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Algebraic Identities Questions

Practice 103 Algebraic Identities questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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103
Total Questions
🟢
12
Easy
🟡
90
Medium
🔴
1
Hard
Practice by Exam:Quantitative Aptitude(94)Mathematics and Science(3)Mathematics(2)Algebra(2)Quantitative Aptitude@NUM: 53(1)Quantitative Aptitude@NUM: 52(1)

About Algebraic Identities — practice questions, PYQs & concepts

Algebraic Identities is a frequently-tested topic on Quantitative Aptitude, Mathematics and Science, Mathematics. ExamTest.live currently lists 103 Algebraic Identities questions spanning previous-year papers from 2017 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Algebraic Identities weight in competitive exams

Across our Algebraic Identities question bank, the largest sources are Quantitative Aptitude (94), Mathematics and Science (3), Mathematics (2), Algebra (2) and Quantitative Aptitude@NUM: 53 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 12 easy Algebraic Identities questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Algebraic Identities Questions(1–100 of 103)

2 pages
Filter:
Q1mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
8% accuracy
The value of is:
Q2mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If , then the value of is:
Q3mediummcqQuantitative AptitudeCompetitive Exam2026
7% accuracy
If and , then the value of is equal to:
Q4mediummcqQuantitative AptitudeCompetitive Exam2026
29% accuracy
Simplify the given expression:
Q5mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If x=3−4y, then (x
3
+64y
3
+36xy) is equal to:
Q6mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Find the value of x
3
−
x
3

1
​
when x−
x
1
​
=5.
Q7mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If y+
y
1
​
=5, then the value of y
6
+
y
6

1
​
is:
Q8easymcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
If (x+y)=17 and xy=9, then what is the value of x
3
+y
3
?
Q9mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the expression:
15×15×15+3×15×12×12−3×15×15×12−12×12×12
Q10mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If p=106, q=105 and r=104, then the value of p
2
+q
2
+r
2
−pq−qr−rp is:
Q11mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
Simplify the following expression:
(x+y)(x−y)(x
2
+y
2
)(x
4
+y
4
)(x
8
+y
8
)(x
1
6+y
1
6)
Q12mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If sinθ+cscθ=5, then the value of sin
3
θ+csc
3
θ is:
Q13mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If x+
x
1
​
=15, then the value of (x
2
+
x
2

1
​
) is:
Q14easymcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
Simplify the following expression:
7.23×7.23−7.23×2.77+2.77×2.77
7.23×7.23×7.23+2.77×2.77×2.77
​
Q15mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x+y=18 and xy=9, then the value of (
y
x
​
+
x
y
​
) will be:
Q16mediummcqQuantitative AptitudeCompetitive Exam Practice2026
33% accuracy
is a/an:
Q17mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
नि म्नलि खि त व्यंजक का मा न क्या हो गा ?
Q18mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the expression:
(0.2)
3
+(0.3)
3
+(0.5)
3
+3×0.5×0.7×0.8
Q19easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the following expression:
49a
2
+70ab+25b
2
Q20mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
नि म्नलि खि त व्यंजक का मा न क्या हो गा ?
Q21mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026
0% accuracy
If the average of and () is , then the average of and is :
Q22mediummcqQuantitative AptitudePrepp2026
0% accuracy
If , , and , then find the value of .
Q23mediummcqQuantitative AptitudeStaff Selection Commission2026
100% accuracy
If x+y+z=5, x
2
+y
2
+z
2
=21 and y
2
=zx, then the value of y is:
Q24mediummcqQuantitative Aptitude@NUM: 52SSC CGL2026
0% accuracy
Square of is:
Q25easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
If x+
x
1
​
=5, then find the value of x
2
+
x
2

1
​
.
Q26mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x
4
+y
4
+x
2
y
2
=21 and x
2
+y
2
−xy=7, then what is the value of
x
2

1
​
+
y
2

1
​
?
Q27mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If and , then one of the values of :
Q28mediummcqQuantitative AptitudeSSC Selection Post 20212026
0% accuracy
If
y
x
​
+
x
y
​
=1, and x,y

=0, then find the value of x
6
+y
6
+2x
3
y
3
.
Q29mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If and , then find the value of .
Q30mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
What is the value of ?
Q31mediummcqMathematicsStaff Selection Commission2026
0% accuracy
Which of the following is correct?
Q32easymcqQuantitative AptitudeCompetitive Exam2026
100% accuracy
Solve the following expression:
Q33mediummcqAlgebraSSC CGL2026
0% accuracy
If (4x−5)=(3x−1), then the numerical value of (x+4)
2
is
Q34mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If and , then find the value of .
Q35mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
If , then one of the values of the expression is _______.
Q36hardmcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If , and , what is the value of ?
Q37mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x+
x
4
​
=4, then find the value of x
2
+
x
2

