ANSWERS  ( EXERCISE 2O)

1.       (b) :  The  relationship is 7x : x.

2.       (d) :  The  relationship is  x : (2x-6)

3.       (b) :  The  relationship is  x : (3x + 1)

4.       (d) :  The  relationship is  x : x^5.

5.       (b) :  The  relationship is  x: (x/2 + 1)

6.       (a) :  The  relationship is  x: (x/2 - 1)

7.       (c) :  The  relationship is  x²  : (x + 1)

8.       (d) :  The  relationship is  x : (x³ + x)

9.       (c) :  The  relationship is  (x² +1) : x.

10.   (c) :  The  relationship is  x² : x³

11.   (c) :  The  relationship is  (2x - 4) : x.

12.   (d) :  The  relationship is  x³ : (x + 1)³ +1 

13.   (c) :  Clearly,68 = 4³ + 4 ; 130 = 5³ +5 ; 350 7³ + 7,   So missing no is = 6³ + 6= 216 + 6= 222.

14.   (d) :  The  relationship is  x : x²

15.   (c) :  The  relationship is  x : x²/2

16.   (b) :   clearly, 42 = 6 X 7 : 56 = 7 x 8 ; 72 = 8 x 9.     So, the missing no is = 9 X 10 = 90.

17.   (b) :  The  relationship is  x² : (x + 2)²

18.   (d) :  The  relationship is  x : (x² - 1).

19.   (b) :  The  relationship is  x : (x - 2222).

20.   (d) :  The  relationship is  x : (x  + 1111).

21.   (b) :  The  relationship is  x : (x + 89).

22.   (b) :  The  relationship is  x : (x - 119).

23.   (d) :  The  relationship is  x² : (x + 1 )² + 1

24.   (c) :  The  relationship is  x : (x³ - 1).

25.   (b) :  The  relationship is  x : (x + 1)²

26.   (b) :  The  relationship is  x : (7x/2).

27.   (a) :  The  relationship is  100x : x.

28.   (c) :  The  relationship is  x : x(x + 1).

29.   (a) :  The  relationship is  x^y : (x - 1)^{y + 1}. 

                        Since 16 = 4², so required no = (4 - 1)^{2 + 1} =3³=27

30.   (d) :  The  relationship is  x^y : (x + 1)^{y + 1}.

Since 64 = 4³, so required no = (4 + 1)^{3 + 1} =5⁴=625.

31.   (d) :  Clearly, 210 = (15)² – 15  and 380= (15 + 5)² – (15 + 5).

                       Now ,182= (13)² + 13.

                       So, required no is =(13 + 5)² + (13 + 5)=(18)² + 18 = 342.

32.   (b) :  Clearly, 42 = 7 X 6 and 56 = 7 X (6 + 2).

Similarly , 110=11 X 10.

  So, required no is =11 X (10 + 2)=11 X 12 =132.

33.   (c) :  The  relationship is  (x² - 1) : [(x + 4)² + 1].

                       Since 168= (13)² – 1, so the  required no is = (13 + 4)² + 1=(17)² + 1=290.

34.   (d) :  The  sum of the digits of the numbers in each pair is the same.

35.   (b) :  sum of the digits of the first no. is 2 more than the sum of digit of second number.

36.   (b) :  we have : 100 = 5 X 20, 64= 4 X 16.

                       Similarly, 80 = 4 X 20.

                       So, the required no. is 3 X 16 = 48.

37.   (b) :  The  relationship is  x : x².

38.   (d) :  The  relationship is  x³ : x²

39.   (a) :  The  first number is multiplied by the next prime number to obtain the second no.

40.   (c) :  The  relationship is   x :  x³/2.

41.   (c) :  The  relationship is  x : (x³ - x²).

42.   (b) :  The  relationship is  x : (3x + 3).

43.   (b) :    Number               Sum of Digit            New Sum  of digit

                            363     ...….        3 + 6 + 3=12                  1 + 2 =3

                            489     ...….        4 + 8 + 9 =21                 2 + 1 =3

                            579     ...….        5 + 7 + 9 =21                 2 + 1 =3

                            471     ...….        4 + 7 + 1 = 12                1 + 2 =3

44.   (a) :  In all the numbers, the sum of digit is 12 and the greatest digit lies in the middle.

45.   (c) : In all the numbers , the middle digit is the sum of the digits of the product of other two        

        digit.

         Now,  9 X 2 = 18  , 1 + 8  = 9  (middle digit in 992 )

                      7 X 3 = 21 ,  2 + 1 = 3  (middle digit in  773)

                      8 X 5 = 40 , 4  + 0 =   (middle digit in 845) ans so on.

46.   (b) : The first digit of the numbers form the series  1,2,3,4. The second digits of the numbers form the series  3,4,5,6.

The last digit of the numbers form the series  4,6,8,0.

47.   (d) : In all the numbers , (1^st digit + 3^rd digit) – middle digit = 10

         Thus , 5 + 8 -3=10 , 7 + 5 – 2=10, 8 + 3 – 1= 10.

48.   (c) : In all the numbers , the product of the first and last digit is a multiple of the sum of the 

        middle two digit.

        Thus, 4 X 8 = 32 is a multiple of (7 + 1) ..8

                  5 X 7 = 35 is a multiple of (6 + 1) ..7 and so on..

49.   (c) :   In each set , 2^nd number = (1^st number X 7 )

                      and  3^rd number = (1^st number X  8)

50.   (b) :   In each set , 2^nd number = (1^st number X 6 )

                      and  3^rd number = (1^st number X 2 )

51.   (d) :   In each set , 2^nd number = (1^st number  + 9)

                      and  3^rd number = (1^st number +13)

52.   (a) :   In each set , 2^nd number = (1^st number  - 4)

                      and  3^rd number = (1^st number  - 8)

53.   (c) :   In each set , 2^nd number = (1^st number  -8 )

                      and  3^rd number = (1^st number  - 16)

54.   (d) :  In each set,( 1^st no + 3^rd no)/2= 2^nd number.

55.   (d) :   In each set , 2^nd number = (1^st number  + 9)

                       and   3^rd number = (2^nd  number  + 9)

56.   (d) :  Each set contains cubes of three  consecutive natural number in order.

57.   (a)  : Each set contains squares of three  alternate  natural number in reverse  order.

58.   (b) : In each set, second number is the square of the first no. and 3^rd no is obtained b  reversing the order of the digits of the 2^nd no.

59.   (d) :  In each set , ( 3^rd number X 2) + 1^st number = 2^nd number.

60.   (b) :  In each set ,1^st number = (2^nd number)² -1.

         2^st number = (3r^d number)² -1.

61.   (d) :  Each set consists of Prime number only.

62.   (d) : Each set consists of even  number only whose  H.C.F.  is 2.

63.   (d) : Each set consists of numbers which are obtained by multiplying a certain no b 9, 7, and 5 respectively.

Thus, in the given set, 63= 7 X 9, 49 = 7 X 7, 35 = 7 X 5

 Similarly, 81 =  9 X 9, 63 = 9 X 7, 45 = 9 X 5.

64.   (c) : The sum of the digits of the numbers in a set are 12,14, and 16 respectively.

65.   (c) :  In each set , 2^nd number = (1^st number  + 101)

                       and   3^rd number = (2^nd  number  + 101)