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Mathematics Test - 2

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Mathematics Test - 2
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  • Question 1
    2.5 / -0.83

     

    If    , then   is equal to  

    Solution

     


    =1(-5) -2(10) + 3(11)
    =-5-20+33 = 8

    =1(-30) - 6(20) + 3(66)

    = -30-120+198= 48

    D = 8 ⇒6D = 48

  • Question 2
    2.5 / -0.83

     

    Let a =  , then Det. A is   

    Solution

     

    Apply C2 →C2 + C3,



     

  • Question 3
    2.5 / -0.83

    Solution

     

    because , the value of the determinant is zero only when , the two of its  rows are identical., Which is possible only when Either x = 3 or x = 4 .

  • Question 4
    2.5 / -0.83

    Solution


  • Question 5
    2.5 / -0.83

    Solution

  • Question 6
    2.5 / -0.83

    The complex numbers z = x + iy which satisfy the equation  = 1 lie on

    Solution

    ∣z −5i ∣/∣z+5i| = 1
     ∣z −5i ∣=∣z+5i| (Using definition ∣z −z1 ∣=∣z −z2 ∣given Perpendicular bisector of z1 and z2.)
    ⇒Perpendicular bisector of points (0,5) and (0,−5). which lies on x-axis.

  • Question 7
    2.5 / -0.83

    The inequality  | z  − 4 | < | z  −2 | represents the region given by

    Solution

     Let, z = x + iy
    Putting in the given inequality,
    |(x −4)−iy| <|(x −2)+iy|
    ⇒[(x −4)2 + y2 ]11/2 <[(x −2)2 + y2 ]1/2
    squaring both sides,
    ⇒(x −4)2 + y2 <(x −2)2 + y2
    ⇒−8x+16 <−4x+4
    ⇒4

  • Question 8
    2.5 / -0.83

    A lady wants to select one cotton saree and one polyster saree from a textile shop. If there are 15 cotton and 13 polyster varieties in that shop, in how many ways can she pick up two sarees?

    Solution

    The lady can select one cotton saree out of 15 cotton varieties in 15 ways since
    any of 15 varieties can be selected. Corresponding to each selection of a cotton saree, she can
    choose a polyester saree in 13 ways. Hence the two sarees (one cotton and one polyester), by
    multiplication principle of counting, can be selected in 15 x 13= 195 ways

  • Question 9
    2.5 / -0.83

    In a class, there are 30 boys and 18 girls. The teacher wants to select one boy and one girl to  represent the class for quiz competition. In how many ways can the teacher make this selection?

    Solution

    Out of 30 Boys,
    No. of ways to select 1 boy = 30 C1 = 30
    Out of 18 Girls,
    No. of ways to select 1 boy = 18 C1 = 18
    No. of ways of selecting 1 boy and 1 girl =
    30*18 = 540

  • Question 10
    2.5 / -0.83

    The middle term in the expansion of  

    Solution

    n = 10

    Middle term = (n/2) + 1
    = (10/2) + 1
    = 6th term

    T(6) = T(5+1)
    = 10 C5 [(2x2 )/3]5 [(3/2x2 )]5
    = 10 C5
    = 252

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