If x2 -  x - 6 = x +

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d), if ad(b + c) = bc(a + d), then R is

  • symmetric only

  • reflexive only

  • transitive only

  • an equivalence relation


2.

A cmplex number z is such that argz - 2z + 2 = z3. The points representing this complex number will lie on

  • an ellipse

  • a parabola

  • a circle

  • a straight line


3.

If a1, a2 and a3 be any positive real numbers, then which of the following statement is not true?

  • 3a1a2a3  a13 + a23 + a33

  • a1a2 + a2a3 + a3a1  3

  • (a1 + a2 + a3)1a1 + 1a2 + 1a3  9

  • (a1 . a2 . a3)1a1 + 1a2 + 1a3  27


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4.

If x2 -  x - 6 = x + 2, then the values of x are

  • - 2, 2, - 4

  • - 2, 2, 4

  • 3, 2, - 2

  • 4, 4, 3


B.

- 2, 2, 4

x2- x - 6 = x + 2, then

Case I : x2 - x - 6 < 0    x - 3x + 2 < 0             - 2 < x < 3

In this case, the equation becomes
x2 - x - 6 = - x - 2

or  x2 - 4 = 0

        x = ± 2

Clearly, x = 2 satisfies the domain of the equation in this case. So, x = 2 is a solution.

Case II : x2 - x - 6  0So,      x  - 2 or x  3

Then, equation reduces to x2 - x - 6 = 0 = x + 2 i.e., x2 - 2x - 8 = 0 or x = - 2, 4

Both these values lies in the domain of the equation in this case, so x = - 2, 4 are the roots. Hence, roots are x = - 2, 2, 4


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5.

The centres of a set of circles, each of radius 3, lie on the circles x2 + y2 = 25. the locus of any point in the set is

  • 4  x2 +_y2  64

  • x2 + y2  25

  • x2 + y2  25

  • 3  x2 + y2  9


6.

A tower AB leans towards West making an angle α with the vertical. The angular elevation of B, the top most point of the tower is β as observed from a point C due East of A at a distance 'd' from A. If the angular elevation of B from a point D due East of C at a distance 2d from C is r, then 2tanα can be given as

  • 3cotβ - 2cotγ

  • 3cotγ - 2cotβ

  • 3cotβ - cotγ

  • cotβ - 3cotγ


7.

If α and β are the roots of x2 - ax + b = 0 and if αn and βn = Vn, then

  • V+ 1 = aVn + bVn - 1

  • V+ 1 = aVn + aVn - 1

  • V+ 1 = aVn - bVn - 1

  • V+ 1 = aVn - 1 + bVn


8.

The sum of the series

- 1rCrn12r + 3r22r + 7r23r + 15r24r + ... m terms is

  • 2mn - 12mn2n - 1

  • 2mn - 12n - 1

  • 2mn + 12n + 1

  • None of these


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9.

The angle of intersection of the circles x2 + y2 - x + y - 8 = 0 and x2 + y2 + 2x + 2y - 11 = 0 is

  • tan-1199

  • tan-119

  • tan-1919

  • tan-19


10.

The number of integral values of K, for which the equation 7cosx + 5sinx = 2K + 1 has a solution

  • 4

  • 8

  • 10

  • 12


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