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Mathematics Test 154
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Mathematics Test 154

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  • Question 1/10
    4 / -1

    The existence of unique solution of the system of equations, 

    x + y + z = β,

    5x – y + αz = 10,

    2x + 3y – z = 6

    depends on

    Solutions

    Here, Δ ≠ 0

    As, Δ = (23 – α) ≠ 0

     

  • Question 2/10
    4 / -1

    The value of 

    Solutions

    = 15C1 × 35C9 × 15C2 × 35C8 +...+15C10 × 35C0

    = 50C10 – 35C10 

     

  • Question 3/10
    4 / -1

    The total number of shortest path from A to B is:-

  • Question 4/10
    4 / -1

    If |z| = 1 then is equal to ?

    Solutions

     

  • Question 5/10
    4 / -1

    A ten digit number is formed (without repetition), the probability that the difference of the digits at equal distances from the begining and the end is always 1 is ?

    Solutions

    dis joint pair are (0,1), (2,3), (4,5), (6,7), (8,9) so required probability =

     

  • Question 6/10
    4 / -1

    The coordinates of the foot of the perpendiculars from the vertices of a triangle on the opposite sides are (20,25), (8,16) and (8,9). The orthocentre of the triangle lies at the point-

    Solutions

     

  • Question 7/10
    4 / -1

    The co-ordinates of the orthocentre of the triangle formed by the lines 2x2 – 2y2 + 3xy + 3x + y + 1 = 0 and 3x + 2y + 1 = 0 are :-

    Solutions

    2x2 – 2y2 + 3xy + 3x + y + 1

    ⇒ 2x2 + 3(y + 1) x – (2y2 – y – 1) = 0

    ⇒ (x + 2y + 1) (2x – y + 1) = 0

    ∴ The sides of the triangle are

    x + 2y + 1 = 0        ....(1)

    2x – y + 1 = 0        ....(2)

    3x + 2y + 1 = 0       ....(3)

    ∵ Lines (1) and (2) are perpendicular

    ∴   Orthocentre H lies on their point of intersection

    ∴ H ≡ 

     

  • Question 8/10
    4 / -1

    The point A on the parabola y2 = 4ax for which |AC – BC| is maximum, whose B(0, a) and C(–a, 0) is :-

    Solutions

     

  • Question 9/10
    4 / -1

    The distance of the point having position vectorfrom the straight line passing through the point (2, 3, –4) and parallel to the vector,

    Solutions

     

  • Question 10/10
    4 / -1

    If the distance of the point P(1,–2,1) from the plane x + 2y – 2z = a, where a > 0, is 5, then the foot of the perpendicular from P to the plane is-

    Solutions

     

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