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.

The principal amplitude of sin40° + icos40°5 is

  • 70°

  • - 110°

  • 110°

  • - 70°


2.

If fx = x - 1x + 1, then f(2x) is

  • fx + 1fx + 3

  • 3fx + 1fx + 3

  • fx + 3fx + 1

  • fx + 33fx + 1


3.

If the distance between the plane Ax - 2 y + z = d and the plane containing the lines x - 12 = y - 23 = z - 34 and x - 23 = y - 34 = z - 45 is 6, then d is equal to

  • 3

  • 4

  • 6

  • 1


4.

If the lines x - 12 = y + 23 = z - 14 and x - 31 = y - k2 = z1 intersect, then the value of k is

  • 3/2

  • 7/2

  • - 2/7

  • - 3/2


Advertisement
5.

If A = {x : x2 - 5x + 6 = 0}, B={2, 4}, C = {4, 5}, then A x (B ∩ C) is

  • {(2, 4), (3, 4)}


  • {(4, 2), (4, 3)}

  • {(2, 4), (3, 4), (4, 4)}

  • {(2, 2), (3, 3), (4, 4), (5, 5)}


6.

Let A and B be two non-empty sets having n elements in common. Then, the number of elements common to A x B and B x A is

  • 2n

  • n

  • n2

  • None of these


7.

∼ (P ∨ q) v ( ∼ p ∧ q) is logically equivalent to

  • - p

  • p

  • q


Advertisement

8.

The foci of a hyperbola are (- 5, 18) and (10, 20) and it touches the Y-axis. The length of its transverse axis is

  • 100

  • 892

  • 89

  • 50


C.

89

Let 2a and 2b be respectively lengths of transverse and conjugate axes of the hyperbola and its eccentricity be e. Then,

2ae = Distance between foci

 2ae = 17   ae = 17/2

We know that, the product of lengths of perpendicular from two foci on any tangent to a hyperbola is b2.

Since, given hyperbola touches Y-axis i.e., x = 0

               b2 = 50 a2e2 - 1 = 50 2894 - a2 = 50 a2 = 894  a = ± 892   a = 892         length is positiveHence, length of transverse axis = 2a = 89


Advertisement
Advertisement
9.

The locus of mid-point of the line segment joining the locus to a moving point on the parabola y2 = 4ax is another parabola with directrix

  • x = - a

  • x = a

  • x = 0

  • x = a/2


10.

The equation of the ellipse with its centre at (1, 2), one locus at (6, 2) and passing through (4, 6) is

  • x - 1245 + y - 2220 = 1

  • x - 1220 + y - 2245 = 1

  • x + 1245 + y + 2220 = 1

  • None of the above


Advertisement