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Quadratic Equation Practice set 3 for IBPS Clerk 2017

Quadratic Equation Practice set 3 for IBPS Clerk 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  y
(4) if x  y
(5) if x = y, or no relation can be established between x and y.

Q.
I. 2x2 + x - 1 = 0
II. 6y2 - 13y + 5 = 0
A). x>y
B). x<y
C). xy
D). x = y or no relation can be established between ‘x’ and ‘y’.
Answer & Explanation
Answer : Option B
Explanation :
I. 2x2 + 2x - x - 1 = 0
or, 2x(x + 1) - 1(x + 1) = 0
or, (x + 1) (2x - 1) = 0
x = -1 , 12

II. 6y2 - 3y - 10y + 5 = 0
or, 3y(2y - 1) - 5(2y - 1) = 0
or, (3y - 5)(2y - 1) = 0
y = -3, 113

x<y
Hide Answer

2 .I. 21x2 - 122x + 165 = 0
II. 3y2 - 2y - 33 = 0
A). x>y
B). xy
C). x<y
D). x = y or no relation can be established between ‘x’ and ‘y’.
Answer & Explanation
Answer : Option D
Explanation :
I. 21x2 - 45x - 77x + 165 = 0
or, 3x(7x - 15) - 11 (7x - 15) = 0
or, (3x - 11) (7x - 15) = 0
x = 113157

II. 3y2 + 9y - 11y - 33 = 0
or,3y(y + 3) - 11(y + 3) = 0
or,(3y - 11) (y + 3) = 0
y = -3 , 113

Hence, no relation can be established between x and y.
Hide Answer

3 .I. 5x2 - 29x + 36 = 0
II. 10y2 - 3y - 27 = 0
A). x>y
B). xy
C). x<y
D). xy
Answer & Explanation
Answer : Option D
Explanation :
I. 5x2 - 20x - 9x + 36 = 0
or, 5x(x - 4) - 9(x - 4) = 0
or,(x - 4) (5x - 9) = 0
x = 4 , 95

II. 10y2 + 15y - 18y - 27 = 0
or, 5y(2y + 3) - 9(2y + 3) = 0
or, (2y + 3) (5y - 9) = 0
y = 95, - 32

 y
Hide Answer

4 .I. 7x + 4y = 3
II. 5x + 3y = 3
A). x>y
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option B
Explanation :
eqn (I) × 3 - eqn (II) × 4

21x + 12y = 9
20x + 12y = 12
- - -
-------------------
x = - 3

and y = 6

x<y
Hide Answer

5 .I. 7x2 - 54x + 99 = 0
II. 4y2 - 16y + 15 = 0
A). x>y
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option A
Explanation :
I. 7x2 - 21x - 33x + 99 = 0
or, 7x(x - 3) - 33(x - 3) = 0
or, (x - 3) (7x - 33) = 0
x = 3, 337

II. 4y2 - 6y - 10y + 15 = 0
or, 2y(2y - 3) - 5(2y - 3) = 0
or, (2y - 3)(2y - 5) = 0
y = 3252

x>y
Hide Answer

6 .I. 5x2 - 87x + 378 = 0
II. 3y2 - 49y + 200 = 0
A). x>y
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option A
Explanation :
I. 5x2 - 45x - 42x + 378 = 0
or, 5x(x - 9) - 42(x - 9) = 0
or, (5x - 42) (x - 9) = 0
x = 9 , 425

II. 3y2 - 24y - 25y + 200 = 0
or, 3y(y - 8) - 25(y - 8) = 0
or, (y - 8) (3y - 25) = 0
y = 8, 253

x>y
Hide Answer

7 .I. 10x2 - x - 24 = 0
II. y2 - 2y = 0
A). x = y or no relation can be established between ‘x’ and ‘y’.
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option A
Explanation :
I. 10x2 - 16x + 15x - 24 = 0
or, 2x(5x - 8) + 3(5x - 8) = 0
or, (2x + 3) (5x - 8) = 0
x = -3285

II.y2 - 2y = 0
or, y(y - 2) = 0
y = 0, 2
ie no relationship exists between x and y
Hide Answer

8 .I. x2 - 5x + 6 = 0
II. 2y2 - 15y + 27 = 0
A). x>y
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option D
Explanation :
I.x2 - 2x - 3x + 6 = 0
or, x(x - 2) - 3(x - 2) = 0
or, (x - 2) (x - 3) = 0
x = 2, 3

II. 2y2 - 6y - 9y + 27 = 0
or, 2y(y - 3) - 9(y - 3) = 0
or, (y - 3) (2y - 9) = 0
y = 3, 92

xy
Hide Answer

9 .I. 3x + 2y = 301
II. 7x - 5y = 74
A). x>y
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option B
Explanation :
eqn (I) × 5 + eqn (II) × 2

15x + 10y = 1505
14x - 10y = 148
------------------------
29x  = 1653

x = 165329 = 57 and y = 65

x<y
Hide Answer

10 .I. 14x2 - 37x + 24 = 0
II. 28y2 - 53y + 24 = 0
A). x>y
B). x<y
C). xy
D). xy
Answer & Explanation
Answer : Option C
Explanation :
I. 14x2 - 37x + 24 = 0
or, 14x2 - 21x - 16x + 24 = 0
or, 7x(2x - 3) - 8(2x - 3) = 0
or, (2x - 3) (7x - 8) = 0
x = 3287

II. 28y2 - 53y + 24 = 0
or, 28y2 - 21y - 32y + 24 = 0
or, 7y(4y - 3) - 8(4y - 3) = 0
or, (7y - 8) (4y - 3) = 0
y = 8734

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