# Algebra

• Last Updated : 13 Oct, 2021

 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 2 Explanation:

x3 + 1/8x3 + 3.x.1/2x(x + 1/2x) = (x+1/2x)3

x3 + 1/8x3 + 3 = 23

x3 + 1/8x3 = 5

8x3 + 1/x3 = 5.8 = 40

 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 )-15 then the value of (x5 - 1x5)
 A 0 B -2 C 2 D 4
Algebra
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 Question 6
If b2 + 1b2 = 1, then value of b3 + 1b3 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 then y is equal to,
 A 9/4 B 7/4 C 1/4 D 5/4
Algebra
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Question 7 Explanation: Now equating power on both side, or or Question 8
If ab+bc+ac = 0, then the value of A 6 B 2 C 3 D 0
Algebra
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Question 8 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 9
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.
(a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
(b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
(c) if the data in each Statement I and Statement II alone is sufficient to answer the question.
(d) if the data even in both Statements I and II together are not sufficient to answer the question.
(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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Question 9 Explanation:
Statement 1: x2 + y2 is an integer Since x and y are integer x2+y2 can be any real number which may not be a perfect square so statement 1 alone cant prove whether (x2+y2)(½) is an integer or not. Statement 2: x2- 3y2 = 0 =>x2+y2-4y2=0 =>x2+y2=4y2 => (x2+y2)(½)= 2y Which is an integer because y is an integer.
 Question 10
4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8. What is half of that number?
 A 630 B 63 C 315 D 105
Algebra
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Question 10 Explanation:
Let the number be x. Then, 4/15 of 5x/7 = 4/9 of 2x/5 + 8 4/15 * 5x/7 = 4/9 * 2x/5 + 8 4x/21 = 8x/45 + 8 x/21 = 2x/45 + 2 x/21 = (2x + 90)/45 45x = 21(2x + 90) 45x = 42x + 90*21 3x = 90*21 x = 30*21 = 630. Half of the number will be x/2 x/2 = 630/2 = 315.
There are 19 questions to complete.
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