Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

31.

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal

  • is linear

  • is homogeneous of second degree

  • has separable variables

  • is of second order


32.

The solution of the equation dydx = cosx - y is

  • x + cotx - y2 = C

  • y + cotx - y2 = C

  • x + tanx - y2 = C

  • None of these


33.

The differential equation of all parabolas each of which has a latusrectum 4a and whose axes are parallel to the Y-axis is

  • of order 1 and degree 2

  • of order 2 and degree 3

  • of order 2 and degree 1

  • of order 2 and degree 2


34.

The value of the parameter a such that the area bounded by y = a2x2 + ax + 1, coordinate axes and the line x = 1 attains its least value is equal to

  • - 1

  • - 14

  • - 34

  • - 12


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35.

0xsintdt, where x  2, 2n + 1π, n  N, is equal to

  • 4n - 1 - cos(x)

  • 4n - sin(x)

  • 4n - cos(x)

  • 4n + 1 - cos(x)


36.

Let I101exdx1 + x and I201x2dxex32 - x3 Then, I1I2 is equal to

  • 13e

  • 3e

  • e3

  • 3e


37.

52525 - x23x4dx is equal to

  • π3

  • 2π3

  • π6

  • 5π6


38.

If n integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9 is

  • 4n5n

  • 2n5n

  • 4 - 2n5n

  • None


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39.

A bag contains (n + 1) coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 712, then the value of n is

  • 5

  • 4

  • 3

  • None of these


A.

5

Let E1 denote the event 'A coin with two heads is selected' and E2 denote the event 'a fair coin is selected'. Again, let A be the event 'The toss results in head.' Then,

    PE1 = 1n + 1, PE2 = nn + 1, PAE1 = 1 and PAE2 = 12 PA = PE1 . PAE1 + PE2 . PAE2  712 = 1n + 1 × 1 + nn + 1 ×12                   PA  = 712 12 +6n = 7n + 7  n = 5


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40.

If A and B are two given events, then P(A ∩ B) is

  • equal to P(A) + P(B)

  • equal to P(A) + P(B) + P(A  B)

  • not less than P(A) + P(B) - 1

  • not greater than P(A) + P(B) - P(A  B)


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