of prime factors = (22 + 5 + 2) = 29.

Ex.12. Simplify :    (i) 896 x 896 - 204 x 204

                                (ii) 387 x 387 + 114 x 114 + 2 x 387 x 114

                                (iii) 81 X 81 + 68 X 68-2 x 81 X 68.

Sol.

(i)  Given exp  =  (896)² - (204)² = (896 + 204) (896 - 204) = 1100 x 692 = 761200.

(ii) Given exp  = (387)²+ (114)²+ (2 x 387x 114)

                        = a² + b² + 2ab,  where a = 387,b=114

                        = (a+b)² = (387 + 114 )² = (501)² = 251001.

(iii) Given exp = (81)² + (68)² – 2x 81 x 68 = a² + b² – 2ab,Where a =81,b=68

                        =  (a-b)² = (81 –68)² = (13)^{2 = 169.}

Ex.13. Which of the following numbers is divisible by 3 ?

(i) 541326                                 (ii) 5967013

Sol.

(i) Sum of digits in 541326 = (5 + 4 + 1 + 3 + 2 + 6) = 21, which is divisible by 3.

Hence, 541326 is divisible by 3.

(ii) Sum of digits in 5967013 =(5+9 + 6 + 7 + 0+1 +3) = 31, which is not divisible by 3.

Hence, 5967013 is not divisible by 3.

Ex.14.What least value must be assigned to * so that the number 197*5462 is r 9 ?

Sol.

Let the missing digit be x.

Sum of digits = (1 + 9 + 7 + x + 5 + 4 + 6 +»2) = (34 + x).

For (34 + x) to be divisible by 9, x must be replaced by 2 .

Hence, the digit in place of * must be 2.

Ex. 15. Which of the following numbers is divisible by 4 ?

(i) 67920594                    (ii) 618703572

Sol.     

(i) The number formed by the last two digits in the given number is 94, which is not divisible by 4.

Hence, 67920594 is not divisible by 4.

(ii) The number formed by the last two digits in the given number is 72, which is divisible by 4.

Hence, 618703572 is divisible by 4.

Ex. 16. Which digits should come in place of * and $ if the number 62684*$ is divisible by both 8 and 5 ?

Sol.     

Since the given number is divisible by 5, so 0 or 5 must come in place of $. But, a number ending with 5 is never divisible by 8. So, 0 will replace $.

Now, the number formed by the last three digits is 4*0, which becomes divisible by 8, if * is replaced by 4.

Hence, digits in place of * and $ are 4 and 0 respectively.

Ex. 17. Show that 4832718 is divisible by 11.

Sol.    (Sum of digits at odd places) - (Sum of digits at even places)

                                          = (8 + 7 + 3 + 4) - (1 + 2 + 8) = 11, which is divisible by 11.

            Hence, 4832718 is divisible by 11.

Ex. 18. Is 52563744 divisible by 24 ?

Sol.  24 = 3 x 8, where 3 and 8 are co-primes.           

        The sum of the digits in the given number is 36, which is divisible by 3. So, the                       given number is divisible by 3.

         The number formed by the last 3 digits of the given number is 744, which is  divisible by 8. So, the given number is divisible by 8.

         Thus, the given number is divisible by both 3 and 8, where 3 and 8 are co-primes.

So, it is divisible by 3 x 8, i.e., 24.

Ex. 19. What least number must be added to 3000 to obtain a number exactly divisible by 19 ?

Sol. On dividing 3000 by 19, we get 17 as remainder.

    \Number to be added = (19 - 17) = 2.

Ex. 20. What least number must be subtracted from 2000 to get a number exactly divisible by 17 ?

Sol. On dividing 2000 by 17, we get 11 as remainder.

     \Required number to be subtracted = 11.

Ex. 21. Find the number which is nearest to 3105 and is exactly divisible by 21.

Sol. On dividing 3105 by 21, we get 18 as remainder.

     \Number to be added to 3105 = (21 - 18) - 3.

        Hence, required number = 3105 + 3 = 3108.

Ex. 22. Find the smallest number of 6 digits which is exactly divisible by 111.

Sol. Smallest number of 6 digits is 100000.

       On dividing 100000 by 111, we get 100 as remainder.

    \Number to be added = (111 - 100) - 11.

        Hence, required number = 100011.-

Ex. 23. On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor.

