IBPS PO/Upcoming Exams 2016-Aptitude Questions (Quadratic Equations)

IBPS PO/Upcoming Exams 2016-Aptitude Questions (Quadratic Equations) Set-3:

Dear Readers, Important Practice Aptitude Questions for IBPS PO and Upcoming Exams was given here with Solutions. Aspirants those who are preparing for the examination can use this.

 

Directions (1-5): For the two given Equations I and II. You have to solve both the equations.

 

Give Answer

 

a)  If p is greater than q

 

b)  If p is smaller than q

 

c)  If p is equal to q
d)  If p is either equal to or greater than q
e)  If p is either equal to or smaller than q
1).
I. p2+5p + 6 = 0
II.q2+ 3q + 2 = 0
2).
I. p2= 4
II.q2+ 4q = -4
3).
I. p2+ p = 56
II.q2– 17q + 72 =0
4).
I. 3p + 2q – 58 = 0
II. 4q + 4p = 92
5).
I. 3p2+ 17p + 10 =0
II. 10q2+ 9q + 2 = 0
Directions (6-10): For the two given Equations I and II. You have to solve both the equations.
Give Answer
a)  If x>y
b)  If x≥y
c)  If x<y
d)  If x≤y
e)  If x=y or the relationship cannot be established
6).
I. √x – √6/√x=0
II. y3– 6(3/2) = 0
7).
I. 3x – 2y = 10
II. 5x – 6y = 6
8).
I. x2+ x – 12 = 0
II.y2– 5y + 6 = 0
9).
I. x2+ 9x + 18 = 0
II.y2– 13y + 40 = 0
10).
I. √(x+6) = √121 – √36
II. y2+ 112 = 473

Answers:
1).e)   2).d)  3).b)   4).a)  5).b)   6).e)  7).a)   8).e)  9).c)   10).b) 
 
SOLUTION:
1).
I.p2+ 3p + 2p + 6 = 0
à p (p+3) + 2 (p+3) = 0
à(p+3)(p+2) = 0
à p = -2 or -3
II. q2+ q + 2q + 2 = 0
à q(q+1) + 2 (q+1) = 0
à(q+1)(q+2)=0
à q=-1 or -2
Clearly, p≤q
Answer: e)
 
2).
I. p = ±2
II. q2+ 2q + 2q + 4 = 0
à q(q+2) + 2(q+2)=0
à(q+2)(q+2) = 0
à q = -2
Clearly, p≥q
Answer: d)
 
3). I. p2+ p – 56 = 0
à p2+ 8p – 7p – 56 = 0
àp(p+8)-7(p+8)=0
à(p+8)(p-7)=0
à p = 7 or -8
II. q2-8q-9q+72 = 0
à q(q-8) – 9(q-8) = 0
à(q-8)(q-9) = 0
q = 8 or 9
Clearly, p<q
 Answer: b)
 
4). We have,
3p + 2q = 58 ……….. (i)
4p + 4q = 92
à 2p+2q = 46  ………(ii)
By Eq. (i) – Eq. (ii), we get p = 12
From eq. (i), 3 × 12 + 2q = 58
à 2q = 58 – 36 = 22
q = 11
Hence, p>q
Answer: a)
 
5).I. 3p2+ 15p + 2p + 10 = 0
à 3p (p+5) + 2 (p+5)=0
à (p+5) (3p+2) = 0
à p = -5 or -2/3
II.à10q2+ 5q + 4q + 2 = 0
5p (2q+1) + 2 (2q+1) = 0
(2q+1) (5q+2) = 0
q= -1/2 or -2/5
clearly, p<q
Answer: b)
 
6).I. √x – √6/√x = 0
x-√6 = 0
x=√6
II. y3= 63/2= (√6)3à y =√6
Clearly x=y
Answer: e)
 
7). I. By Eq. I × 3 – Eq. II,
9x – 6y – 5x + 6y = 30 – 6
4x = 24à x = 6
From Eq. I, 3 × 6 – 2y = 10
à 2y = 18 – 10 = 8ày =4
Clearly, x>y
Answer: a)
 
8). I.x2+ x – 12 = 0
à x2+ 4x – 3x – 12 = 0
x(x+4) – 3 (x+4) = 0
(x-3) (x+4) = 0
x=3 or -4
II. y2– 5y + 6 =0
y2– 3y – 2y + 6 =0
y(y-3) – 2(y-3) = 0
y = 2 or 3
Answer: e)
 
9).I. x2+ 9x + 18 = 0
x2+ 6x + 3x +18 = 0
x(x+6) + 3(x+6) = 0
(x+3) (x+6) =0
x=-3 or -6
II. y2– 13y + 40 = 0
y2– 8y – 5y + 40 = 0
y(y-8) – 5(y-8) = 0
(y-5)(y-8) = 0
y=5 or 8
Clearly x<y
Answer: c)
 
10).
I. √(x+6) = 11-6 = 5
x+6 = 25
x=25-6 = 19
II. y2= 473 – 112 = 361
y= √361 = ±19
Clearly, x≥y
Answer: b)
 
  
 
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