What is the sum of the serie 0.3 + 0.33 + 0.333 +... n terms 

Subject

Mathematics

Class

NDA Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct ?

  • The relation is an equivalent relation

  • The relation is not reflexive but it is symmetric and transitive

  • The relation is not symmetric but it is reflexive and transitive

  • The relation is not transitive but it is reflexive and symmetric


2.

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then, the number of subsets of A containing two or three elements is

  • 45

  • 120

  • 165

  • 330


3.

The value of  i2n + i2n + 1 + i2n + 2 + i2n + 3, where i =   - 1 is

  • 0

  • 1

  • i

  • - i


4.

If the difference between the roots of the equation x2 + kx + 1 = 0 is strictly less than 5, where  k  2, then k can be any element of the interval

  • ( - 3, - 2]  [2, 3)

  • ( - 3, 3)

  •  - 3,  - 2  2, 3

  • None of the above


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5.

If the roots of the equation x2 + px + q = 0 are in the same ratio as those of the equation x2 + lx + m = 0, then which one of the following is correct ?

  • p2m = l2q

  • m2p = l2q

  • m2p = q2l

  • m2p2 = l2q


6.

The value of   - 1 + i32n +  - 1 - i32n where n is not a multiple of 3 and i =  - 1, is

  • 1

  •  - 1

  • i

  •  - i


7.

Three-digit numbers are formed from the digits 1, 2 and 3 in  such a way that the digits are ot repeated. What is the sum of such three-digit numbers ?

  • 1233

  • 1322

  • 1323

  • 1332


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8.

What is the sum of the serie 0.3 + 0.33 + 0.333 +... n terms 

  • 13n - 191 - 110n

  • 13n - 291 - 110n

  • 13n - 131 - 110n

  • 13n - 191 + 110n


A.

13n - 191 - 110n

0.3 +0.33 + 0.333 +...= 310 + 33100 + 3331000 + ...= 131 - 110 + 1 - 1100 + 1 - 11000 + ...= 13n - 1101 - 110n910= 13n - 191 - 110n


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9.

If 1, ω, ω2 are the cube roots of unity, then (1 + ω)(1 + ω2)(1 + ω3)(1 + ω + ω2) is equal to

  •  - 2

  •  - 1

  • 0

  • 2


10.

If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is

  • mn

  • m + n

  • 2(m + n)

  • - (m + n)


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