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Algebra
TEST : 1
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q1.
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
View Solution
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Answer :
Option B
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) = (x
2
– y
2
)
= [ (2 + √3) / (4 – 3) ]
= ( 2 + √3)
à (a + b√3) = ( 2 + 1√3)
à a = 2, and b = 1
à a:b = 2:1
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q2.
Find the value of a
3
+ b
3
+ c
3
– 3abc when a = 225, b = 226, c = 227.
A.
2034
B.
2340
C.
2304
D.
2430
View Solution
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Answer :
Option A
Explaination / Solution:
Applying this a
3
+ b
3
+ c
3
– 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
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q3.
If 4x = 18y, then the value of
is
A.
1/3
B.
7/2
C.
2/3
D.
3/2
View Solution
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Answer :
Option B
Explaination / Solution:
4x = 18y
x/y = 18/4 = 9 /2
so,
(x/y – 1) = 9 /2 – 1 = 7 / 2
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q4.
If x = 3+2√2, then solve for √x - 1/√x?
A.
3√3
B.
2√2
C.
2
D.
1
View Solution
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Answer :
Option C
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
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q5.
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
View Solution
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Answer :
Option B
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
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q6.
If
then the value of
is
A.
53.6003
B.
53.603
C.
153.6003
D.
213.0003
View Solution
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Answer :
Option C
Explaination / Solution:
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q7.
The value of
is
A.
B.
C.
D.
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q8.
If
then the value of
is
A.
√3
B.
√3/2
C.
2 + √3
D.
2 - √3
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
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Q9.
If
then the value of
is
A.
8
B.
7
C.
0
D.
5
View Solution
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Answer :
Option C
Explaination / Solution:
=0 as 28-27-1= 0
# CAT Entrance Exams
# Mathematics or Quantitative Aptitude
# Algebra
# General Aptitude
Prepare / Learn
Q10.
If
, where x is positive, then find the value of
A.
48
B.
56
C.
52
D.
46
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
(a + b)
2
= a
2
+ b
2
+ 2ab
(a + b)
3
= a
3
+ b
3
+ 3ab(a + b)
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