Monday, 13 March 2017

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.   $x \leq y$

1 .
 Answer : Option B Explanation : I. $2x^ 2$ + 2x - x - 1 = 0or, 2x(x + 1) - 1(x + 1) = 0or, (x + 1) (2x - 1) = 0x = -1 , $1\over 2$II. $6y^ 2$ - 3y - 10y + 5 = 0or, 3y(2y - 1) - 5(2y - 1) = 0or, (3y - 5)(2y - 1) = 0y = -3, $11\over 3$$x < y 2 .  Answer : Option D Explanation : I. 21x ^ 2 - 45x - 77x + 165 = 0or, 3x(7x - 15) - 11 (7x - 15) = 0or, (3x - 11) (7x - 15) = 0x = 11\over 3, 15\over 7II. 3y^ 2 + 9y - 11y - 33 = 0or,3y(y + 3) - 11(y + 3) = 0or,(3y - 11) (y + 3) = 0y = -3 , 11\over 3Hence, no relation can be established between x and y. 3 .  Answer : Option D Explanation : I. 5x^ 2 - 20x - 9x + 36 = 0or, 5x(x - 4) - 9(x - 4) = 0or,(x - 4) (5x - 9) = 0x = 4 , 9\over 5II. 10y ^ 2 + 15y - 18y - 27 = 0or, 5y(2y + 3) - 9(2y + 3) = 0or, (2y + 3) (5y - 9) = 0y = 9\over 5, - 3\over 2x \geq y 4 .  Answer : Option B Explanation : eqn (I) × 3 - eqn (II) × 4 21x + 12y = 920x + 12y = 12-\,\,\,\,\,\,\,\,\, -\,\,\,\,\,\,\,\,\, - -------------------x = - 3and y = 6x < y 5 .  Answer : Option A Explanation : I. 7x^ 2 - 21x - 33x + 99 = 0or, 7x(x - 3) - 33(x - 3) = 0or, (x - 3) (7x - 33) = 0x = 3, 33\over 7II. 4y^ 2 - 6y - 10y + 15 = 0 or, 2y(2y - 3) - 5(2y - 3) = 0or, (2y - 3)(2y - 5) = 0y = 3\over 2, 5\over 2$$x > y$
6 .
 Answer : Option A Explanation : I. $5x^ 2$ - 45x - 42x + 378 = 0or, 5x(x - 9) - 42(x - 9) = 0or, (5x - 42) (x - 9) = 0x = 9 , $42\over 5$II. $3y^ 2$ - 24y - 25y + 200 = 0or, 3y(y - 8) - 25(y - 8) = 0or, (y - 8) (3y - 25) = 0y = 8, $25\over 3$$x > y 7 .  Answer : Option A Explanation : I. 10x^ 2 - 16x + 15x - 24 = 0or, 2x(5x - 8) + 3(5x - 8) = 0or, (2x + 3) (5x - 8) = 0x = -3\over 2, 8\over5II.y^ 2 - 2y = 0or, y(y - 2) = 0y = 0, 2ie no relationship exists between x and y 8 .  Answer : Option D Explanation : I. x^ 2 - 2x - 3x + 6 = 0or, x(x - 2) - 3(x - 2) = 0or, (x - 2) (x - 3) = 0x = 2, 3II. 2y ^ 2 - 6y - 9y + 27 = 0or, 2y(y - 3) - 9(y - 3) = 0or, (y - 3) (2y - 9) = 0y = 3, 9\over 2$$x \leq y$
9 .
 Answer : Option B Explanation : eqn (I) × 5 + eqn (II) × 215x + 10y = 150514x - 10y = 148------------------------29x $\,\,\,\,\,\,\,\,\,\,$ = 1653$x$ = $1653\over 29$ = 57 and y = 65 $x < y$
10 .
 Answer : Option C Explanation : I. $14x^ 2$ - 37x + 24 = 0or, $14x^ 2$ - 21x - 16x + 24 = 0or, 7x(2x - 3) - 8(2x - 3) = 0or, (2x - 3) (7x - 8) = 0x = $3\over 2$, $8\over 7$II. $28y^ 2$ - 53y + 24 = 0or, $28y^ 2$ - 21y - 32y + 24 = 0or, 7y(4y - 3) - 8(4y - 3) = 0or, (7y - 8) (4y - 3) = 0y = $8 \over 7$, $3\over 4$$x \geq y$