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SBI PO Quadratic Equation Questions and Answers Quiz

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SBI PO Quadratic Equation Questions and Answers Quiz

     
     
     
    1 . Directions (Q. 1-5): 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. $6x^ 2 - 19x + 15 = 0 $
    II.$ 10y^ 2 - 29y + 21 = 0$

    A.   x > y
    B.   x < y
    C.   x $\geq$ y
    D.   x $\leq$ y
    2 . I. 12 $x^ 2 $ + 11x - 56 = 0
    II. 4 $y^ 2 $ - 15y + 14 = 0

    A.   x > y
    B.   x < y
    C.   x $\geq$ y
    D.   x $\leq$ y
    3 . I. $3x 2 + 13x + 12 $= 0
    II.$ y^ 2 + 9y + 20 $= 0

    A.   x > y
    B.   x < y
    C.   x $\geq$ y
    D.   x $\leq$ y
    4 . I. $8x^ 2 $ - 15x + 7 = 0
    II. $2y^ 2 $ - 7y + 6 = 0

    A.   x > y
    B.   x < y
    C.   x $\geq$ y
    D.   x $\leq$ y
    5 . I. 7x - 3y = 13
    II. 5x + 4y = 40

    A.   x > y
    B.   x < y
    C.   x $\geq$ y
    D.   x $\leq$ y
    6 . I.$ 2x^ 2 $ - 11x + 15 = 0
    II.$ 21y^2$ - 23y + 6 = 0

    A.   x > y
    B.   x < y
    C.   x $\geq$ y
    D.   x = y or no relation can be established between ‘x’ and ‘y’.
    7 . I. $5x^ 2 $ - 16x + 11= 0
    II. $5y^ 2 $ - 3y - 2 = 0

    A.   x>y
    B.   x $\geq$ y
    C.   x< td>
    D.   x $\leq$ y
    8 . I. $x^ 2 $ + 11x + 28 = 0
    II. $2y^ 2 $ + 13y + 20 = 0

    A.   x > y
    B.   x < y
    C.   $ x \geq y $
    D.   $ x \leq y$
    9 . I. $6x^ 2$ + 29x + 35 = 0
    II. $3y^ 2 $ + 19y + 30 = 0

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
    10 . I. 2x + 5y = 6
    II. 5x + 11y = 9

    A.   $ x > y $
    B.   $ x < y $
    C.   $ x \geq y $
    D.   $ x \leq y$
      Answers & Solutions
       
      1 .    
      Answer : Option C
      Explanation :
      $6x^ 2 - 19x + 15 = 0 $
      $3x(2x - 3) - 5(2x - 3) = 0$
      $ (3x - 5) (2x - 3) = 0$
      $x$ = $5\over 3$ , $3\over 2$

      $10y 2 - 15y - 14y + 21 = 0$
      $ 5y(2y - 3) - 7(2y - 3) = 0$
      $(5y - 7) (2y - 3) = 0$
      y = $7\over5$ , $3\over 2$
      $x \geq y$
      2 .    
      Answer : Option D
      Explanation :
      I. $12 x^ 2 + 32x - 21x - 56 $ = 0
      or, 4x(3x + 8) - 7(3x + 8) = 0
      or, (4x - 7) (3x + 8) = 0
      X = $7\over 4$ , $-8\over 3$

      II. $ 4y^ 2 - 8y - 7y + 14 $= 0
      or, 4y(y - 2) - 7(y - 2) = 0
      or, (4y - 7) (y - 2) = 0
      y = 2, $7\over 4$

      $x \leq y$
      3 .    
      Answer : Option A
      Explanation :
      I . $3x^ 2$ + 9x + 4x + 12 = 0
      or, 3x(x + 3) + 4(x + 3) = 0
      or, (3x + 4) (x + 3) = 0
      x = $-4\over 3$, -3

      II.$ y^ 2$ + 5y + 4y + 20 = 0
      or, y(y + 5) + 4(y + 5) = 0
      or, (y + 4) (y + 5) = 0
      y = - 4, - 5

      $ x > y$
      4 .    
      Answer : Option B
      Explanation :
      I. $8x^ 2$ - 8x - 7x + 7 = 0
      or, 8x(x - 1) -7(x - 1) = 0
      or, (8x - 7) (x - 1) = 0
      x = $7\over 8$ , 1

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

      $x < y$
      5 .    
      Answer : Option B
      Explanation :
      Eqn (I) × 4 + Eqn (II) × 3

      28x - 12y = 52
      15x + 12y = 120
      -----------------------
      43x $\,\,\,\,\,\,\,\,\,\,\,$ = 172
      -----------------------

      x = 4 & y = 5

      $x < y $
      6 .    
      Answer : Option A
      Explanation :
      I. $ 2x^ 2 $ - 6x - 5x + 15 = 0
      or,2x(x - 3) - 5(x - 3) = 0
      or, (2x - 5) (x - 3) = 0
      x = 3 , $5\over 2$

      II. $21y^ 2$ - 14y - 9y + 6 = 0
      or,7y(3y - 2) - 3 (3y - 2) = 0
      or,(7y - 3)(3y - 2) = 0
      y = $3\over 7$ , $2\over 3$

      $x > y$
      7 .    
      Answer : Option B
      Explanation :
      I. $ 5x^ 2 $ - 5x - 11x + 11 = 0
      or,5x(x - 1) - 11(x - 1) = 0
      or,(x - 1) (5x - 11) = 0

      x = 1 , $11\over 5$

      II. $5y^ 2$ - 5y + 2y - 2 = 0
      or, 5y (y - 1) + 2(y - 1) = 0
      or, (5y + 2)(y - 1) = 0

      y = 1 , - $2\over 5$

      x $\geq$ y
      8 .    
      Answer : Option D
      Explanation :
      I. $x^ 2$ + 4x + 7x + 28 = 0
      or, x(x + 4) +7(x + 7) = 0
      or, (x + 4) (x + 7) = 0

      x = - 4, - 7

      II. $2y^ 2$ + 8y + 5y + 20 = 0
      or, 2y(y + 4) + 5(y + 4) = 0
      or, (y + 4) (2y + 5) = 0
      y = -4, -$5\over 2$

      x $\leq$ y
      9 .    
      Answer : Option A
      Explanation :
      I. $6x ^ 2$ + 15x + 14x + 35 = 0
      or, 3x(2x + 5) + 7(2x + 5) = 0
      or,(3x + 7) (2x + 5) = 0
      x = - $7\over 3$ , - $5\over 2$

      II. $3y^ 2$ + 9y + 10y + 30 = 0
      or, 3y(y + 3) +10(y + 3) = 0
      or,(3y + 10) (y + 3) = 0
      y = 3, -$10\over 3$

      $ x > y $
      10 .    
      Answer : Option B
      Explanation :
      eq (I) × 5 - eq (II) × 2

      10x + 25y = 30
      10x ± 22y = 18
      - $\,\,\,\,\,\,$ - $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$-
      ---------------------
      $\,\,\,\,\,\,\,\,\,\,\,$ 3y = 12
      y = 4 and x = - 7

      $x < y$



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