If 0 < a < 1, the value of log10(a) is negative. This is ju

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 Multiple Choice QuestionsMultiple Choice Questions

11.

What is 1log2N + 2log3N + 1log4N + ... + 1log100N = N  1?

  • 1log100!N

  • 1log99!N

  • 99log100!N

  • 99log99!N


12.

What is the greatest integer among the following by which the number 55 + 75 is divisible ?

  • 6

  • 8

  • 11

  • 12


13.

What is the number of non-zero terms in the expansion of(1 + 23}11 + (1 - 23)11 (after simplification) ?

  • 4

  • 5

  • 6

  • 11


14.

If x = 1 - y + y2 - y3 + ... up to infinite terms, where IyI < 1, then which one of the following is correct?

  • x = 11 + y

  • x = 11 - y

  • x = y1 + y

  • x = y1 - y


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15.

What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder ?

  • 1565

  • 1585

  • 1635

  • 1655


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16.

If 0 < a < 1, the value of log10(a) is negative. This is justified by:

  • Negative power of 10 is less than 1

  • Negative power of 10 is between 0 and 1

  • Negative power of 10 is positive

  • Negative power of 10 is negative


B.

Negative power of 10 is between 0 and 1

a < x < 1Let log10a = - x a = 10 - x10 - x can have values only between 0 and 1

 Negative power of 10 is between 0 and 1


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17.

The third term of a GP is 3. What is the product of the first five terms ?

  • 216

  • 226

  • 243

  • Cannot be determined due to insufficient data


18.

fx, 3/2, z If x, 32, z are in AP; x, 3, z are in GP; then which one of the following will be in HP ?

  • x, 6, z

  • x, 4, z

  • x, 2, z

  • x, 1, z


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19.

What is the value of the sum (in + in + 1), where i =  - 1 ?

  • i

  • 2i

  •  - 2i

  • 1 + i


20.

If x, x - y and x + y are the angles of a triangle (not an equilateral triangle) such that tan(x - y), tan x and tan (x + y) are in GP, then what is x equal to ?

  • π4

  • π3

  • π6

  • π2


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