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SBI PO Quadratic Equation Questions and Answers Set – 6

IBPS EXAM Guru
     
     
     
    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. $15x^ 2 $ - 19x + 6 = 0
    II. $6y^ 2 $ - 5y + 1 = 0

    A.   $ x > y$
    B.   $ x < y$
    C.   $ x \geq y $
    D.   $ x \leq y$
    2 . I. x = $\sqrt{172}$
    II. $y^ 2 $ - 29y + 210 = 0

    A.   $ x > y$
    B.   $ x < y$
    C.   $ x \geq y $
    D.   $ x \leq y$
    3 . I. $3x^ 2 $ - 20x + 32 = 0
    II. $2y^ 2 $ - 19y + 44 = 0

    A.   $ x > y$
    B.   $ x < y$
    C.   $ x \geq y $
    D.   $ x \leq y$
    4 . I. 3x + 8y = -2
    II. 4x + 18y = 1

    A.   $ x > y$
    B.   $ x < y$
    C.   $ x \geq y $
    D.   $ x \leq y$
    5 . I. $2x^ 2 $ - 15x + 28 = 0
    II.$ 10y^ 2 $ - y - 119 = 0

    A.   $ x > y$
    B.   $ x < y$
    C.   $ x \geq y $
    D.   $ x \leq y$
    6 . Directions (Q. 6-10): 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. 676$x^2$ - 1 = 0
    II. y = $1\over \sqrt[3]{13824}$

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    7 . I. 8x + 13y = 62
    II 13x - 17y + 128 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    8 . I. $x^ 2$ = 7x
    II. $(y + 7)^ 2$ = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    9 . I.$ 7x^ 2$ + 2x = 120
    II. $y^ 2$ + 11y + 30 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    10 . I.$ 2x^ 2$ + 5x - 33 = 0
    II. $y^ 2 $ - y - 6 = 0

    A.   $ x \geq y $
    B.   $ x < y$
    C.   $ x \leq y$
    D.   x = y or no relation can be established between ‘x’ and ‘y’.
      Answers & Solutions
       
      1 .    
      Answer : Option A
      Explanation :
      I. $15x^ 2$ - 10x - 9x + 6 = 0
      or, 5x(3x - 2) -3(3x - 2) = 0
      or, (5x - 3) (3x - 2) = 0
      x = $3\over 5$, $2\over 3$

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

      x > y
      2 .    
      Answer : Option B
      Explanation :
      I. x = $\sqrt{172}$
      x = 13.11

      II. $y^ 2$ - 14y - 15y + 210 = 0
      or, y(y - 14) - 15(y - 14) = 0
      or, (y - 14) (y - 15) = 0
      y = 14, 15

      x < y
      3 .    
      Answer : Option D
      Explanation :
      I. $ 3x^ 2$ -12x - 8x + 32 = 0
      or, 3x(x - 4) - 8(x - 4) = 0
      or, (x - 4) (3x - 8) = 0
      x = 4 , $8\over 3$

      II. $2y^ 2 $ - 8y - 11y + 44 = 0
      or, 2y(y - 4) -11(y - 4) = 0
      or, (y - 4) (2y - 11) = 0
      y = 4, $11\over 2$

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

      12x + 32y = -8
      12x + 54y = 3
      -$\,\,\,\,\,\,\,\,$ -$\,\,\,\,\,\,\,\,\,\,$ - .
      -------------------
      -22y = -11
      y = $1\over 2 $ amd x = -2

      X < Y
      5 .    
      Answer : Option C
      Explanation :
      I. $ 2x^ 2$ - 8x - 7x + 28 = 0
      or, 2x(x - 4) - 7(x - 4) = 0
      or, (x - 4) (2x - 7) = 0
      x = 4, $7\over 2$

      II. $10y^ 2 $ - 35y + 34y - 119 = 0
      or, 5y(2y - 7) + 17(2y - 7) = 0
      or, (2y - 7)(5y + 17) = 0
      y = $7\over 2$ , -$17\over 5$

      x $\geq$ y
      6 .    
      Answer : Option C
      Explanation :
      I. 676$x^2$ - 1 = 0
      $x^2$ = $1\over 676$
      x = ±$1\over 26$

      II. y = $1\over \sqrt[3]{13824}$
      y = $1\over 24$
      ie,. x < y
      7 .    
      Answer : Option C
      Explanation :
      On solving these two equations, we get
      x = -2, y = 6

      ie, x < y
      8 .    
      Answer : Option A
      Explanation :
      I. $ x^ 2$ = 7x
      or, $x 2$ - 7x = 0
      or, x(x - 7) = 0
      x = 0, 7

      II. $(y + 7) 2$ = 0
      or, (y + 7) = 0
      y = -7

      ie, x > y
      9 .    
      Answer : Option A
      Explanation :
      I. $7x^ 2$ - 28x + 30x - 120 = 0
      or, 7x(x - 4) + 30(x - 4) = 0
      or, (x - 4) (7x + 30) = 0
      x = 4, -$30\over 7$

      II. $y^ 2 $ + 6y + 5y + 30 = 0
      or, y(y + 6) + 5(y + 6) = 0
      or, (y + 5) (y + 6) = 0
      y = -5, - 6

      ie,. x > y
      10 .    
      Answer : Option D
      Explanation :
      I. $2x^ 2 $ - 6x + 11x - 33 = 0
      or, 2x(x - 3) + 11(x - 3) = 0
      or, (2x + 11) (x - 3) = 0
      x = 3, -$11\over 2$

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

      i.e no relation exists between x and y

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