# Algebra (Test 1)

## Problem Solving And Reasoning : Mathematics Or Quantitative Aptitude

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| Algebra |
Q.1
If a and b are rational numbers and , then a : b is equal to
A. -2 : 5
B. 2 : 1
C. √3 : 1
D. -√3 : 1
Explaination / Solution:

(a + b√3) = [1 / (2 - √3)]
= [(2 + √3) / (2 - √3) (2 + √3)]……..(multiplying numerator and denominator by conjugate of denominator)
= [(2 + √3) / {(2)2 – (√3)2}] …………(x – y) (x + y) = (x2 – y2
= [ (2 + √3) / (4 – 3) ]
= ( 2 + √3)
Ã (a + b√3) = ( 2 + 1√3)
Ã a = 2, and b = 1
Ã a:b = 2:1

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Q.2
Find the value of a3 + b3 + c3 – 3abc when a = 225, b = 226, c = 227.
A. 2034
B. 2340
C. 2304
D. 2430
Explaination / Solution:

Applying this a3 + b3 + c3 – 3abc = 1/2(a+b+c)[(a-b)2 + (b-c)2 + (c-a)2]
=1/2(225+226+227)*[(225-226)2 + (226-227)2 + (227-225)2]
=1/2(678)*(1+1+4)
=2034

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Q.3
If 4x = 18y, then the value of is
A. 1/3
B. 7/2
C. 2/3
D. 3/2
Explaination / Solution:

4x = 18y
x/y = 18/4 = 9 /2
so,
(x/y – 1) = 9 /2 – 1 = 7 / 2

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Q.4
If x = 3+2√2, then solve for √x - 1/√x?
A. 3√3
B. 2√2
C. 2
D. 1
Explaination / Solution:

(√x - 1/√x)2 = x + 1/ x – 2
= (3 + 2√2) + 1 / (3+2√2) – 2
= (3 + 2√2) + 1/ (3+2√2) * (3-2√2)/(3 - 2√2) – 2
= (3 + 2√2) + (3 - 2√2) – 2 = 4
= (√x - 1/√x) = 2

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Q.5
Which of the following is not is in increasing order.
A. 11/23,15/23,17/23,45/23
B. 23/12, 23/15, 23/17, 23/19
C. 14/25, 14/23, 14/15, 14/11
D. ½, 3/5, 7/10,4/3
Explaination / Solution:

if num are same then fraction having bigger deno is lesser than the fraction having smaller deno. so, b is in decreasing order

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Q.6
If then the value of is
A. 53.6003
B. 53.603
C. 153.6003
D. 213.0003
Explaination / Solution: Workspace
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Q.7
The value of is
Explaination / Solution: Workspace
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Q.8
If then the value of is
A. √3
B. √3/2
C. 2 + √3
D. 2 - √3
Explaination / Solution: Workspace
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Q.9
If then the value of is
A. 8
B. 7
C. 0
D. 5
Explaination / Solution: =0       as 28-27-1= 0

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Q.10
If , where x is positive, then find the value of A. 48
B. 56
C. 52
D. 46 