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Algebra Questions

Practice 110 Algebra questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

📚
110
Total Questions
🟢
9
Easy
🟡
96
Medium
🔴
5
Hard
Practice by Exam:Quantitative Aptitude(62)Mathematics(45)Quantitative Aptitude@NUM: 53(1)Quantitative Aptitude@NUM: 74(1)General Awareness(1)

About Algebra — practice questions, PYQs & concepts

Algebra is a frequently-tested topic on Quantitative Aptitude, Mathematics, Quantitative Aptitude@NUM: 53. ExamTest.live currently lists 110 Algebra questions spanning previous-year papers from 2004 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.

Algebra weight in competitive exams

Across our Algebra question bank, the largest sources are Quantitative Aptitude (62), Mathematics (45), Quantitative Aptitude@NUM: 53 (1), Quantitative Aptitude@NUM: 74 (1) and General Awareness (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 9 easy Algebra 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 Algebra Questions(1–100 of 110)

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Q1easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
21% accuracy
If , then what is the value of ?
Q2mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
7% accuracy
The value of is:
Q3mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
Simplify the given expression:
Q4mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If , then the value of is:
Q5mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If and , then the value of is equal to:
Q6mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the expression:
15×15×15+3×15×12×12−3×15×15×12−12×12×12
Q7mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
If and , then matrix is:
Q8mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
Let and , then the values of and are:
Q9mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026
0% accuracy
If the average of and () is , then the average of and is :
Q10mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x+y=18 and xy=9, then the value of (
y
x
​
+
x
y
​
) will be:
Q11mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If for a matrix , , where is the identity matrix of order 2, then can be:
Q12mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If , satisfy

then
Q13mediummcqQuantitative 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:
Q14mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
Four distinct positive numbers, 'a', 'b', 'c' and 'd', in the order given, are in proportion. 'b' is 35 more than 'a' and 'd' is 60 more than 'c'. The product of 'a' and 'c' is 5376. What is the sum of 'a', 'b', 'c' and 'd'?
Q15mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If
1+
39
x
​


​
=5, then the value of x is equal to:
Q16mediummcqQuantitative 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)
Q17mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If x+
x
1
​
=15, then the value of (x
2
+
x
2

1
​
) is:
Q18mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
The sum of two numbers is . If the sum of their reciprocals is , then find the two numbers?
Q19mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
On the set of positive rational numbers, a binary operation is defined by . If , then the maximum value of is:
Q20mediummcqQuantitative AptitudePrepp2026
0% accuracy
What will be the possible value of that satisfies the given equation?
Q21mediummcqQuantitative 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
.
Q22mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
100% accuracy
If x+
x
1
​
=1−
2

​
, then find the value of x
3
+
x
3

1
​
.
Q23mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
Two numbers are in the ratio . If is added to each, the ratio becomes . Find the smaller number.
Q24mediummcqQuantitative AptitudePrepp2026
0% accuracy
If , , and , then find the value of .
Q25mediummcqQuantitative AptitudePrepp2026
0% accuracy
The fourth proportional of , , and is . What is the value of ?
Q26mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
If the sum of two numbers and is and their product is , then find the sum of their cubes.
Q27mediummcqQuantitative AptitudePrepp2026
0% accuracy
The sum of two numbers and (where ) is equal to four times their difference. Find the value of .
Q28mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
If , what is the possible range of values for ?
Q29mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The system of equations and has:
Q30mediummcqMathematicsAIEEE 20062026
0% accuracy
If and are square matrices of size such that , then which of the following will be always true?
Q31mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If and , then find the value of .
Q32mediummcqMathematicsAIEEE 20072026
0% accuracy
In the binomial expansion of , the sum of and terms is zero, then equals:
Q33mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If , then:
Q34mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
The ratio of the sums of money Arun and Ahaan had is . If Arun gives ₹ from his share to Ahaan, then the ratio will change to . How much money did Arun have initially?
Q35mediummcqGeneral AwarenessCompetitive Exam Practice2026
0% accuracy
Name the person who had a major influence in the field of Algebra in India.
Q36mediummcqMathematicsAIEEE 20062026
0% accuracy
If is real, the maximum value of is:
Q37easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , find the value of .
Q38easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
If x+
x
1
​
=5, then find the value of x
2
+
x
2

1
​
.
Q39mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
नि म्नलि खि त व्यंजक का मा न क्या हो गा ?
Q40mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
नि म्नलि खि त व्यंजक का मा न क्या हो गा ?
Q41mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
The LCM of two numbers is times their HCF. The sum of HCF and LCM is . If one of the numbers is , then find the other number.
Q42easymcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
S varies directly as (R+7), and S=42 when R=17. What is the value of S when R=29?
Q43mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify (x−2y)
3
−6xy(x−2y).
Q44mediummcqMathematicsJEE Main2026
A multiple choice examination has questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get or more correct answers just by guessing is:
Q45mediummcqQuantitative AptitudeCompetitive Exam2026
If a+b+c=3, ab+bc+ca=−10 and abc=−24, then the value of
bc
a
2

