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

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

51.

limxαtanxcotx1x - α is equal to

  • 2csc2α

  • 12sin2α

  • - 2csc2α

  • None of these


52.

The value of limx2xn1ex - 3xn1ex xn (where, x  N) is

  • 0

  • n logn23

  • log23

  • not defined


53.

limxπ4tanx - 1cos2x is equal to

  • 1

  • 0

  • - 2

  • - 1


54.

Which of the following inequality is true for x > 0?

  • log1 + x < x1 + x < x

  • x1 + x < x < log1 + x

  • x < log1 + x < x1 + x

  • x1 + x < log1 +x < x


Advertisement
55.

The value of limxπ2 - tan-1x1x is

  • 0

  • 1

  • - 1

  • e


56.

Find the value of the limit limx01 - cosxx

  • 0

  • 1

  • 2

  • does not exist


57.

The values of constants a and b so that

limxx2 + 1x + 1 - ax - b = 0 are

  • a = 0, b = 0

  • a = 1, b = - 1

  • a = - 1, b = 1

  • a = 2, b = - 1


58.

limn11 . 2 + 12 . 3 + 13 . 4 + ... + 1nn + 1 is equal to

  • 1

  • - 1

  • 0

  • None of these


Advertisement
59.

limxx + 5x + 2x + 3 equals

  • e

  • e2

  • e3

  • e5


Advertisement

60.

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


Advertisement
Advertisement