                            Dividend - Remainder      15968-37     

Sol.     Divisor = -------------------------- = ------------- = 179.

                                       .Quotient                    89

Ex. 24. A number when divided by 342 gives a remainder 47. When the same number ift divided by 19, what would be the remainder ?

Sol.   On dividing the given number by 342, let k be the quotient and 47 as remainder.

          Then, number – 342k + 47 = (19 x 18k + 19 x 2 + 9) = 19 (18k + 2) + 9.

       \The given number when divided by 19, gives (18k + 2) as quotient and 9 as remainder.

Ex. 25. A number being successively divided by 3, 5 and 8 leaves remainders 1, 4

and 7 respectively. Find the respective remainders if the order of divisors be reversed,

Sol.

3	X
5	y	- 1
8	z	- 4
	1	- 7

\z = (8 x 1 + 7) = 15; y = {5z + 4) = (5 x 15 + 4) = 79; x = (3y + 1) = (3 x 79 + 1) = 238.

Now,

8	238
5	29	- 6
3	5	- 4
	1	- 9,

\Respective remainders are 6, 4, 2.

Ex. 26. Find the remainder when 2³¹ is divided by 5.

 Sol.    2¹⁰ = 1024. Unit digit of 2¹⁰ x 2¹⁰ x 2¹⁰ is 4 [as 4 x 4 x 4 gives unit digit 4].

        \Unit digit of 231 is 8.

            Now, 8 when divided by 5, gives 3 as remainder.

            Hence, 231 when divided by 5, gives 3 as remainder.

Ex. 27. How many numbers between 11 and 90 are divisible by 7 ?

Sol.  The required numbers are 14, 21, 28, 35, .... 77, 84.

        This is an A.P. with a = 14 and d = (21 - 14) = 7.

        Let it contain n terms.

        Then, T_n = 84   =>  a + (n - 1) d = 84

                                  =>   14 + (n - 1) x 7 = 84   or n = 11.

     \Required number of terms = 11.

Ex. 28. Find the sum of all odd numbers upto 100.

Sol. The given numbers are 1, 3, 5, 7, ..., 99.

        This is an A.P. with a = 1 and d = 2.

        Let it contain n terms. Then,

        1 + (n - 1) x 2 = 99 or n = 50.

     \Required sum = n (first term + last term)

                                   2

                                = 50 (1 + 99) = 2500.

                                     2

Ex. 29. Find the sum of all 2 digit numbers divisible by 3.

 Sol. All 2 digit numbers divisible by 3 are :

        12, 51, 18, 21, ..., 99.

        This is an A.P. with a = 12 and d = 3.

        Let it contain n terms. Then,

        12 + (n - 1) x 3 = 99 or n = 30.

     \Required sum = 30 x (12+99) = 1665.

                                    2

Ex.30.How many terms are there in 2,4,8,16……1024?

Sol.Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2 =2.

       Let the number of terms be n  . Then

       2 x 2^n-1 =1024 or 2^{n-1 =512 = 2}9.

    \n-1=9 or n=10.

Ex. 31. 2 + 2² + 2³ + ... + 2⁸ = ?

 Sol.    Given series is a G.P. with a = 2, r = 2 and n = 8.

        \sum =  a(rⁿ-1) = 2 x (2⁸ –1) = (2 x 255) =510

                         (r-1)        (2-1)

KEY BOARD SHORTCUT KEYS

The General Shortcuts

We’ll kickoff the list with some really general shortcuts that you often used.

