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Algebra Questions

Practice 311 Algebra questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

📚
311
Total Questions
🟢
27
Easy
🟡
275
Medium
🔴
9
Hard
Practice by Exam:Quantitative Aptitude(216)Mathematics(59)Mathematics and Science(28)Quantitative Aptitude@NUM: 74(1)Quantitative Aptitude@NUM: 53(1)Quantitative Aptitude@NUM: 51(1)Quantitative Aptitude@NUM: 52(1)Quantitative Aptitude@NUM: 56(1)

About Algebra — practice questions, PYQs & concepts

Algebra is a frequently-tested topic on Quantitative Aptitude, Mathematics, Mathematics and Science. ExamTest.live currently lists 311 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 (216), Mathematics (59), Mathematics and Science (28), Quantitative Aptitude@NUM: 74 (1) 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: 27 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 311)

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Q1easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
17% accuracy
If , then what is the value of ?
Q2mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
8% accuracy
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 , then the value of is:
Q6mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
If 4+3x≤6+x and 3x+5>2+2x; then x can take which of the following values?
Q7mediummcqQuantitative AptitudeCompetitive Exams2026
0% accuracy
Which of the following quadratic equations has equal roots?
Q8mediummcqQuantitative AptitudeStaff Selection Commission2026
20% accuracy
Simplify
23ab
437bxaz
​
.
Q9mediummcqQuantitative AptitudeCompetitive Exam2026
25% accuracy
If x% of 190 is 15 less than (x+10)% of 180, then (x+30)% of 90 is what per cent more than x% of 150?
Q10mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If a 9-digit number 1039m837n is divisible by 72, then find the value of
n
2
−m
4


​
.
Q11mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If y+
y
1
​
=5, then the value of y
6
+
y
6

1
​
is:
Q12mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
Find the value of
0.09
0.23
2
−0.04
2

​
.
Q13mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If P=
x
2
−16
x
2
−100
​
and Q=
x−4
x+10
​
, then the value of
Q
P
​
is:
Q14mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If x=3−4y, then (x
3
+64y
3
+36xy) is equal to:
Q15mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Find the value of x
3
−
x
3

1
​
when x−
x
1
​
=5.
Q16mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
On dividing 111a
2
b
2
c
2
by 37a
2
, we get __________.
Q17mediummcqQuantitative AptitudeCompetitive Exam Practice2026
33% accuracy
The sum of two numbers is . If the sum of their reciprocals is , then find the two numbers?
Q18mediummcqQuantitative AptitudeCompetitive Exam Practice2026
33% 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?
Q19mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the expression:
15×15×15+3×15×12×12−3×15×15×12−12×12×12
Q20mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If x+
x
1
​
=15, then the value of (x
2
+
x
2

1
​
) is:
Q21mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
The value of x for which the expressions 5x+17 and 17x−5 become equal is __________.
Q22mediummcqGeneral AwarenessCompetitive Exam Practice2026
0% accuracy
Name the person who had a major influence in the field of Algebra in India.
Q23mediummcqQuantitative 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:
Q24mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
If 5x−4≤2−x and 4x+5>2x−5, then x can take which of the following values?
Q25mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If 4x−5y=−37 and 7x+y=−16, then x−y=________.
Q26mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
If
7
6
​
th of
5
8
​
th of a number is 192, then
4
3
​
th of that number is __________.
Q27mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x+y=18 and xy=9, then the value of (
y
x
​
+
x
y
​
) will be:
Q28mediummcqQuantitative 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)
Q29mediummcqQuantitative 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'?
Q30mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If
1+
39
x
​


​
=5, then the value of x is equal to:
Q31mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
नि म्नलि खि त व्यंजक का मा न क्या हो गा ?
Q32mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
नि म्नलि खि त व्यंजक का मा न क्या हो गा ?
Q33mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If 5x−3≥3+
2
x
​
and 4x−2≤6+x, then x can take which of the following values?
Q34mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If the sum of the roots of a quadratic equation is −7 and the product of the roots is 12, find the quadratic equation.
Q35mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
Let and , then the values of and are:
Q36mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026
0% accuracy
If the average of and () is , then the average of and is :
Q37mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the expression:
(0.2)
3
+(0.3)
3
+(0.5)
3
+3×0.5×0.7×0.8
Q38mediummcqQuantitative AptitudeSSC CGL2026
50% accuracy
Factorise x
2
+3x−18.
Q39easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
Simplify the following expression:
49a
2
+70ab+25b
2
Q40mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Coefficient of x in (x+6)(7−3x) is:
Q41mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If , satisfy

