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Mathematics Test 119

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Mathematics Test 119
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  • Question 1
    4 / -1

    If the complete set of values of 'x' satisfying the inequality  (where a,b,c ∈ N), then value of a + b + c is

    Solution

     

  • Question 2
    4 / -1

    The value of λ for which the system of equations sinx cosy = 2λ – 4 & siny cosx = 1 – λ have solutions -

    Solution

    sinx cosy = 2λ – 4        .....(i)

    sinycosx = 1 – λ           .....(ii)

    (i) + (ii) gives sin(x + y) = λ – 3

    &    |λ – 3| ≤ 1              ......(iii)

    (i) – (ii)  gives sin(x – y) = 3λ – 5

    &    |3λ – 5| ≤ 1        ......(iv)

    from (iii) & (iv),  λ = {2}

     

  • Question 3
    4 / -1

    Let A be matrix of order 3 × 3 such that 
    |A| = 1, let B = 2A–1, C=   then the value |AB2C3| is

    Solution

     

  • Question 4
    4 / -1

    If a and b ∈ R and satisfy the relation 4a2 + 3b2 – 4ab – 4b + 2 < 0 then value of determinant  is equal to -

    Solution

    Given 4a2 + 3b2 – 4ab – 4b + 2 < 0 

    (2a – b)2 + 2(b – 1)< 0

     

     

  • Question 5
    4 / -1

    Solution

     

  • Question 6
    4 / -1

    3sinβ + 4cosβ, then value of  y can be equal to -

    Solution

     

  • Question 7
    4 / -1

    Let A and B be two square matrices of order 3 then which of the following statements is/are correct -

    Solution

    adjA / |A| = A-1

    ∴    adjA = B and adj(AT) = BT

    Now  X = adj(AT) – B

              XT = (BT)T – adj(AT)

              XT = B – adj(AT)   ∴     XT = –X

        Option : D

        AT = –A and B + AT = 0   ∴  B = A

        Now X = B15

        XT = (BT)15 = (–A)15 = –(A15) = –B15    

        XT = –x

     

  • Question 8
    4 / -1

    Consider the following system of equations 

            αx + y + z = m

            x + αy + z = n

            x + y + αz = p

    then which of the following statement is/are correct -

    Solution

    D2 = (α – 1)(n(α + 1) – (m + p)) 

    D3 = (α – 1)(p(α + 1) – (m + n)) 

    no solution if α = 1, 

    (D = D1 = D2 = D3 = 0) and m ≠ n or n ≠ p or p ≠ m

    Infinite solution α = –2 

    (D = D1 = D2 = D3 = 0)

     

  • Question 9
    4 / -1

    Directions For Questions

    If t is real and positive and matrix A and B are such that 

    and X = (AB)–1 + (AB)–2 + (AB)–3 +...∞

    Y = X–1, then

    On the basis of above information, answer the following questions :

    ...view full instructions

    Which option is correct 

    Solution

     

  • Question 10
    4 / -1

    Directions For Questions

    If t is real and positive and matrix A and B are such that

    and X = (AB)–1 + (AB)–2 + (AB)–3 +...∞

    Y = X–1, then

    On the basis of above information, answer the following questions :

    ...view full instructions

    Let Z = X–1–I (where I is an identity matrix), then 

    Solution

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