• CTRL+C (Copy)
• CTRL+X (Cut)
• CTRL+V (Paste)
• CTRL+Z (Undo)
• Delete (Delete)
• Shift+Delete (Delete the selected item permanently without placing the item in the Recycle Bin)
• CTRL while dragging an item (Copy the selected item)
• CTRL+Shift while dragging an item (Create a shortcut to the selected item)
• F2 key (Rename the selected item)
• CTRL+RIGHT ARROW (Move the insertion point to the beginning of the next word)
• CTRL+LEFT ARROW (Move the insertion point to the beginning of the previous word)
• CTRL+DOWN ARROW (Move the insertion point to the beginning of the next paragraph)
• CTRL+UP ARROW (Move the insertion point to the beginning of the previous paragraph)
• CTRL+Shift with any of the arrow keys (Highlight a block of text)
• Shift with any of the arrow keys (Select more than one item in a window or on the desktop, or select text in a document)
• CTRL+A (Select all)
• F3 key (Search for a file or a folder)
• Alt+Enter (View the properties for the selected item)
• Alt+F4 (Close the active item, or quit the active program)
• Alt+Enter (Display the properties of the selected object)
• Alt+Spacebar (Open the shortcut menu for the active window)
• CTRL+F4 (Close the active document in programs that enable you to have multiple documents open simultaneously)
• Alt+Tab (Switch between the open items)
• Alt+ESC (Cycle through items in the order that they had been opened)
• F6 key (Cycle through the screen elements in a window or on the desktop)
• F4 key (Display the Address bar list in My Computer or Windows Explorer)
• Shift+F10 (Display the shortcut menu for the selected item)
• Alt+Spacebar (Display the System menu for the active window)
• CTRL+ESC (Display the Start menu)
• Alt+Underlined letter in a menu name (Display the corresponding menu)
• Underlined letter in a command name on an open menu (Perform the corresponding command)
• F10 key (Activate the menu bar in the active program)
• RIGHT ARROW (Open the next menu to the right, or open a submenu)
• LEFT ARROW (Open the next menu to the left, or close a submenu)
• F5 key (Update the active window)
• Backspace (View the folder one level up in My Computer or Windows Explorer)
• ESC (Cancel the current task)
• Shift when you insert a CD-ROM into the CD-ROM drive (Prevent the CD-ROM from automatically playing)

Dialog Box Keyboard Shortcuts

• CTRL+Tab (Move forward through the tabs)
• CTRL+Shift+Tab (Move backward through the tabs)
• Tab (Move forward through the options)
• Shift+Tab (Move backward through the options)
• Alt+Underlined letter (Perform the corresponding command or select the corresponding option)
• Enter (Perform the command for the active option or button)
• Spacebar (Select or clear the check box if the active option is a check box)
• Arrow keys (Select a button if the active option is a group of option buttons)
• F1 key (Display Help)
• F4 key (Display the items in the active list)
• Backspace (Open a folder one level up if a folder is selected in the Save As or Open dialog box)

Microsoft Natural Keyboard Shortcuts

• Win (Display or hide the Start menu)
• Win+BREAK (Display the System Properties dialog box)
• Win+D (Display the desktop)
• Win+M (Minimize all of the windows)
• Win+Shift+M (Restore the minimized windows)
• Win+E (Open My Computer)
• Win+F (Search for a file or a folder)
• CTRL+Win+F (Search for computers)
• Win+F1 (Display Windows Help)
• Win+ L (Lock the keyboard)
• Win+R (Open the Run dialog box)
• Win+U (Open Utility Manager)

Accessibility Keyboard Shortcuts

• Right Shift for eight seconds (Switch FilterKeys either on or off)
• Left Alt+left Shift+PRINT SCREEN (Switch High Contrast either on or off)
• Left Alt+left Shift+NUM LOCK (Switch the MouseKeys either on or off)
• Shift five times (Switch the StickyKeys either on or off)
• NUM LOCK for five seconds (Switch the ToggleKeys either on or off)
• Win +U (Open Utility Manager)

Windows Explorer Keyboard Shortcuts

• END (Display the bottom of the active window)
• HOME (Display the top of the active window)
• NUM LOCK+* (Display all of the subfolders that are under the selected folder)
• NUM LOCK++ (Display the contents of the selected folder)
• NUM LOCK+- (Collapse the selected folder)
• LEFT ARROW (Collapse the current selection if it is expanded, or select the parent folder)
• RIGHT ARROW (Display the current selection if it is collapsed, or select the first subfolder)

Shortcut Keys for Character Map

• After you double-click a character on the grid of characters, you can move through the grid by using the keyboard shortcuts:
• RIGHT ARROW (Move to the right or to the beginning of the next line)
• LEFT ARROW (Move to the left or to the end of the previous line)
• UP ARROW (Move up one row)
• DOWN ARROW (Move down one row)
• PAGE UP (Move up one screen at a time)
• PAGE DOWN (Move down one screen at a time)
• HOME (Move to the beginning of the line)
• END (Move to the end of the line)
• CTRL+HOME (Move to the first character)
• CTRL+END (Move to the last character)
• Spacebar (Switch between Enlarged and Nor mal mode when a character is selected)

