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Mathematics Test 7
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Mathematics Test 7

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  • Question 1/10
    4 / -1

    The pole of the straight line 9x + y – 28 = 0 with respect to the circle 2x2 + 2y2– 3x + 5y – 7 = 0 is-

    Solutions

     

  • Question 2/10
    4 / -1

    If f(x) =  is to be made continuous at x = 0, then f(0) should be equal to -

    Solutions

     

  • Question 3/10
    4 / -1

    Angle between diagonals of a parallelogram whose side are represented by 

    Solutions

    Let the angle be t

    Therefore, cos t = (p.q)/|p||q|

    here, p is the first diagnol and p is the second diagnol.

    p = a+b = i+2j+2k

    q = a-b = 3i

    therefore, cos t = 1/3

    Hence, option A is right.

     

  • Question 4/10
    4 / -1

    The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0, and their ordinates are the roots of the equation x2 + 2px – q2 = 0. The radius of the circle with AB as diameter is

    Solutions

    Let A ≡ (x1, y1) and B ≡ (x2, y2) since x1, x2 are roots of x2 + 2ax – b2 = 0 there fore 

    x1 + x2 = – 2a 

    x1x2 = – b2 

    Also y1, y2 are roots of x2 + 2px – q2 = 0 

    ∴ y1 + y2 = – 2p 

    y1y2 = – q2 

     

  • Question 5/10
    4 / -1

    If D, E, F are the mid points of the sides BC, CA and Ab respectively of a triangle ABC and 'O' is any point then  is-

    Solutions

     

  • Question 6/10
    4 / -1

    Evaluate dx -

    Solutions

     

  • Question 7/10
    4 / -1

    The total number of matrices formed with the help of 6 different numbers are -

    Solutions

    Taking any six digits as 1, 2, 3, 4, 5, 6 

    No. of matrices = they are either in 6 × 1 or 1 × 6 or 2 × 3 or 3 × 2 matrix form = 4 × (6!) 

    ∴ Option D is correct answer.

     

  • Question 8/10
    4 / -1

    For any square matrix A, A + AT will be symmetric matrix then A – AT will be-

    Solutions

    Every square matrix can be uniquely expressed as the sum of symmetric and skew

     

  • Question 9/10
    4 / -1

    If lines px2 – qxy – y2 = 0 make angle 'α' and 'β' with x-axis then value of tan(α + β) is -

    Solutions

    Since lines px2 – qxy – y2 = 0 makes angle ‘α’ and ‘β’ with x-axis 

     

  • Question 10/10
    4 / -1

    The vector  perpendicular to the vectors  and satisfying the condition = – 6 is

    Solutions

     

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