Algebra (Test 2)

Problem Solving And Reasoning : Mathematics Or Quantitative Aptitude

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Algebra

Algebra
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Q.1
Simplify: 
A. 1/2 - 5√3
B. 2 - 5√3
C. 1
D. 0
Answer : Option C
Explaination / Solution:



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Q.2
If  then:
A. 3(x + y + z) = a
B. 2a = x + y + z
C. x + y + z = 0
D. x = y = z = a/3
Answer : Option D
Explaination / Solution:



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Q.3
If  then y is equal to
A. 1/3
B. 2/3
C. 3/4
D. 4/3
Answer : Option D
Explaination / Solution:



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Q.4
If and the value of is
A. 4/7
B. 3/8
C. 5/6
D. 3/5
Answer : Option C
Explaination / Solution:

X+y=5 
Cubing both sides, we get:
x3+y3+3xy(x+y)=125 OR xy = 6
((1/x) + (1/y)) = (x+y)/xy=5/6

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Q.5
If  and xyz = 288, the value of 
A. 11/12
B. 11/96
C. 29/96
D. 27/96
Answer : Option B
Explaination / Solution:




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Q.6
If ab + bc + ca = 0, then the value of  is
A. 2
B. -1
C. 0
D. 1
Answer : Option C
Explaination / Solution:

ab + bc + ca = 0 ⇒ bc = -ab –ac and similar for others 
Hence 


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Q.7
If  and the value of  is
A. 14
B. 13
C. 15
D. 10
Answer : Option A
Explaination / Solution:



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Q.8
If  then the value of is
A. 8√5
B. 2√5
C. 5√5
D. 7√5
Answer : Option B
Explaination / Solution:



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Q.9
If (2x)(2y) = 8 and (9x)(3y) = 81, then (x, y) is :
A. (1,2)
B. (2,1)
C. (1,1)
D. (2,2)
Answer : Option A
Explaination / Solution:

(2x)(2y) = 8 = 23
Applying the law of indices 
x + y = 3----- eqn 1 
(9x)(3y) = 81 = 34 
2x + y = 4----- eqn 2 
Solving the two equations simultaneously we get x=1 
And substituting the value of x in any of the two equations y=2 

Hence option A is correct

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Q.10
If , then the value of  is
A. 3
B. 0
C. 1
D. -1
Answer : Option B
Explaination / Solution:



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