The number of irrational terms in the binomial expansion of 

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let a, b, c and d be any four real numbers. Then, an +bn = cn + dn holds for any natural number n, if

  • a + b = c + d

  • a - b = c - d

  • a + b = c + d, a2 + b2 = c2 + d2

  • a - b = c - d, a2 - b2 = c2 - d2


2.

If α and β are the roots of x2 - px +1 = 0 and γ is aroot of x2 + px +1 = 0, then α + γβ + γ is

  • 0

  • 1

  • - 1

  • ρ


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3.

The number of irrational terms in the binomial expansion of 315 + 713100

  • 90

  • 88

  • 94

  • 95


C.

94

General term of 315 + 713100 is given by

Tr + 1 = Cr100315100 - r713r

        = Cr100 . 3100 - r5 . 7r3

For a rational term, 100 - r5 and r3 must be integer.

Hence, r = 0, 15, 30, 45, 60, 75, 90

Thus, There are seven rational terms. 

Hence, number of irrational terms = 101 - 7 = 94


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4.

The quadratic expression 2x +12 - px + q  0 for any real x, if

  • p2 - 16p - 8q < 0

  • p2 - 8p + 16q < 0

  • p2 - 8p - 16q < 0

  • p2 - 16p + 8q < 0


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5.

In a certain town, 60% of the families own a car, 30% own a house and 20% own both car and house. If a family is randomly chosen, then what is the probability that this family owns a car or a house but not both?

  • 0.5

  • 0.7

  • 0.1

  • 0.9


6.

The letters of the word 'COCHIN' are permuted and all the permutations are arranged in alphabetical order as in English dictionary. The number of words that appear before the word 'COCHIN', is

  • 360

  • 192

  • 96

  • 48


7.

Let f: R  R be defmed as f(x) = x2 - x + 4x2 +  x + 4 Then, range of the function f(x) is

  • 35, 53

  • 35, 53

  • - , 35  53, 

  • - 53, - 35


8.

The least value of 2x2 + y2 + 2xy + 2x -3y + 8 for real numbers x and y, is

  • 2

  • 8

  • 3

  • - 1/2


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9.

The minimum value of cosθ + sinθ + 2sinθ for θ  0, π2

  • 2 + 2

  • 2

  • 1 + 2

  • 22


10.

If cot2x3 + tanx3 = csckx3, then the value of k is

  • 1

  • 2

  • 3

  • - 1


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