If g(x) is a polynomial satisfying g(x) g(y) = g(x) + g(y) + g(xy

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If z - 25z - 1 = 5,  find the value of z

  • 3

  • 4

  • 5

  • 6


2.

Argument of the complex number - 1 - 3i2 +i is

  • 45°

  • 135°

  • 225°

  • 240°


3.

The shortest distance between the straight lines through the points A1 = (6, 2, 2) and A2 = (- 4, 0, - 1) in the directions of (1, - 2, 2) and (3, - 2, - 2) is

  • 6

  • 8

  • 12

  • 9


4.

The centre and radius of the sphere x2 + y2 + z2 + 3x - 4z + 1 = 0 are

  • - 32, 0, - 2; 212

  • 32, 0, 2; 21

  • - 32, 0, 2; 212

  • - 32, 0, 2; 212


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5.

Let A and B are two fixed points in a plane, then locus of another point Con the same plane such that CA + CB = constant, (> AB) is

  • circle

  • ellipse

  • parabola

  • hyperbola


6.

The directrix of the parabola y2 + 4x + 3 = 0 is

  • x - 43 = 0

  • x + 14 = 0

  • x - 34 = 0

  • x - 14 = 0


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7.

If g(x) is a polynomial satisfying g(x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g(2) = 5, then limx3 g(x) is

  • 9

  • 10

  • 25

  • 20


B.

10

Since, g(x) g(y) = g(x) + g(y) + g(xy) - 2

Now, at x = 0, y = 2, we get

g(0) g(2) = g(0) + g(2) + g(0) - 2

                       g2 = 5

 5g0 = 5 + 2g0 - 2 3g0 = 3   g0 = 1

g(x) is given in a polynomial and by the relation given g(x) cannot be linear.

Let g(x) = x2 + k       g0 = 1

 From Eq. (i)  x2 + 1y2 + 1 = x2 + 1 + y2 + 1 + x2y2 + 1 - 2 limx3gx = g3 = 32 + 1 = 10


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8.

The length of the parabola y2 = 12x cut off by the latusrectum is

  • 62 + log1 + 2

  • 32 + log1 + 2

  • 62 - log1 + 2

  • 32 - log1 + 2


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9.

Area enclosed by the curve π4x - 22 + y2 = 8 is

  • π sq unit

  • 2 sq unit

  • 3π sq unit

  • 4 sq unit


10.

Let p, q, r and s be statements and suppose that p  q  r  p. If ~ s  r, then

  • s  ~ q

  • ~ q  s

  • ~ s  ~ q

  • q  ~ s


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