If f : IR → IR is defined

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

 In ABC, if bcosθ = c - a, (where θ is an acute angle), then (c - a) tanθ = ?

  • 2cacosB2

  •  2acsinB2

  •  2cacosB2

  • 2casinB2


2.

Given below is the distribution of a random variable X
X = x 1 2 3 4
P(X = x) λ 2λ 3λ 4λ

If α = PX < 3 and β = PX > 2, then α : β = ?

  • 2 5

  • 3 4

  • 4 5

  • 3 7


3.

If the pair of lines x - 16pxy - y2 = 0 and x2 - 16qxy - y = 0 are such that each pair bisects the angle between the other pair, then pq = 

  • - 164

  • 164

  •  - 18

  • 18


4.

limn1k + 2k + 3k + ... + nknk + 1 = ?

  • 1k

  • 2k + 1

  • 1k + 1

  • 2k


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5.

The coefficient of x5 in the expansion of(1 + x)21 + (1 +x)22 + ... + (1 + x)30 is

  • C631 - C621

  • C551

  • C59

  • C530 + C520


6.

Let A = {- 4, - 2, - 1, 0, 3, 5} and f : A  IR be defined by

fx = 3x - 1 for x > 3x2 + 1 for - 3  x  32x - 3 for x < - 3Then the range of f is

  • - 11, 5, 2, 1, 10, 14

  • - 11, - 7, 2, 1, 8, 14

  • - 11, 5, 2, 1, 8, 14

  • - 11, - 7, - 5, 1, 10, 14


7.

If a circle with radius 2.5 units passes through the points (2, 3) and (5, 7), then its centre is

  • (1 5, 2)

  • (7, 10)

  • (3, 4)

  • (3 5, 5)


8.

The circumcentre of the triangle formed by the points (1, 2, 3) (3, - 1, 5), (4, 0, - 3) is

  • (1, 1, 1)

  • (2, 2, 2)

  • (3, 3, 3)

  • 72,  - 12, 1


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9.

If f : IR  IR is defined byf(x) = x - 1, for x  12 - x2, for 1 < x  3x - 10, for 3 < x < 52x, for x  5then the set of points of discontinuity of f is

  • IR - 1, 5

  • 1, 3, 5

  • 1, 5

  • IR - 1, 3, 5


C.

1, 5

c Clearly, f(x) will be continuous in the intervals(- , 1), (1, 3), (3, 5) and (5, ) fx is a polynomial function in these intervalsNow, let us check the continuity at x = 1, 3 and 5Here,i limx1-fx = 1 - 1 = 0 and limx1+fx = 2 - 1 = 1therefore f is not continuous at x = 1ii limx3-fx = 2 - 9 = - 7 f(3) = - 7and limx3+fx = 3 - 10 = - 7therefore f is not continuous at x = 3iii limx5-fx = 5 - 10 = - 5 and limx5+fx = 2 × 5 = 10therefore f is not continuous at x = 5Thus, points of discontinuity of f is 1, 5


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10.

A bag P contains 5 white marbles and 3 black marbles. Four marbles are drawn at random from P and are put in an empty bag Q. If a marble drawn at random from Q is found to be black then the probability that all the three black marbles in P are transfered to the bag Q

  • 17

  • 67

  • 18

  • 78


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