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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 $
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B). $ x < y $
| C). $ x \geq y $
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D). x = y or no relation can be established between ‘x’ and ‘y’. |
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Answer & Explanation
Answer : Option
B
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Explanation : |
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I. $2x^
2$
+ 2x - x - 1 = 0
or, 2x(x + 1) - 1(x + 1) = 0
or, (x + 1) (2x - 1) = 0
x = -1 , $1\over 2$
II. $6y^
2$
- 3y - 10y + 5 = 0
or, 3y(2y - 1) - 5(2y - 1) = 0
or, (3y - 5)(2y - 1) = 0
y = -3, $11\over 3$
$x < y$ |
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2 . |
I. $21x ^
2 $
- 122x + 165 = 0 II. $3y^2 $
- 2y - 33 = 0 |
A). $ x > y $
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B). $ x \geq y $
| C). $ x < y $
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D). x = y or no relation can be established between ‘x’ and ‘y’. |
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Answer & Explanation
Answer : Option
D
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Explanation : |
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I. $ 21x ^
2$
- 45x - 77x + 165 = 0
or, 3x(7x - 15) - 11 (7x - 15) = 0
or, (3x - 11) (7x - 15) = 0
x = $11\over 3$, $15\over 7$
II. $3y^
2$
+ 9y - 11y - 33 = 0
or,3y(y + 3) - 11(y + 3) = 0
or,(3y - 11) (y + 3) = 0
y = -3 , $11\over 3$
Hence, no relation can be established between x and y. |
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3 . |
I. $5x
2 $
- 29x + 36 = 0 II. $10y
2 $
- 3y - 27 = 0 |
A). $ x > y $
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B). $ x \leq y$
| C). $ x < y $
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D). $ x \geq y $
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Answer & Explanation
Answer : Option
D
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Explanation : |
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I. $5x^
2$
- 20x - 9x + 36 = 0
or, 5x(x - 4) - 9(x - 4) = 0
or,(x - 4) (5x - 9) = 0
x = 4 , $9\over 5$
II. $10y
^
2$
+ 15y - 18y - 27 = 0
or, 5y(2y + 3) - 9(2y + 3) = 0
or, (2y + 3) (5y - 9) = 0
y = $9\over 5$, - $3\over 2$
x $\geq$ y |
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4 . |
I. 7x + 4y = 3 II. 5x + 3y = 3 |
A). $ x > y $
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B). $ x < y $
| C). $ x \leq y$
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D). $ x \geq y $
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Answer & Explanation
Answer : Option
B
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Explanation : |
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eqn (I) × 3 - eqn (II) × 4
21x + 12y = 9
20x + 12y = 12
-$\,\,\,\,\,\,\,\,\,$ -$\,\,\,\,\,\,\,\,\,$ -
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x = - 3
and y = 6
$x < y$ |
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5 . |
I. $7x^
2 $
- 54x + 99 = 0 II. $4y^
2 $
- 16y + 15 = 0 |
A). $ x > y $
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B). $ x < y $
| C). $ x \geq y $
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D). $ x \leq y$
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Answer & Explanation
Answer : Option
A
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Explanation : |
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I. $7x^
2$
- 21x - 33x + 99 = 0
or, 7x(x - 3) - 33(x - 3) = 0
or, (x - 3) (7x - 33) = 0
x = 3, $33\over 7$
II. $4y^
2$
- 6y - 10y + 15 = 0
or, 2y(2y - 3) - 5(2y - 3) = 0
or, (2y - 3)(2y - 5) = 0
y = $3\over 2$, $5\over 2$
$x > y$ |
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6 . |
I. $5x^
2 $
- 87x + 378 = 0
II. $3y^
2 $
- 49y + 200 = 0 |
A). $ x > y $
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B). $ x < y $
| C). $ x \geq y $
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D). $ x \leq y$
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Answer & Explanation
Answer : Option
A
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Explanation : |
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I. $5x^
2$
- 45x - 42x + 378 = 0
or, 5x(x - 9) - 42(x - 9) = 0
or, (5x - 42) (x - 9) = 0
x = 9 , $42\over 5$
II. $3y^
2$
- 24y - 25y + 200 = 0
or, 3y(y - 8) - 25(y - 8) = 0
or, (y - 8) (3y - 25) = 0
y = 8, $25\over 3$
$x > y$ |
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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 $
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D). $ x \leq y$
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Answer & Explanation
Answer : Option
A
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Explanation : |
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I. $ 10x^
2$
- 16x + 15x - 24 = 0
or, 2x(5x - 8) + 3(5x - 8) = 0
or, (2x + 3) (5x - 8) = 0
x = -$3\over 2$, $8\over5$
II.$y^
2$
- 2y = 0
or, y(y - 2) = 0
y = 0, 2
ie no relationship exists between x and y |
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8 . |
I. $x^
2 $
- 5x + 6 = 0 II. $2y^
2 $
- 15y + 27 = 0 |
A). $ x > y $
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B). $ x < y $
| C). $ x \geq y $
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D). $ x \leq y$
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Answer & Explanation
Answer : Option
D
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Explanation : |
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I.$ x^
2$
- 2x - 3x + 6 = 0
or, x(x - 2) - 3(x - 2) = 0
or, (x - 2) (x - 3) = 0
x = 2, 3
II. $ 2y ^
2$
- 6y - 9y + 27 = 0
or, 2y(y - 3) - 9(y - 3) = 0
or, (y - 3) (2y - 9) = 0
y = 3, $9\over 2$
$x \leq y$ |
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9 . |
I. 3x + 2y = 301 II. 7x - 5y = 74 |
A). $ x > y $
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B). $ x < y $
| C). $ x \geq y $
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D). $ x \leq y$
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Answer & Explanation
Answer : Option
B
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Explanation : |
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eqn (I) × 5 + eqn (II) × 2
15x + 10y = 1505
14x - 10y = 148
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29x $\,\,\,\,\,\,\,\,\,\,$ = 1653
$x$ = $1653\over 29$ = 57 and y = 65
$x < y$ |
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10 . |
I. $14x ^
2 $
- 37x + 24 = 0 II. $28y^
2 $
- 53y + 24 = 0 |
A). $ x > y $
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B). $ x < y $
| C). $ x \geq y $
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D). $ x \leq y$
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Answer & Explanation
Answer : Option
C
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Explanation : |
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I. $ 14x^
2$
- 37x + 24 = 0
or, $14x^
2$
- 21x - 16x + 24 = 0
or, 7x(2x - 3) - 8(2x - 3) = 0
or, (2x - 3) (7x - 8) = 0
x = $3\over 2$, $8\over 7$
II. $28y^
2$
- 53y + 24 = 0
or, $ 28y^
2$
- 21y - 32y + 24 = 0
or, 7y(4y - 3) - 8(4y - 3) = 0
or, (7y - 8) (4y - 3) = 0
y = $8 \over 7$, $3\over 4$
$x \geq y$ |
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