Microsoft Management Console (MMC) Main Window Keyboard Shortcuts

• CTRL+O (Open a saved console)
• CTRL+N (Open a new console)
• CTRL+S (Save the open console)
• CTRL+M (Add or remove a console item)
• CTRL+W (Close window/tab)
• F5 key (Update the content of all console windows)
• Alt+Spacebar (Display the MMC window menu)
• Alt+F4 (Close the console)
• Alt+A (Display the Action menu)
• Alt+V (Display the View menu)
• Alt+F (Display the File menu)
• Alt+O (Display the Favorites menu)

MMC Console Window Keyboard Shortcuts

• CTRL+P (Print the current page or active pane)
• Alt+- (Display the window menu for the active console window)
• Shift+F10 (Display the Action shortcut menu for the selected item)
• F1 key (Open the Help topic, if any, for the selected item)
• F5 key (Update the content of all console windows)
• CTRL+F10 (Maximize the active console window)
• CTRL+F5 (Restore the active console window)
• Alt+Enter (Display the Properties dialog box, if any, for the selected item)
• F2 key (Rename the selected item)
• CTRL+F4 (Close the active console window. When a console has only one console window, this shortcut closes the console)

Remote Desktop Connection Navigation

• CTRL+Alt+END (Open the m*cro$oft Windows NT Security dialog box)
• Alt+PAGE UP (Switch between programs from left to right)
• Alt+PAGE DOWN (Switch between programs from right to left)
• Alt+INSERT (Cycle through the programs in most recently used order)
• Alt+HOME (Display the Start menu)
• CTRL+Alt+BREAK (Switch the client computer between a window and a full screen)
• Alt+Delete (Display the Windows menu)
• CTRL+Alt+- (Place a snapshot of the active window in the client on the Terminal server clipboard and provide the same functionality as pressing PRINT SCREEN on a local computer.)
• CTRL+Alt++ (Place a snapshot of the entire client window area on the Terminal server clipboard and provide the same functionality as pressing Alt+PRINT SCREEN on a local computer.)

Internet Explorer navigation

• CTRL+B (Open the Organize Favorites dialog box)
• CTRL+E (Open the Search bar)
• CTRL+F (Start the Find utility)
• CTRL+H (Open the History bar)
• CTRL+I (Open the Favorites bar)
• CTRL+L (Open the Open dialog box)
• CTRL+N (Start another instance of the browser with the same Web address)
• CTRL+O (Open the Open dialog box, the same as CTRL+L)
• CTRL+P (Open the Print dialog box)
• CTRL+R (Update the current Web page)
• CTRL+W (Close the current window)

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JNTUK R10 1-2 REG/SUP RESULTS OUT

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date: 12/10/2013

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How To Reset Samsung Galaxy y

Samsung Galaxy Y runs on Android OS and one of the best phone in Android series because it gives value for Money and it's cheap. You must have got bored of Installing and uninstalling apps on your phone. Also this effects your phone memory and slow downs your Mobile such as your mobile will get hang when you press Keypad Button and other apps. If your Galaxy Y has become Slow, unpredictable or Unresponsive then Don't worry Today I will show you how to make your Samsung Galaxy Y run faster and format all unwanted apps and Installing clean apps on your phone.

How to Reset Samsung Galaxy y from Boot Menu

Step 1 :- Press the Volume Up and the Menu key at the same time.

Step 2:-  Now, while pressing Volume & Menu,Press the power Key to turn ON your Phone.

 Step 3:- You will see the factory reset screen.

Step 4:-  Select “Wipe data/factory reset” (3rd option)

 Step 5:- Now select Delete all User

 Step 6:- Now select Reboot System.

 It will take some time to reboot Don't worry, After Few minutes your Phone will be New Mobile as you got it earlier while Buying.

Formatting Using Settings Menu

Settings -> Privacy -> Factory data reset -> Reset phone -> Erase everything

 Reset your settings to the factory default values and delete all your data.

or

 Use this method to reset your Samsung Galaxy Y GT-S5360: Enter *2767*3855#.

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if you want to know any reliance mobile balance then click on the following link http://dnd.megarush.net/balance-check.php?n=8099237304

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