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SBI PO Quadratic Equation Questions and Answers set 3

IBPS EXAM Guru
     
     
     
    1 . Directions (Q. 1-10): Two equations (I) and (II) are given in each question. On the basis of these equations, you have to decide the relation between x and y and give answer

    (1) if x > y
    (2) if x < y
    (3) if x $\geq$ y
    (4) if x $\leq$ y
    (5) if x = y, or no relation can be established between x and y.

    $Q.$
    I. $2x^ 2$ + x - 1 = 0
    II. $6y^ 2 $ - 13y + 5 = 0

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   x = y or no relation can be established between ‘x’ and ‘y’.
    2 . I. $21x ^ 2 $ - 122x + 165 = 0
    II. $3y^2 $ - 2y - 33 = 0

    A.   $ x > y $
    B.   $ x \geq y $
    C.   $ x < y $
    D.   x = y or no relation can be established between ‘x’ and ‘y’.
    3 . I. $5x 2 $ - 29x + 36 = 0
    II. $10y 2 $ - 3y - 27 = 0

    A.   $ x > y $
    B.   $ x \leq y$
    C.   $ x < y $
    D.   $ x \geq y $
    4 . I. 7x + 4y = 3
    II. 5x + 3y = 3

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \leq y$
    D.   $ x \geq y $
    5 . I. $7x^ 2 $ - 54x + 99 = 0
    II. $4y^ 2 $ - 16y + 15 = 0

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
    6 . I. $5x^ 2 $ - 87x + 378 = 0
    II. $3y^ 2 $ - 49y + 200 = 0

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
    7 . I. $10x^ 2 $ - x - 24 = 0
    II. $y^ 2 $ - 2y = 0

    A.   x = y or no relation can be established between ‘x’ and ‘y’.
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
    8 . I. $x^ 2 $ - 5x + 6 = 0
    II. $2y^ 2 $ - 15y + 27 = 0

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
    9 . I. 3x + 2y = 301
    II. 7x - 5y = 74

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
    10 . I. $14x ^ 2 $ - 37x + 24 = 0
    II. $28y^ 2 $ - 53y + 24 = 0

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
      Answers & Solutions
       
      1 .    
      Answer : Option B
      Explanation :
      I. $2x^ 2$ + 2x - x - 1 = 0
      or, 2x(x + 1) - 1(x + 1) = 0
      or, (x + 1) (2x - 1) = 0
      x = -1 , $1\over 2$

      II. $6y^ 2$ - 3y - 10y + 5 = 0
      or, 3y(2y - 1) - 5(2y - 1) = 0
      or, (3y - 5)(2y - 1) = 0
      y = -3, $11\over 3$

      $x < y$
      2 .    
      Answer : Option D
      Explanation :
      I. $ 21x ^ 2$ - 45x - 77x + 165 = 0
      or, 3x(7x - 15) - 11 (7x - 15) = 0
      or, (3x - 11) (7x - 15) = 0
      x = $11\over 3$, $15\over 7$

      II. $3y^ 2$ + 9y - 11y - 33 = 0
      or,3y(y + 3) - 11(y + 3) = 0
      or,(3y - 11) (y + 3) = 0
      y = -3 , $11\over 3$

      Hence, no relation can be established between x and y.
      3 .    
      Answer : Option D
      Explanation :
      I. $5x^ 2$ - 20x - 9x + 36 = 0
      or, 5x(x - 4) - 9(x - 4) = 0
      or,(x - 4) (5x - 9) = 0
      x = 4 , $9\over 5$

      II. $10y ^ 2$ + 15y - 18y - 27 = 0
      or, 5y(2y + 3) - 9(2y + 3) = 0
      or, (2y + 3) (5y - 9) = 0
      y = $9\over 5$, - $3\over 2$

      x $\geq$ y
      4 .    
      Answer : Option B
      Explanation :
      eqn (I) × 3 - eqn (II) × 4

      21x + 12y = 9
      20x + 12y = 12
      -$\,\,\,\,\,\,\,\,\,$ -$\,\,\,\,\,\,\,\,\,$ -
      -------------------
      x = - 3

      and y = 6

      $x < y$
      5 .    
      Answer : Option A
      Explanation :
      I. $7x^ 2$ - 21x - 33x + 99 = 0
      or, 7x(x - 3) - 33(x - 3) = 0
      or, (x - 3) (7x - 33) = 0
      x = 3, $33\over 7$

      II. $4y^ 2$ - 6y - 10y + 15 = 0
      or, 2y(2y - 3) - 5(2y - 3) = 0
      or, (2y - 3)(2y - 5) = 0
      y = $3\over 2$, $5\over 2$

      $x > y$
      6 .    
      Answer : Option A
      Explanation :
      I. $5x^ 2$ - 45x - 42x + 378 = 0
      or, 5x(x - 9) - 42(x - 9) = 0
      or, (5x - 42) (x - 9) = 0
      x = 9 , $42\over 5$

      II. $3y^ 2$ - 24y - 25y + 200 = 0
      or, 3y(y - 8) - 25(y - 8) = 0
      or, (y - 8) (3y - 25) = 0
      y = 8, $25\over 3$

      $x > y$
      7 .    
      Answer : Option A
      Explanation :
      I. $ 10x^ 2$ - 16x + 15x - 24 = 0
      or, 2x(5x - 8) + 3(5x - 8) = 0
      or, (2x + 3) (5x - 8) = 0
      x = -$3\over 2$, $8\over5$

      II.$y^ 2$ - 2y = 0
      or, y(y - 2) = 0
      y = 0, 2
      ie no relationship exists between x and y
      8 .    
      Answer : Option D
      Explanation :
      I.$ x^ 2$ - 2x - 3x + 6 = 0
      or, x(x - 2) - 3(x - 2) = 0
      or, (x - 2) (x - 3) = 0
      x = 2, 3

      II. $ 2y ^ 2$ - 6y - 9y + 27 = 0
      or, 2y(y - 3) - 9(y - 3) = 0
      or, (y - 3) (2y - 9) = 0
      y = 3, $9\over 2$

      $x \leq y$
      9 .    
      Answer : Option B
      Explanation :
      eqn (I) × 5 + eqn (II) × 2

      15x + 10y = 1505
      14x - 10y = 148
      ------------------------
      29x $\,\,\,\,\,\,\,\,\,\,$ = 1653

      $x$ = $1653\over 29$ = 57 and y = 65

      $x < y$
      10 .    
      Answer : Option C
      Explanation :
      I. $ 14x^ 2$ - 37x + 24 = 0
      or, $14x^ 2$ - 21x - 16x + 24 = 0
      or, 7x(2x - 3) - 8(2x - 3) = 0
      or, (2x - 3) (7x - 8) = 0
      x = $3\over 2$, $8\over 7$

      II. $28y^ 2$ - 53y + 24 = 0
      or, $ 28y^ 2$ - 21y - 32y + 24 = 0
      or, 7y(4y - 3) - 8(4y - 3) = 0
      or, (7y - 8) (4y - 3) = 0
      y = $8 \over 7$, $3\over 4$

      $x \geq y$

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