​
+
ac
b
2

​
+
ab
c
2

​
is:
Q46mediummcqQuantitative Aptitude@NUM: 53Competitive Exam2026
If , and , then what is the value of ?
Q47mediummcqMathematicsAIEEE 20092026
The remainder left out when is divided by is:
Q48mediummcqMathematicsJEE Main2026
If the equations and , , have a common root, then is:
Q49mediummcqQuantitative AptitudePrepp2026
The possible value of satisfying the equation is:
Q50mediummcqMathematicsJEE Main2026
The term independent of in expansion of is:
Q51easymcqQuantitative AptitudeSSC CGL2026
Simplify the following expression:
49a
2
+70ab+25b
2
Q52mediummcqQuantitative AptitudeCompetitive Exam2026
Find the value of when .
Q53mediummcqMathematicsAIEEE2026
The value of is:
Q54mediummcqMathematicsAIEEE 20092026
1: where is a matrix.
2: .
Q55mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify :
Q56mediummcqQuantitative AptitudeCompetitive Exam2026
If x+y=10 and xy=12, find the value of x
2
−xy+y
2
.
Q57mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify the given expression.
(2.3)
2
+(15.9)
2
+(3.7)
2
−2.3×15.9−15.9×3.7−3.7×2.3
(2.3)
3
+(15.9)
3
+(3.7)
3
−3×2.3×15.9×3.7
​
Q58mediummcqQuantitative AptitudeCompetitive Exam2026
If a+b=2 and ab=4, then find the value of a
4
+b
4
+ab
3
+ba
3
.
Q59mediummcqMathematicsJEE Main2026
Let and be two sets containing elements and elements respectively. The number of subsets of having or more elements is:
Q60mediummcqQuantitative AptitudeCompetitive Exam2026
When x is subtracted from each of the numbers 64,81,85 and 109, the numbers so obtained in this order are in proportion. What is the mean proportional between (x+3) and (2x−1)?
Q61mediummcqMathematicsAIEEE 20092026
If , then the maximum value of is equal to:
Q62mediummcqQuantitative AptitudeCompetitive Exam2026
What is the simplified form of the following expression?
(x−
y
1
​
)
3
+(x+
y
1
​
)
3
Q63mediummcqMathematicsJEE Main2026
If is a complex number of unit modulus and argument , then equals:
Q64mediummcqQuantitative Aptitude@NUM: 74Competitive Exam2026
Simplify .
Q65mediummcqMathematicsAIEEE-CBSE-ENG-032026
If , then:
Q66mediummcqQuantitative AptitudeSSC CGL2026
Simplify the expression:
(0.2)
3
+(0.3)
3
+(0.5)
3
+3×0.5×0.7×0.8
Q67mediummcqMathematicsAIEEE 20092026
The sum to the infinity of the series is:
Q68mediummcqQuantitative 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):
Q69mediummcqQuantitative AptitudeStaff Selection Commission2026
Simplify the following expression: (x−3y)
3
+27(y
3
−xy
2
)
Q70hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
The coefficient of in the expansion of is:
Q71hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
Let be real and be a complex number. If has two distinct roots on the line , then it is necessary that:
Q72mediummcqMathematicsCompetitive Exam2026
The LCM of two numbers is and their HCF is . If the sum of the numbers is , then find their difference.
Q73mediummcqMathematicsAIEEE2026
The value of for which the sum of the squares of the roots of the equation assumes the least value is:
Q74mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify the following expression:
4×4×4
(8.25)
3
−3×(8.25)
2
×0.25+24.75×(0.25)
2
−(0.25)
3

​
Q75mediummcqMathematicsAIEEE2026
If the coefficients of , and terms in the binomial expansion of are in A.P., then and satisfy the equation:
Q76mediummcqMathematicsAIEEE2026
If is so small that and higher powers of may be neglected, then may be approximated as:
Q77mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
A man saves Rs. in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. more than the saving of immediately previous month. His total saving from the start of service will be Rs. after:
Q78mediummcqQuantitative AptitudePrepp2026
If and , then find the value of .
Q79mediummcqQuantitative AptitudePrepp2026
Simplify the following expression:
Q80easymcqMathematicsAIEEE2026
If and are the roots of the equation , then
Q81mediummcqQuantitative AptitudePrepp2026
If , then what is the value of ?
Q82mediummcqQuantitative AptitudePractice Mock2026
If 23% of 'x' is 46, then 'x' is ________
Q83mediummcqQuantitative AptitudePractice Mock2026
Find the simplest value of 5
3
2
​
×2
6
1
​
−2
3
1
​
Q84easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
If x
3
−y
3
=40 and x−y=4, then find the value of xy.
Q85hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
The vectors and are not perpendicular and and are two vectors satisfying: and . Then the vector is equal to:
Q86mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
If , then what is the value of ?
Q87mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
The number of values of for which the linear equations , , and possess a non-zero solution is:
Q88mediummcqQuantitative 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:
Q89mediummcqMathematicsAIEEE2026
If both the roots of the quadratic equation are less than , then lies in the interval:
Q90mediummcqMathematicsAIEEE 20092026
Let be such that . If

then the value of ' ' is:
Q91mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
Let and be two symmetric matrices of order .Statement-1 : and are symmetric matrices.Statement-2 : is a symmetric matrix if matrix multiplication of and is commutative.
Q92easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Find the value of .
Q93mediummcqQuantitative AptitudePrepp2026
If , then find the value of .
Q94hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If and , then the value of is:
Q95mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If is a cube root of unity, and . Then equals:
Q96mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify the following expression:
33×31×(2
10
+1)
(3
2
)
4
−1
​
Q97mediummcqMathematicsAIEEE 20092026
If the roots of the equation be imaginary, then for all real values of , the expression is:
Q98mediummcqMathematicsJEE Main2026
Let be the number of all possible triangles formed by joining vertices of an -sided regular polygon. If , then the value of is:
Q99mediummcqQuantitative AptitudeCompetitive Exam2026
If x=7−4
3

​
, then find the value of (x
2
+
x
2

1
​
).
Q100mediummcqMathematicsJEE Main2026
If is the adjoint of a matrix and , then is equal to:
12

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We have 110 Algebra questions spread across 2 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
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Algebra questions are commonly asked in Quantitative Aptitude, Mathematics, Quantitative Aptitude@NUM: 53, Quantitative Aptitude@NUM: 74, General Awareness. You can filter by exam using the links above.
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