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Algebra
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Problem Solving and Reasoning
Mathematics or Quantitative Aptitude
Algebra
TEST : 3
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q1.
If
then the ratio x:y:z is
A.
1 : 3 : 2
B.
1 : 2 : 3
C.
3 : 1 : 2
D.
3 : 2 : 1
View Solution
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Answer :
Option B
Explaination / Solution:
Only if 2x – y = 0
= x/y = 1/2
⇒ x : y = 1 : 2
and, 3y – 2z = 0
= y/z = 2/3
⇒ y : z = 2 : 3
∴ x : y : z = 1 : 2 : 3
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q2.
If
, then the relation among a, b, c would be
A.
abc = 1
B.
b
2
= ac
C.
b
2
= 4ac
D.
2b = a + c
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Answer :
Option C
Explaination / Solution:
Comparing the corresponding coefficients,
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q3.
If
, then the value of
is
A.
3(x - 1)(y + 2)(z - 3)
B.
3(x + 1)(y - 2)(z - 3)
C.
3(x - 1)(y - 2)(z + 3)
D.
3(x - 1)(y - 2)(z - 3)
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Answer :
Option D
Explaination / Solution:
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q4.
If m + n = 1, then the value of m
3
+ n
3
+ 3mn is equal to
A.
0
B.
1
C.
2
D.
3
View Solution
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Answer :
Option B
Explaination / Solution:
We are given m+n=1 ....(1)
Lets cube the both sides (m + n)
3
= 1
m3+n3+3mn(m+n) =1
⇒
m
3
+n
3
+3mn(1) =1 ..as eq (1)
⇒
m
3
+ n
3
+ 3mn = 1
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q5.
Find the value of √3x - √5y where
A.
7√3 – 9√5
B.
7√5 – 9√3
C.
9√3 -7√5
D.
None of these
View Solution
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Answer :
Option C
Explaination / Solution:
⇒ x = (√5 – 2)
2
and y = (2 - √3)
2
x = 9 – 4√5 and y = 7 – 4√3
√3x - √5y
= 9√3 – 4√15 – 7√5 + 4√15
= 9√3 – 7√5
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q6.
If
find the value of a^2 + 16/a^2
A.
390
B.
392
C.
394
D.
400
View Solution
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Answer :
Option B
Explaination / Solution:
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q7.
A fraction is twice the other fraction. If their product is 2/25.find the sum of these two fractions.
A.
2/5
B.
3/5
C.
1/5
D.
4/5
View Solution
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Answer :
Option B
Explaination / Solution:
let A=2B B=1/2A
AB=2/25
1/2A
2
=2/25
A=2/5
B=1/5
sum=2/5+1/5=3/5
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q8.
when the numerator of a fraction is increased by 4, the fraction increases by 4/7 .The denominator is.
A.
7
B.
4
C.
3
D.
2
View Solution
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Answer :
Option A
Explaination / Solution:
let fraction =x/y
(x+4)/y =x/y + 4/7
y=7
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q9.
If
then the value of
is
A.
1
B.
-1
C.
0
D.
2
View Solution
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Answer :
Option C
Explaination / Solution:
⇒ a
2
+1=a ...(1)
So from the question put value of eq (1) in
We can put the value in both numerator and denomenator and get -
(a-a)/(a+a) = 0
# Problem Solving and Reasoning
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q10.
If (2a – 3)
2
+ (3b + 4)
2
+ (6c + 1)
2
= 0, then the value of
is:
A.
abc + 3
B.
6
C.
0
D.
3
View Solution
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Answer :
Option D
Explaination / Solution:
(2a – 3
)
2
+ (3b +4
)
2
+ (6c + 1
)
2
∴ 2a – 3 = 0 ⇒ a = 3/2,
3b + 4 = 0 ⇒ b = -4/3
6c + 1 = 0 ⇒ c = -1/6
(a+b+c) = (9-8-1)/6 = 0
∴ a
3
+ b
3
+ c
3
– 3abc =0
= 0 + 3 = 3
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