SBI PO Quadratic Equation Questions and Answers Quiz

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 $x < y$