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

Subject

Mathematics

Class

JEE Class 12

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

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


Advertisement
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


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


Advertisement

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


A.

62 + log1 + 2

Given equation of parabola is

         y2 = 12x         ...(i)

and equation of latusrectum is

           x = 3             ...(ii)

From Eqs. (i) and (ii), we get

         y2 = 36

        y = ± 6

 Coordinates of end points of a latusrectum are (3, 6) and (3, - 6).

 Required length = 2031 + dydx2dx= 2031 + 6y2= 20312x + 3612xdx= 203x + 3x2 + 3xdx= 2x2 + 3x + 32logx + 32 + x2 + 3x03= 232 + 32log92 + 32 - 32log32= 232 + 3log2 + 1= 62 + log1 + 2


Advertisement
Advertisement
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


Advertisement