Three numbers are chosen at random from 1 to 20. The probability

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If a, b, c are in GP (a> 1, b > 1, c > 1), then for any real number x (with x > 0, x  1), are in

  • GP

  • AP

  • HP

  • GP but not in HP


22.

A line through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15°. Then, the equation of the straight line in the new position is

  • 2 - 3x + y - 4 + 23 = 0

  • 2 - 3x - y - 4 + 23 = 0

  • 2 - 3x - y + 4 + 23 = 0

  • 2 - 3x + y + 4 + 23 = 0


23.

The equation 3sinx + cosx = 4 has

  • only one solution

  • two solutions

  • infinitely many solutions

  • no solution


24.

The modulus of 1 - i3 + i + 4i5 is

  • 5 unit

  • 115 unit

  • 55 unit

  • 125


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25.

The equation of the tangent to the conic x2 - y2 - 8x + 2y + 11 = 0 at (2, 1) is

  • x + 2 = 0

  • 2x + 1 = 0

  • x + y + 1 = 0

  • x - 2 = 0


26.

A and B are two independent events such that P(A B') = 0.8, and P(A) = 0.3. Then, P(B) is

  • 27

  • 23

  • 38

  • 18


27.

The total number of tangents through the point ( 3, 5) that can be drawn to the ellipses 3x2 + 5y2 = 32 and 25x + 9y2 = 450 is

  • 0

  • 2

  • 3

  • 4


28.

The value of limnnn2 + 12 + nn2 + 22 + ... + nn2 + n2 is

  • π4

  • log2

  • 0

  • 1


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29.

A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t - 6t2 + t3. Its acceleration will be zero at

  • t = 1 unit time

  • t = 2 unit time

  • t = 3 unit time

  • t = 4 unit time


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30.

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive is

  • 1190

  • 1120

  • 3190

  • 5190


C.

3190

The total number of favourable cases, n(E) = 18

The total number of cases, n(S) = C320

                                              = 20 × 19 × 183 × 2 × 1 = 1140

    Required probability = 181140 = 3190


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