Quadratic Equation Practice set for IBPS Clerk 2017

Quadratic Equation Practice set for IBPS Clerk 2017

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 Answer & Explanation 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 = $7\over5$ , $3\over 2$ $x \geq y$ View Answer 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 Answer & Explanation 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, $7\over 4$ $x \leq y$ View Answer 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 Answer & Explanation 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$ View Answer 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 Answer & Explanation 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 , $3\over 2$ $x < y$ View Answer 5 . I. 7x - 3y = 13 II. 5x + 4y = 40 A). x > y B). x < y C). x $\geq$ y D). x $\leq$ y Answer & Explanation Answer : Option B   Explanation :   Eqn (I) × 4 + Eqn (II) × 3 28x - 12y = 52 15x + 12y = 120 ----------------------- 43x $\,\,\,\,\,\,\,\,\,\,\,$ = 172 ----------------------- x = 4 & y = 5 $x < y $ View Answer 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’. Answer & Explanation 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 = $3\over 7$ , $2\over 3$ $x > y$ View Answer 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 Answer & Explanation 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 View Answer 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$ Answer & Explanation 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 View Answer 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$ Answer & Explanation 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 $ View Answer 10 . I. 2x + 5y = 6 II. 5x + 11y = 9 A). $ x > y $ B). $ x < y $ C). $ x \geq y $ D). $ x \leq y$ Answer & Explanation Answer : Option B   Explanation :   eq (I) × 5 - eq (II) × 2 10x + 25y = 30 10x ± 22y = 18 - $\,\,\,\,\,\,$ - $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$- --------------------- $\,\,\,\,\,\,\,\,\,\,\,$ 3y = 12 y = 4 and x = - 7 $x < y$ View Answer