# Algebra (Test 3)

## Cat Entrance Exams : Mathematics Or Quantitative Aptitude

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Algebra
| Algebra |
Q.1
If  then the ratio x:y:z is
A. 1 : 3 : 2
B. 1 : 2 : 3
C. 3 : 1 : 2
D. 3 : 2 : 1
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

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Q.2
If , then the relation among a, b, c would be
A. abc = 1
B. b2 = ac
C. b2 = 4ac
D. 2b = a + c
Explaination / Solution:

Comparing the corresponding coefficients,

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Q.3
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)
Explaination / Solution:

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Q.4
If m + n = 1, then the value of m3 + n3 + 3mn is equal to
A. 0
B. 1
C. 2
D. 3
Explaination / Solution:

We are given m+n=1 ....(1)
Lets cube the both sides  (m + n)= 1
m3+n3+3mn(m+n) =1
m3+n3+3mn(1) =1 ..as eq (1)
m3 + n3 + 3mn = 1

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Q.5
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
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

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Q.6
If  find the value of a^2 + 16/a^2
A. 390
B. 392
C. 394
D. 400
Explaination / Solution:

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Q.7
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
Explaination / Solution:

let A=2B B=1/2A
AB=2/25
1/2A2=2/25
A=2/5
B=1/5
sum=2/5+1/5=3/5

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Q.8
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
Explaination / Solution:

let fraction =x/y
(x+4)/y =x/y + 4/7
y=7

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Q.9
If  then the value of  is
A. 1
B. -1
C. 0
D. 2
Explaination / Solution:

⇒ a2+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

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Q.10
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
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
∴ a3 + b3 + c3 – 3abc =0

= 0 + 3 = 3

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