then
Q42mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
If and , then matrix is:
Q43mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If for a matrix , , where is the identity matrix of order 2, then can be:
Q44mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
A number lies between and . Which of the following is true?
Q45mediummcqQuantitative AptitudeIndian Competitive Exam Prep2026
0% accuracy
Given the simultaneous linear equations and , what are the values of and ?
Q46mediummcqMathematicsCompetitive Exam Mock2026
0% accuracy
In an enclosure, there are crows as well as cows. If there are 30 heads and 100 legs, what is the ratio of the cows to crows?
Q47mediummcqMathematicsStaff Selection Commission2026
0% accuracy
If 5x+5>2+2x and 5x+3≤4x+5, then x can take which of the following values?
Q48mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If , then:
Q49mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
If the sum of two numbers and is and their product is , then find the sum of their cubes.
Q50mediummcqMathematicsStaff Selection Commission2026
0% accuracy
Which of the following is correct?
Q51mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
If , what is the possible range of values for ?
Q52mediummcqMathematicsStaff Selection Commission2026
0% accuracy
Which of the following quadratic equations has real roots?
Q53mediummcqMathematicsMathematics 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:
Q54mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The system of equations and has:
Q55mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
The coefficient of x
2
in (x+3)(2−4x)(5x−6) is:
Q56mediummcqQuantitative AptitudeSSC CGL2026
100% accuracy
If , then what is the average of and ?
Q57mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If and , then find the value of .
Q58mediummcqMathematicsAIEEE 20062026
0% accuracy
If is real, the maximum value of is:
Q59mediummcqQuantitative AptitudePrepp2026
0% accuracy
The fourth proportional of , , and is . What is the value of ?
Q60mediummcqQuantitative AptitudePrepp2026
0% accuracy
If , , and , then find the value of .
Q61mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Determine the value of ' ' for which the equation has no solution.
Q62mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If x+
x
4
​
=4, then find the value of x
2
+
x
2

1
​
.
Q63mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
What is the value of ?
Q64mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , then find the range/value of .
Q65mediummcqQuantitative Aptitude@NUM: 60SSC CGL2026
0% accuracy
Which of the following is not a quadratic equation?
Q66mediummcqMathematicsAIEEE 20062026
0% accuracy
If and are square matrices of size such that , then which of the following will be always true?
Q67mediummcqQuantitative Aptitude@NUM: 51SSC CGL2026
0% accuracy
If , then what is the value of ?
Q68mediummcqQuantitative 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
.
Q69mediummcqQuantitative AptitudePrepp2026
0% accuracy
What will be the possible value of that satisfies the given equation?
Q70mediummcqQuantitative AptitudePrepp2026
0% accuracy
The sum of two numbers and (where ) is equal to four times their difference. Find the value of .
Q71mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
For what value of does the system of equations and have no solution?
Q72mediummcqQuantitative Aptitude@NUM: 52SSC CGL2026
0% accuracy
Square of is:
Q73easymcqQuantitative AptitudeCompetitive Exam2026
100% accuracy
Two numbers are in the ratio of . If the difference between their squares is , then the numbers are:
Q74mediummcqMathematicsAIEEE 20072026
0% accuracy
In the binomial expansion of , the sum of and terms is zero, then equals:
Q75mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If a+b=10 and a
2
+b
2
=58, then find ab.
Q76mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If 2x−2(4−x)<2x−3<3x+3, then x can take which of the following values?
Q77mediummcqQuantitative Aptitude@NUM: 56SSC CGL2026
0% accuracy
If and ; then can take which of the following values?
Q78mediummcqQuantitative AptitudeStaff Selection Commission2026
100% accuracy
If 60% of (x−y) = 45% (x+y) and y=k% of x, then 49% of k is equal to:
Q79mediummcqQuantitative 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:
Q80easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , find the value of .
Q81mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
100% accuracy
If x+
x
1
​
=1−
2

​
, then find the value of x
3
+
x
3

1
​
.
Q82mediummcqQuantitative 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
)?
Q83easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
If x+
x
1
​
=5, then find the value of x
2
+
x
2

1
​
.
Q84mediummcqQuantitative 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.
Q85mediummcqQuantitative Aptitude@NUM: 58SSC CGL2026
0% accuracy
What will be the roots of the quadratic equation ?
Q86mediummcqQuantitative 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
)?
Q87mediummcqQuantitative 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
​
?
Q88mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
Two numbers are in the ratio . If is added to each, the ratio becomes . Find the smaller number.
Q89easymcqQuantitative 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?
Q90mediummcqQuantitative AptitudeCompetitive Exam2026
Simplify (x−2y)
3
−6xy(x−2y).
Q91mediummcqMathematicsJEE Main2026
If is the adjoint of a matrix and , then is equal to:
Q92mediummcqQuantitative AptitudeCompetitive Exam2026
If a+b=2 and ab=4, then find the value of a
4
+b
4
+ab
3
+ba
3
.
Q93mediummcqQuantitative 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:
Q94mediummcqMathematicsAIEEE 20092026
Let be such that . If

then the value of ' ' is:
Q95mediummcqMathematicsJEE Main2026
The term independent of in expansion of is:
Q96mediummcqQuantitative 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)?
Q97mediummcqQuantitative AptitudeCompetitive Exam2026
What is the simplified form of the following expression?
(x−
y
1
​
)
3
+(x+
y
1
​
)
3
Q98mediummcqMathematicsJEE Main2026
The number of values of , for which the system of equations has no solution, is:
Q99mediummcqQuantitative Aptitude@NUM: 74Competitive Exam2026
Simplify .
Q100mediummcqQuantitative Aptitude@NUM: 53Competitive Exam2026
If , and , then what is the value of ?
1234

Frequently Asked Questions

How many Algebra questions are on ExamTest.live?▼
We have 311 Algebra questions spread across 4 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Algebra MCQs free?▼
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Which exams include Algebra questions?▼
Algebra questions are commonly asked in Quantitative Aptitude, Mathematics, Mathematics and Science, Quantitative Aptitude@NUM: 74, Quantitative Aptitude@NUM: 53. You can filter by exam using the links above.
How do I practice Algebra 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.