1
​
.
Q38mediummcqQuantitative AptitudeSSC Selection Post 20212026
0% accuracy
Find the value of 22.2×22.2+124.32+2.8×2.8.
Q39mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x−y=
9
7
​
and
x
1
​
−
y
1
​
=
21
11
​
, then what is the value of (x
3
−y
3
)?
Q40mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x
2
+9y
2
=40 and xy=4, where x>0,y>0, then what is the value of (x
3
+27y
3
)?
Q41mediummcqQuantitative AptitudeSSC CGL2026
100% accuracy
Simplify:
Q42mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If a+b=10 and a
2
+b
2
=58, then find ab.
Q43mediummcqAlgebraCompetitive Exam2026
0% accuracy
Simplify the following product:
(x+
x
1
​
)(x−
x
1
​
)(x
2
+
x
2

1
​
)
Q44mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
100% accuracy
If x+
x
1
​
=1−
2

​
, then find the value of x
3
+
x
3

1
​
.
Q45mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
If the sum of two numbers and is and their product is , then find the sum of their cubes.
Q46easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , find the value of .
Q47mediummcqQuantitative AptitudeCompetitive Exam2026
If a+b+c=7, and a
2
+b
2
+c
2
=33, then what is the value of a
3
+b
3
+c
3
−3abc?
Q48mediummcqQuantitative AptitudeCompetitive Exam2026
If x−x
−1
=6, then the value of x
4
+x
−4
is:
Q49mediummcqQuantitative AptitudeSSC CGL2026
Find the value of 13
3
+(−8)
3
+(−5)
3
.
Q50mediummcqQuantitative AptitudeStaff Selection Commission2026
If x+y=10 and x
2
+y
2
=68, then find xy.
Q51mediummcqQuantitative AptitudeSSC CGL2026
If a−b=−5 and a
2
+b
2
=73, then find ab.
Q52mediummcqQuantitative AptitudeCompetitive Exam2026
If a+b=2 and ab=4, then find the value of a
4
+b
4
+ab
3
+ba
3
.
Q53mediummcqQuantitative AptitudePrepp2026
Simplify the following expression:
Q54mediummcqQuantitative AptitudeStaff Selection Commission2026
Find the value of 27a
3
+
a
3

1
​
, if 9a
2
+
a
2

1
​
=43.
Q55mediummcqQuantitative AptitudeSSC CGL2026
If and , then find the value of .
Q56mediummcqQuantitative AptitudeCompetitive Exam2026
What is the simplified form of the following expression?
(x−
y
1
​
)
3
+(x+
y
1
​
)
3
Q57mediummcqQuantitative AptitudeCompetitive Exam2026
If x+y=14 and x
2
+y
2
=100, then find xy.
Q58easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
If x
3
−y
3
=40 and x−y=4, then find the value of xy.
Q59mediummcqQuantitative AptitudeSSC CGL2026
What is the value of xy if x−y=3 and x
2
+y
2
=15?
Q60mediummcqQuantitative Aptitude@NUM: 53Competitive Exam2026
If , and , then what is the value of ?
Q61mediummcqQuantitative AptitudeSSC CGL2026
Find the value of 1006×994.
Q62mediummcqQuantitative AptitudeSSC CGL2026
What is the simplified value of
(0.04)
3
+(0.21)
3

(0.04)
2
+(0.21)
2
−0.0084
​
?
Q63mediummcqQuantitative AptitudeStaff Selection Commission2026
What will be the value of when , , and ?
Q64mediummcqQuantitative AptitudeCompetitive Exam Practice2026
Simplify the expression (0.3−0.2)(0.3
2
+0.3×0.2+0.2
2
).
Q65mediummcqQuantitative AptitudeSSC CGL2026
If a−b=−7 and a
2
+b
2
=85, then find ab.
Q66mediummcqQuantitative AptitudeCompetitive Exam2026
If x+y+z=3 and xy+yz+zx=−11, then what is the value of x
3
+y
3
+z
3
−3xyz?
Q67mediummcqQuantitative AptitudeSSC CGL2026
If x−y=6 and xy=40, then find x
2
+y
2
.
Q68easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Find the value of .
Q69mediummcqQuantitative AptitudeCompetitive Exam2026
If x
2
−3x+1=0, then (x
3
+x
−3
) is equal to:
Q70mediummcqQuantitative AptitudeCompetitive Exam2026
The simplified value of is:
Q71mediummcqQuantitative AptitudePrepp2026
If , then what is the value of ?
Q72mediummcqQuantitative AptitudeCompetitive Exam2026
If , , and , then the value of is:
Q73mediummcqQuantitative AptitudeSSC CGL2026
If x+y+z=4, xy+yz+zx=1, and x
3
+y
3
+z
3
=34, then what is the value of 6xyz?
Q74mediummcqQuantitative AptitudeWBCS Mains2026
If
image
then which of the following relations is correct?
Q75mediummcqQuantitative AptitudeStaff Selection Commission2026
If y=
3

