# Aptitude Algebraic Expressions Test Paper 2

6) The solution of is

1. 1/8
2. -1/8
3. 8/3
4. -8/3

Explanation:

Given equation is
(2x+3) (3x+1) = (3x-1) (2x-1)
= 6x2 + 11x + 3
= 6x2 - 5x + 1
= 16x +2
16x = -2
x = -

7) If the equation 4x2+x(p+1)+1=0 has exactly two equal roots, one of the value of p is

1. 5
2. -3
3. 0
4. 3

Explanation:

Roots are equal if discriminant
b2 - 4ac = 0
In given equation:
(P+1)2 - 4.41 = 0
(p+1)2 = 16 = (4)2
p+1 = +4, -4
p= 3 or - 5

8) A journey of 300 km takes two hours more when the speed of a care is reduced by 5km/hr. What is the original speed of the car?

1. 30
2. 40
3. 70
4. 80

Explanation:

Let the speed of the car is x km/hr. Then
Speed = distance/ time:

=2

=>

x2 - 5x - 750 = 0
x2 - 30x + 25x - 750 = 0
(x - 30) (x + 25) = 0
x =30 or x = -25
The negative value of x is inadmissible; therefore the speed of the car is 30 km/hr.

9) The solution for is

1. -5
2. -1
3. -3
4. 3

Explanation:

The given equation:

x2 - 3x - 4x -12 = - 6x +18
x2 - x - 30 = 0
x2 + 5x - 6x - 30 = 0
(x+5) (X-6) = 0
x = - 5 or 6

10) If x2+ax+b=0 and x2+bx+a=0 is double the other; a, b, c are related as

1. 2a2 = 9bc
2. 9a2 = 2bc
3. 2b2 = 9ac
4. 9b2 = 2ac

Explanation:

If α and β be the roots of the equation:
Then α + β = , and αβ =

Also, α = 2β. Then
3β==>β =

And,
2=

=>=

=>2b2=9ac

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