The value of 1 + sin2π9 + i

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in

  • - , - 3  9, 

  •  - , - 9  3, 

  • - 3, 

  •  - , 9


2.

Box I contains 30 cards numbered I to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :

  • 23

  • 25

  • 817

  • 417


3.

The domain of the function f(x) = sin-1x + 5x2 + 1 is  - , - a  a, , Then a =?

  • 1 + 172

  • 17 - 12

  • 172

  • 172 + 1


4.

If |x| < 1, |y| < 1 and x  y, then the sum to infinity of the following series (x + y) + (x2 + xy + y2) + (x+ x2y + xy2 + y3) + ..... is :

  • x +y + xy1 - x1 - y

  • x + y - xy1 - x1 - y

  • x + y - xy1 - x1 + y

  • x + y + xy1 + x1 + y


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5.

The value of 1 + sin2π9 + icos2π91 + sin2π9 - icos2π93 is : 

  • - 123 - i

  • 123 - i

  •  121 - i3

  • - 121 - i3


A.

- 123 - i

1 + cos5π18 +isin5π181 + cos5π18 -isin5π183 = 2cos25π36 + 2isin5π36cos5π362cos25π36 - 2isin5π36cos5π363= cos5π36 +isin5π36cos5π36 -isin5π363 = cos5π36 +isin5π366= cos6 × 5π36 + isin6 × 5π36 = cos5π6 +isin5π6 - 32 + i12


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6.

Let α > 0, β > 0 be such that α3 + β2 = 4. If the maximum value of the term independent of x in the binomial expansion of αx19 + βx- 1610 is 10k, then k is equal to :

  • 176

  • 336

  • 352

  • 84


7.

If R = x, y :x, y  Z, x2 + 3y2  8 is a relation on the set of integers Z,then the domain R - 1 is ; 

  •   - 1, 0, 1

  •  - 2, - 1, 1, 2

  • 0, 1

  •  - 2, - 1, 0, 1, 2


8.

If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0)is equal to

  •  - 24

  •  - 12

  • 6

  • 12


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9.

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola x24 - y22 = 1  at the point (x1, y1). Then x12 + 5y12 is equal to :

  • 10

  • 5

  • 8

  • 6


10.

The contrapositive of the statement “If I reach the station in time, then I will catch the train” is:

  • If I will catch the train, then I reach the station in time.

  • If do not reach the station in time, then I will not catch the train

  • If I do not reach the station in time,then I will catch the train.

  • If I will not catch the train, then I do not reach the station in time.


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