The greatest positive integer which divides (n + 16)(n + 17)(n +

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The domain of the function f(x) = log0.5x! is

  • 0, 1, 2, 3, ...

  • 0, 1, 2, 3, ...

  • 0, 

  • 0, 1


2.

If f(x) = x - 1 + x - 2 + x - 3, 2 < x < 3, then f is

  • an onto function but not one-one

  • one-one function but not onto

  • a bijection

  • neither one-one nor onto


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3.

The greatest positive integer which divides (n + 16)(n + 17)(n + 18)(n +19), for all positive integers n, is

  • 6

  • 24

  • 28

  • 20


B.

24

We have, (n + 16)(n + 17)(n + 18)(n + 19)These numbers are the product of four consecutive natural number Thus number divides by 4! = 24


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4.

If x1, x2, x3 as well as y1, y2, yare in geometric progression with the same common ratio,then the points, x1, y1, x2, y2, x3, y3 are

  • vertices of an equilateral triangle

  • vertices of a right angled triangle

  • vertices of a right angled isosceles triangle

  • collinear


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5.

The locus of the point representing the complex number z for which z + 32 - z - 32 = 15 is

  • a circle

  • a parabola

  • a straight line

  • an ellipse


6.

1 + i20161 - i2014 = ?

  • - 2i

  • 2i

  • 2

  •  - 2


7.

 If 1, z1, z2, ..., zn - 1 are the nth roots of unity,then 1 - z11 - z2 ... 1 - zn - 1 = ?

  • 0

  • n - 1

  • n

  • 1


8.

If 124 + 2x2 = 2433x2 - 2, then x is equal to

  • ± 1312

  • ± 145

  • ± 1213

  • ± 514


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9.

The product and sum of the roots of the equation x2 - 5x - 24 = 0 are respectively

  • - 64, 0

  • - 24, 5

  • 5, - 24

  • 0, 72


10.

The number of real roots of the equation x5 +3x3 + 4x + 30 = 0 is

  • 1

  • 2

  • 3

  • 5


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