The number of terms in the series 105 + 103 + 101 + ... + 49 + 47

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

The value of tan9° - tan27° - tan63°° + tan31° is

  • 3

  • 2

  • 8

  • 4


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12.

The number of terms in the series 105 + 103 + 101 + ... + 49 + 47 is

  • 28

  • 30

  • 25

  • 22


B.

30

Given, series is105 + 103 + 101 + .. + 49 + 47which is an AP.Here, a = 105 and d = 103 - 105 = - 2Let nth term = 47 a + n - 1d = 47 105 + n - 1- 2 = 47 - 2n - 1 = 47 - 105          n - 1 = - 58- 2                 n = 29 + 1                 n = 30

Hence, number of terms in given series is 30.


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13.

If the variance oftwo variables x and y are respectively 9 and 16 and covariance is 8, then the coefficient of correlation between x and y will be

  • 23

  • 832

  • 982

  • 29


14.

If the points (k, 2 - 2k), (- k + 1, 2k) and (- 4 - k, 6 - 2) are collinear, then k is equal to

  • - 1

  • 13

  • 1

  • - 12


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15.

If log104x = y, then log108x4 is equal to

  • 23y

  • 3y

  • 4y

  • 2y


16.

The largest term in the expansion of (3 + 2x)50 where x = 15, is

  • 7th

  • 5th

  • 8th

  • 49th


17.

If x = acos3t and y = asin3t, then dydxt = π4 is equal to

  • 1

  • - 1

  • 0


18.

The anti-derivative F of f defined by f(x) = 4x3 - 6x2 + 2x + 5, F(0) = 5, is

  • x4 - 2x3 + x2 + 5x

  • 12x2 - 12x + 2

  • 16x4 - 18x3 + 4x2 + 5x

  • x4 - 2x3 + x2 + 5x + 5


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19.

Scanner is

  • an input device

  • an output device

  • a memory device

  • None of the above


20.

The geometric mean of roots of the equation x2 - 18x + 81 = 0 is

  • 18

  • 6

  • 9

  • 3


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