Algebra

12
Question 1
If x3 + y3 = 9 and x + y = 3, then the value of x4+y4 is,
A
21
B
0
C
17
D
25
Algebra    
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Question 1 Explanation: 
x3+y3 = (x + y) × (x2 − xy + y2)

Putting given values of x3+y3 and (x + y)
9 = 3 × ((x+y)2 − 3xy)
  = 3 × (9 − 3xy) 
  = 27 − 9xy

9xy = 18
xy = 2

x4 + y4 = (x2 + y2)2 - 2x2y2
   = (x2 + y2)2 - 2*4 
                                  [Putting value of xy]
   = ((x + y)2 - 2xy)2 - 2*4 
                            [Putting values of (x+y) and xy]
   = (9 - 4)2 - 2*4 
   = 17
Question 2
If x+1/2x = 2, find the value of 8x3+1/x3
A
40
B
20
C
28
D
35
Algebra    
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Question 3
For any real number x the maximum value of 4−6x−x2 is at x=,
A
4
B
6
C
-3
D
3
Algebra    
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Question 3 Explanation: 
Differentiate and equate to 0 6+2x =0 x=−3
Question 4
If 5√x +12√x =13√x then value of x is,
A
2
B
1
C
3
D
4
Algebra    
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Question 4 Explanation: 
say x=1
17!=13

for, x=2 and 3 also not possible
x=4
52+122=132
169=169
Question 5
if x = (√2 + 1 )-1⁄5 then the value of (x5 - 1⁄x5)
A
0
B
-2
C
2
D
4
Algebra    
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Question 5 Explanation: 
1_q_sol
Question 6
If b2 + 1⁄b2 = 1, then value of b3 + 1⁄b3 is ,
A
0
B
6
C
-4
D
4
Algebra    
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Question 6 Explanation: 
E = (b + 1⁄b)(b2 - 1 + 1⁄b2)
Question 7
If x1/3 + y1/3 - z1/3 = 0 then value of (x + y - z)3 + 27xyz is
A
8
B
2
C
0
D
6
Algebra    
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Question 7 Explanation: 
x1/3 + y1/3 = z1/3
Now cubing both sides we get 
x + 3x1/3y1/3(x1/3 + y1/3) + y = z
or, (x + y - z) = -3x1/3y1/3z1/3
Cubing again both sides, (x + y - z) = -27xyz.
So answer is zero
Question 8
{\mathbf{y^{y{\sqrt[]{y}}}} = {\mathbf{(y\sqrt{y})^{y}}} then y is equal to,
A
9/4
B
7/4
C
1/4
D
5/4
Algebra    
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Question 8 Explanation: 
Now equating power on both side, y \sqrt{y} = \frac{3y}{2} or or
Question 9
If ab+bc+ac = 0, then the value of \frac{1}{a^{2}-bc} + \frac{1}{b^{2}-ac} + \frac{1}{c^{2}-ab}
A
6
B
2
C
3
D
0
Algebra    
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Question 9 Explanation: 
Put -ac = ab + bc ; -ab = ac+ bc and -bc =ab + ac
(ab + bc + ca)/[(a+b+c)(abc)]
as, ab+bc+ca=0
= 0
Question 10
Following instructions are to be used throughout the quiz: Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question. Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question. Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question. Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question. Give answer (e) if the data in both Statements I and II together are necessary to answer the question. If x,y are integers, then (x2 + y2)1/2 is an integer? I) x2 + y2 is an integer II) x2 - 3y2 = 0
A
A
B
B
C
C
D
D
E
E
Algebra    Data Sufficiency    
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There are 19 questions to complete.
12


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