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SBI PO Quadratic Equation Questions and Answers Set – 4

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    1 . Directions (Q. 1 - 5): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

    (1) if $ x > y $
    (2) if $ x \geq y $
    (3) if $ x < y $
    (4) if $ x \leq y$
    (5) if x = y or relationship between x and y cannot be established

    $Q.$
    I.11x + 5y = 117
    II. 7x + 13y = 153

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    2 . I.$6x^ 2$ + 51x + 105 = 0
    II. $2y^ 2$ + 25y + 78 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    3 . I.6x + 7y = 52
    II. 14x + 4y = 35

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    4 . I.$x^ 2$ + 11x + 30 = 0
    II. $y^ 2$ + 12y + 36 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    5 . I.$2x^ 2$ + x - 1 = 0
    II. $2y^ 2$ - 3y + l = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    6 . Directions (Q.6-10) : In the following questions three equations numbered I, II and III are given. You have to solve all the equations either together or separately, or two together and one separately, or by any other method and give answer If
    (1) x < y = z
    (2) x < y < z
    (3) x < y > z
    (4) x = y > z
    (5) x = y = z or if none of the above relationship is established

    $Q.$
    I. 7x + 6y + 4z = 122
    II. 4x + 5y + 3z = 88
    III. 9x + 2y + z = 78

    A.   x < y = z
    B.   x < y < z
    C.   x < y > z
    D.   x = y > z
    7 . I. 7x + 6y =110
    II. 4x + 3y = 59
    III. x + z = 15

    A.   x < y = z
    B.   x < y < z
    C.   x < y > z
    D.   x = y > z
    8 . I. x = $\sqrt{[(36)^{1\over 2} \times [1296]^{1\over 4}]}$
    II. 2y + 3z = 33
    III. 6y + 5z = 71

    A.   x < y = z
    B.   x < y < z
    C.   x < y > z
    D.   x = y < z
    9 . I. 8x + 7y= 135
    II. 5x + 6y = 99
    III. 9y + 8z = 121

    A.   x < y = z
    B.   x < y < z
    C.   x < y > z
    D.   x = y > z
    10 . I. $(x + y)^ 3$ = 1331
    II. x - y + z = 0
    III. xy = 28

    A.   x < y = z
    B.   x < y < z
    C.   x < y > z
    D.   x = y = z or if none of the above relationship is established
      Answers & Solutions
       
      1 .    
      Answer : Option C
      Explanation :
      eqn (I) × 7
      eqn (II) × 11
      $\,\,\,$77x + 35y = 819
      - 77x ± 143y = 1683
      ------------------------------
      - 108y = - 864
      y = 8, x = 7

      ie x < y
      2 .    
      Answer : Option C
      Explanation :
      I. $6x^ 2$ + 21x + 30x + 105 = 0
      or, 3x(2x + 7) + 15(2x + 7) = 0
      or, (3x + 15) (2x + 7) = 0
      x = -5 , -$7\over 2$

      II. $ 2y^ 2$ + 12y + 13y + 78 = 0
      or, 2y(y + 6) + 13(y + 6) = 0
      or, (2y + 13) (y + 6) = 0
      y = -$13\over 2$ , -6

      $x < y$
      3 .    
      Answer : Option C
      Explanation :
      eqn (I) × 4
      eqn (II) × 7

      24x + 28y = 208
      98x ± 28y = 245
      -
      ----------------------
      - 74x = - 37
      x = $1\over 2$, y = 7

      $x < y$
      4 .    
      Answer : Option B
      Explanation :
      I. $x^ 2$ + 5x + 6x + 30 = 0
      or, x(x + 5) + 6(x + 5) = 0
      or, (x + 5) (x + 6) = 0
      x = - 5, - 6

      II. $y^ 2$ + 12y + 36 = 0
      or, $(y + 6)^ 2$ = 0
      or, y + 6 = 0
      y = - 6

      ie x $\geq$ y
      5 .    
      Answer : Option D
      Explanation :
      I. $2x^ 2$ + 2x - x - 1 = 0
      or, 2x(x + 1) - 1(x + 1) = 0
      or, (2x - 1) (x + 1) = 0
      x = $1\over 2$ , -1

      II. $2y^ 2$ - 2y - y + 1 = 0
      or, 2y(y - 1) - 1(y - 1) = 0
      or, (2y - 1)(y - 1) = 0
      y = $1\over 2$, 1

      i.e., $x \leq y$
      6 .    
      Answer : Option A
      Explanation :
      7x + 6y + 4z = 122 ... (i)
      4x + 5y + 3z = 88 ... (ii)
      9x + 2y + z = 78 ... (iii)
      From (i) and (ii)
      5x - 2y = 14... (iv)
      From (ii) and (iii)
      23x + y = 146 ... (v)
      From (iv) and (v),
      x = 6, y = 8
      Putting the value of x and y in eqn (i), we get
      z = 8

      :. x < y = z
      7 .    
      Answer : Option C
      Explanation :
      7x + 6y = 110 ... (i)
      4x + 3y = 59 ... (ii)
      x + z = 15 ... (iii)
      From eqn (i) and (ii), x = 8, y = 9
      Put the value of x in eqn (iii).
      Then, z = 7

      x < y > z
      8 .    
      Answer : Option D
      Explanation :
      x = $\sqrt{(6^2)^{1\over 2} \times (6^4)^{1\over 4}}$
      $\sqrt{6\times6}$ = 6 ..(i)
      2y + 3z = 33 ... (ii)
      6y + 5z = 71 ... (iii)
      From eqn (ii) and (iii),
      y = 6 and z = 7

      x = y < z
      9 .    
      Answer : Option D
      Explanation :
      8x + 7y = 135 ... (i)
      5x + 6y = 99 ... (ii)
      9y + 8z = 121 ... (iii)
      From eqn (i) and (ii),
      x = 9, and y = 9
      Putting the value of y in eqn (iii),
      z = 5

      :. x = y > z
      10 .    
      Answer : Option D
      Explanation :
      $(x + y)^ 3$ = 1331
      or, x + y = 11 ... (i)
      $(x + y)^ 2$ = 121
      $(x - y)^ 2$ + 4xy = 121
      x - y = 3... (ii)
      [value of xy from eqn (iii)]
      From eqn (i) and (ii), x = 7, y = 4
      Put the value x and y in the eqn
      x - y + z = 0
      7 - y + z = 0
      3 + z = 0
      z = -3



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