# Aptitude Algebraic Expressions Test Paper 1

1) If x2+ = 34,x+ is equal to

1. 3
2. 4
3. 5
4. None of these

Explanation:

Adding 2 to the L.H.S and R.H.S of the equation:

x2+2+ =34+2[∵(a+b)2=a2+b2+2ab]

(x+ )2= 36

(x+ )= +6,-6

2) The value of x in the equation: 16x + = 8 is Explanation:

16x+ =8 =8

16x2+1=8x

=>16x2+1-8x=0

=>(4x-1)2=0

=>x = 3) The equation whose roots are 4 and 5, is

1. x2+9x-20=0
2. x2+9x+20=0
3. x2-9x+20=0
4. x2-9x-20=0

Explanation:

The required equation is:
x2-(sum of roots)x+product of roots=0
=>x2-(4+5)x+4 �5=0
=>x2-9x+20=0

4) The perimeter of a rectangle is 48 meters, and its area is 135 m2. The sides of the rectangle are

1. 15 m, 9m.
2. 19m, 5m.
3. 45m, 3m.
4. 27m, 5m.

Explanation:

Let the sides of the rectangle be x and y meters respectively. Then
2x + 2y = 48
2 (x+y) = 48
x+y = 24
y = 24 -x

We have, xy = 135
So, x (24 - x) = 135
24x - x2 = 135
x2 -24x + 135 = 0
x2 - 9x - 15x + 135 = 0
(x-9) (x -15) = 0
x = 9 m or 15 m
So, when x = 9m, y = 24 - 9 = 15m
And when x = 15, y = 24 -15 = 9 m
So, the sides of rectangle are 15m and 9m.

5) The roots of the equation (x + 3) (x - 3) = 160 are

1. + 13
2. 13, 13
3. + 12
4. 12, 12

Explanation:

(x + 3) (x - 3) = 160
x2 - 9 = 160
x2 = 169
x = +13, - 13

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Aptitude Algebraic Expressions Test Paper 4   