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Mathematics Test 96
Result
Mathematics Test 96

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  • Question 1/10
    4 / -1

    Solutions

     

  • Question 2/10
    4 / -1

    Solutions

     

  • Question 3/10
    4 / -1

    Consider a triangle ABC so that sides AB and AC are respectively bisected at right angle by lines 
    y2 – 8xy – 9x2 = 0, where slope of AB is positive.

    If coordinates of B are (2, 3) and internal angle bisector of angle at B is 2x – y – 1 = 0, then equation of side BC is-

    Solutions

     

  • Question 4/10
    4 / -1

    Consider a triangle ABC so that sides AB and AC are respectively bisected at right angle by lines 
    y2 – 8xy – 9x2 = 0, where slope of AB is positive.

    If BC passes through (1,0) then locus of A is-

    Solutions

     

  • Question 5/10
    4 / -1

    Let  (where ℓ, m,k ∈ N & l/m is in lowest terms, C is the constant of integration).

    Match List-I with List-II and select the correct answer using the code given below the list.

      List-I   List-II
    (P) ℓ = (1) 3
    (Q) m = (2) 2
    (R) k = (3) 1
    (S) n + 2 = (4) 4
    Solutions

     

  • Question 6/10
    4 / -1

    Consider the line L1 : 4x + 3y – 6 = 0 and L2 : 5x + 12y + 9 = 0 then match List-I with List-II and select the correct answer using the code given below the list.

    Solutions

    L1 : –4x – 3y + 6 = 0
    L2 : 5x + 12y + 9 = 0
    a1a2 + b1b2 = (–4)(5) + (–3)(12) < 0
    Hence –sign gives obtuse angle bisector :  
                          9x – 7y – 41 = 0
    +sign gives bisector containing origin :
                           7x + 9y – 3 = 0
    Line through intersection of L1 and L2 is L1 + λL2 = 0
    (4 + 5λ)x + (3 + 12λ)y – 6 + 9λ = 0

     

  • Question 7/10
    4 / -1

    Solutions

     

  • Question 8/10
    4 / -1

    Let  where ƒ(0) = –ℓn2 &  then k is equal to

    Solutions


     

  • Question 9/10
    4 / -1

    Solutions

     

  • Question 10/10
    4 / -1

    A diagonal of rhombus ABCD is member of both the families of lines (x + y –1) + λ1 (2x + 3y – 2) = 0 & (x – y + 2) + λ2(2x – 3y + 5) = 0 where λ1,λ2 ∈ R & one of its vertex is (5,4). If area of rhombus is 12√5 square units, then the length of its smaller diagonal is

    Solutions

     

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