Let a = 10nn! for n = 1, 2, 3 . . . then the greatest 

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 Multiple Choice QuestionsMultiple Choice Questions

171.

The sum of the series 34 . 8 - 3 . 54 . 8 . 12 + 3 . 5 . 74 . 8 . 12 . 16 - ...

  • 32 - 34

  • 23 - 34

  • 32 - 14

  • 23 - 14


172.

12 - 12 . 22 + 13 . 23 - 14 . 24 + ... is equal to

  • 14

  • loge34

  • loge32

  • loge23


173.

For any integer n  1, the sum k = 1nkk + 2 is equal to

  • nn + 1n + 26

  • nn +12n + 16

  • nn + 12n + 76

  • nn +12n + 96


174.

If 1 +x + x2 + x35 = k = 015akxk, then a2k = 07k = 0

  • 128

  • 256

  • 512

  • 1024


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175.

If α = 52 ! 3 + 5 . 73 ! 32 + 5 . 7. 94! 33 + . . . , thenα2 + 4α is equal to

  • 21

  • 23

  • 25

  • 27


176.

11 . 3 + 12 . 5 + 13 . 7 +14 . 9 + . . .  = ? 

  • 2loge2 - 2

  • 2 - loge2 

  • 2loge4

  • loge4


177.

If l, m, n are in arithmetic progression, then the straight line b + my + n = 0 will pass through the point

  • (- 1, 2)

  • (1, - 2)

  • (1, 2)

  • (2, 1)


178.

1e3xex + e5x = a0 + a1x + a2x2 + . .  2a1 + 23a3 + 25a5 + . . . = ?

  • e

  • e - 1

  • 1

  • 0


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179.

Let n = 1! + 4! + 7! + . . . + 400!. Then ten's digit of n is

  • 1

  • 6

  • 2

  • 7


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180.

Let a = 10nn! for n = 1, 2, 3 . . . then the greatest  value of n for which a is the greatest is

  • 11

  • 20

  • 10

  • 8


C.

10

Given, an = 10nn!, n = 1, 2, 3 . . . , here we see

that when we increase the value of n like as 1, 2, 3 . . . the value of a, increases but when we reach at n = 9 or 10 the value of an remain unchanged, ie, minor difference in after decimal places and when we cross the value n = 10 ie, n = 11, then we see that the value of a, is monotonically decreasing.

Hence, an have its maximum value at n = 9 or 10.


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