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Mathematics Test 206
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Mathematics Test 206
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  • Question 1/10
    4 / -1

    if the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0

    Solutions


     

  • Question 2/10
    4 / -1

    The circle x2 + y2 - 8x + 4y + 4 = 0 touches

  • Question 3/10
    4 / -1

    The foci of the ellipse 25(x+1)2 + 9(y+2)2 = 225 are

    Solutions

     

  • Question 4/10
    4 / -1

    The differential equation of the family of lines passing through the origin is

    Solutions

     

  • Question 5/10
    4 / -1

    The area bounded by the curve y = x2 - 4x, x-axis and line x = 2 is

    Solutions

     

  • Question 6/10
    4 / -1

    The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is

    Solutions

    We have, probability that A can solve the problem = P(A) = 1/2 ,

    And in this way P(B) = 1/3 and P(C) = 1/4.

    P(A cannot solve the problem) = 1 – P(A) = 1/2 ,

    P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,

    P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.

    P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.

    Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)

    = 1 – 1/4 = 3/4

     

  • Question 7/10
    4 / -1

    If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is

    Solutions

    Odd no. on the first die

    1, 3, 5

    multiple of 3 on the other die

    3, 6

    now let's see the combination of these two events happening simultaneously

    as the question says

    (1,3) , (1,6) , (3,3) , (3,6) , (5,6) , (5,3)

    total no of favourable events = 6

    total no of events throwing two dice simultaneously = 6² = 36

    so probability = 6/36 = 1/6

     

     

  • Question 8/10
    4 / -1

    If the roots of ax2 + bx + c = 0 are α,β and roots of Ax2 + Bx + C = 0 are α + K, β + K, then B2 - 4AC/b2 - 4ac is equal to

  • Question 9/10
    4 / -1

    The orthocentre of a triangle whose vertices are [(2),((√3-1)/2)], ((1/2),-(1/2)) and (2,-(1/2)) is

  • Question 10/10
    4 / -1

    Solutions

     

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