EXERCISE 6.A (OBJECTIVE TYPE QUESTIONS) (IN 11 15 SOLUTION)

11.       The average of the, two – digit numbers, which remain the same when the digits interchange their positions, is:

a)      33

b)      44

c)       55

d)      66

12.       The average of first 50 natural numbers is:

a)      12.25

b)      21.25

c)       25

d)      25.5

13.       The mean of 1², 2², 3², 4², 5²,6²,7² is:

a)      10

b)      20

c)       30

d)      40

14.       The average of all odd numbers up to 100 is:

a)      49

b)      49.5

c)       50

d)      51

15.       If a, b, c, d, e are five consecutive odd numbers, their average is:

a)      5 (a +4 )

b)      abcde /5

c)       5 (a + b + c +d + e)

d)      None of these 

ANSWERS

  11. C

12.D

13.B

14.C

15.D

SOLUTION 

11.       Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 / 9)

= [(11 + 99 ) + (22 ) 88 ) + (33 + 77 ) + (44 + 66) + 55/9]

= ( 4 x 110 + 55 /9) = 495 / 9 = 55.

12.       Sum of first n natural numbers = m (m + 1) / 2.

So, average of first n natural numbers = n( n + 1 ) / 2n = N + 1   / 2.

 Required average = (50 + 1 /2) = 51 / 2 = 25.5.

13.       1² + 2² + 3² + ….. n² = N (n + 1) (2n + 1) / 6

 1² + 2² + 3² + …..7² = (7 x 8 x 15/6) = 140.

So, required average = (140 / 7) = 20.

14.       Sum of odd numbers up to 100= 1 + 3 + 5 + 7 + … + 95 + 97 + 99.

   = (1 + 99) + (3 + 97) +(5 + 95) +…. + up to 25 pairs

                                 = 100 + 100 + 100 + …. 25 times) = 2500.

                                   Average = (2500 / 50) = 50.

15.       Clearly, b = a + 2, c = a + 4, d = a + 6 and e = a + 8.

Average = (a + 2) + ( a + 4) +( a + 6) + ( a + 8)/5= (5 a + 20 / 5) = (a +4).