​
−
2

​
, then find the value of (
y
3

1
​
−y
3
).
Q76mediummcqQuantitative AptitudePrepp2026
If , then find the value of .
Q77mediummcqQuantitative AptitudeSSC CGL2026
If 2x+
3x
1
​
+1=0 and x

=0, then find the value of 2x+
3x
1
​
.
Q78mediummcqMathematicsCompetitive Exam2026
If , then the value of is
Q79mediummcqQuantitative AptitudeCompetitive Exam2026
Which of the following is the output of ?
Q80mediummcqQuantitative AptitudeSSC CGL2026
If x−y=−9 and xy=−20, then find x
2
+y
2
.
Q81mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
If 4x
2
+y
2
+z
2
+41=2(4x+y+6z), then the value of 2x+y−z is:
Q82mediummcqQuantitative AptitudeCompetitive Exam2026
Find the value of when .
Q83mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify :
Q84mediummcqQuantitative AptitudeSSC CGL2026
If , then the value of is:
Q85mediummcqQuantitative AptitudeSSC CGL2026
If for a non-zero x, 7x
2
+5x+7=0, then x
3
+
x
3

1
​
is ________.
Q86mediummcqQuantitative AptitudeCompetitive Exam2026
If x+y=10 and xy=12, find the value of x
2
−xy+y
2
.
Q87mediummcqQuantitative AptitudePractice Test2026
If (x
2
+
x
2

1
​
)=18 and x>1, what is the value of (x
3
−
x
3

1
​
)?
Q88mediummcqQuantitative AptitudeCompetitive Exam2026
If Psin60
∘
=Qcsc45
∘
, then the value of
P
2
−Q
2

P
2
+Q
2

​
is equal to:
Q89mediummcqQuantitative AptitudeStaff Selection Commission2026
If x
3
=184+y
3
and x=4+y, then the value of (x+y) is (given that x>0 and y>0):
Q90mediummcqQuantitative AptitudeWBCS Mains2026
If and , then which of the following relations is correct?
Q91mediummcqQuantitative AptitudeStaff Selection Commission2026
Simplify the following expression: (x−3y)
3
+27(y
3
−xy
2
)
Q92mediummcqQuantitative AptitudeCompetitive Exam2026
If and , then which one of the following relations is correct?
Q93mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
If , then what is the value of ?
Q94mediummcqQuantitative AptitudeCompetitive Exam2026
If x=7−4
3

​
, then find the value of (x
2
+
x
2

1
​
).
Q95mediummcqQuantitative AptitudeWBCS Prelims2026
Which of the following is the value of ?
Q96mediummcqQuantitative AptitudeWBCS Prelims 20212026
If , then
Q97mediummcqQuantitative AptitudeCompetitive Exam2026
Which of the following is the value of ?
Q98easymcqQuantitative AptitudeAdda2472026
Which of the following is the output of ?
Q99mediummcqQuantitative AptitudeStaff Selection Commission2026
Find the value of (a−2x)
3
+(b−2x)
3
+(c−2x)
3
−3(a−2x)(b−2x)(c−2x), given that a+b+c=6x.
Q100mediummcqQuantitative AptitudeStaff Selection Commission2026
[(4a−5b) 3 +(5b−3c) 3 −(4a−3c) 3 ] is equal to:
12

Frequently Asked Questions

How many Algebraic Identities questions are on ExamTest.live?▼
We have 103 Algebraic Identities questions spread across 2 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Algebraic Identities MCQs free?▼
Yes. All Algebraic Identities questions, answers, and explanations on ExamTest.live are completely free. No account or subscription required.
Which exams include Algebraic Identities questions?▼
Algebraic Identities questions are commonly asked in Quantitative Aptitude, Mathematics and Science, Mathematics, Algebra, Quantitative Aptitude@NUM: 53. You can filter by exam using the links above.
How do I practice Algebraic Identities questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.