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

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

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

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

a)ย ย If p is greater than q

b)ย ย If p is smaller than q

c)ย ย If p is equal to q
d)ย ย If p is either equal to or greater than q
e)ย ย 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.q2โ 17q + 72 =0
4).
I. 3p + 2q โ 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.
a)ย ย If x>y
b)ย ย If xโฅy
c)ย ย If x<y
d)ย ย If xโคy
e)ย ย If x=y or the relationship cannot be established
6).
I. โx – โ6/โx=0
II. y3โ 6(3/2) = 0
7).
I. 3x โ 2y = 10
II. 5x โ 6y = 6
8).
I. x2+ x โ 12 = 0
II.y2โ 5y + 6 = 0
9).
I. x2+ 9x + 18 = 0
II.y2โ 13y + 40 = 0
10).
I. โ(x+6) = โ121 – โ36
II. y2+ 112 = 473

1).e)ย ย  2).d)ย ย 3).b)ย ย  4).a)ย ย 5).b)ย ย  6).e)ย  7).a)ย ย  8).e)ย  9).c)ย ย  10).b)ย
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SOLUTION:
1).
I.p2+ 3p + 2p + 6 = 0
ร  p (p+3) + 2 (p+3) = 0
ร (p+3)(p+2) = 0
ร  p = -2 or -3
II. q2+ q + 2q + 2 = 0
ร  q(q+1) + 2 (q+1) = 0
ร (q+1)(q+2)=0
ร  q=-1 or -2
Clearly, pโคq
ย
2).
I. p = ยฑ2
II. q2+ 2q + 2q + 4 = 0
ร  q(q+2) + 2(q+2)=0
ร (q+2)(q+2) = 0
ร  q = -2
Clearly, pโฅq
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3). I. p2+ p โ 56 = 0
ร  p2+ 8p โ 7p โ 56 = 0
ร p(p+8)-7(p+8)=0
ร (p+8)(p-7)=0
ร  p = 7 or -8
II. q2-8q-9q+72 = 0
ร  q(q-8) โ 9(q-8) = 0
ร (q-8)(q-9) = 0
q = 8 or 9
Clearly, p<q
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4). We have,
3p + 2q = 58 โฆโฆโฆ.. (i)
4p + 4q = 92
ร  2p+2q = 46ย  โฆโฆโฆ(ii)
By Eq. (i) โ Eq. (ii), we get p = 12
From eq. (i), 3 ร 12 + 2q = 58
ร  2q = 58 โ 36 = 22
q = 11
Hence, p>q
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5).I. 3p2+ 15p + 2p + 10 = 0
ร  3p (p+5) + 2 (p+5)=0
ร  (p+5) (3p+2) = 0
ร  p = -5 or -2/3
II.ร 10q2+ 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
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6).I. โx – โ6/โx = 0
x-โ6 = 0
x=โ6
II. y3= 63/2= (โ6)3ร  y =โ6
Clearly x=y
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7). I. By Eq. I ร 3 โ Eq. II,
9x – 6y โ 5x + 6y = 30 โ 6
4x = 24ร  x = 6
From Eq. I, 3 ร 6 โ 2y = 10
ร  2y = 18 โ 10 = 8ร y =4
Clearly, x>y
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8). I.x2+ x โ 12 = 0
ร  x2+ 4x โ 3x โ 12 = 0
x(x+4) โ 3 (x+4) = 0
(x-3) (x+4) = 0
x=3 or -4
II. y2โ 5y + 6 =0
y2โ 3y โ 2y + 6 =0
y(y-3) โ 2(y-3) = 0
y = 2 or 3
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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. y2โ 13y + 40 = 0
y2โ 8y โ 5y + 40 = 0
y(y-8) โ 5(y-8) = 0
(y-5)(y-8) = 0
y=5 or 8
Clearly x<y
ย
10).
I. โ(x+6) = 11-6 = 5
x+6 = 25
x=25-6 = 19
II. y2= 473 โ 112 = 361
y= โ361 = ยฑ19
Clearly, xโฅy
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