JEE Main · Maths · Complex Numbers and Quadratic Equations

Location of Roots: JEE Main previous year questions

Name: Location of Roots: JEE Main previous year questions
Creator: Lumi

6 questions in the 108 JEE Main shifts Lumi analysed, in 3 of 8 years. Pattern: Frequent. 5 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 6; in 6 of 108 shifts
Years asked: 3/8; last asked 2026
Chance in a shift: 19%; calibrated model, how we compute it
Weighted estimate: 0.1; model; history: 0.1 a shift on average, typically 0.0–0.3

Key findings

01
Asked in 3 of 8 years with analysed shifts and in 6 of 108 shifts: 6 questions, #189 of 196 topics. The years that asked it were 3.0 apart on average.
02
83% of its questions since 2020 tested an idea no earlier year had asked; 1 repeated an idea from the year before.
03
The most repeated idea is Both Roots Positive, asked 2 times in 2 shifts (2025, 2026), most often as “count integer parameters for root condition”.
04
JEE Main has asked 5 of the 63 ideas in this topic; 53 have never been asked, directly or inside another question.
05
Mostly asked as single correct (83%); 17% need a numerical answer, 17% are easy and 33% hard.
06
The skill tested most is multi-step (83%), then calculation (17%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 2 in 8 shifts · 2026: 3 in 9 shifts.

Up to 2023: 0.0; a shift, of 25
Since 2024: 0.2; 0.2
Usual gap: 3.0 yrs; between years asking it
Shifts with it: 6/108; 6% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 6 questions on Location of Roots since 2017.

Difficulty

QUESTIONS

132

Easy1 · 17%
Medium3 · 50%
Hard2 · 33%

Format

Single correct · 5 Q83%
Numerical value · 1 Q17%

Skill tested

Multi-step · 5 Q83%
Calculation · 1 Q17%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 5 of the 63 ideas in this topic. 53 have never been asked yet.

Asked directly5 · 8%
Touched inside another question5 · 8%
Never asked53 · 84%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Chapter, idea, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

chapterAskedShareYears’17’20’21’22’23’24’25’26

Open5 · 83%83%3/822
4 ideas inside
- OpenRepeated2 · 40%40%2/8
- Open1 · 20%20%1/8
- Open1 · 20%20%1/8
- Open1 · 20%20%1/8
Open1 · 17%17%1/8

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

5 different ideas were tested; 1 came more than once.

Both Roots Positive2×
count integer parameters for root condition
Numerical value · 2 shifts · 1 numerical
Both roots greater than k1×
location of roots with eccentricity constraints
Single correct · 1 shift
Both roots in interval1×
roots in interval after limit-determined coefficients
Single correct · 1 shift
Both Roots Negative1×
parameter range for negative roots
Single correct · 1 shift
Exactly one root in interval1×
parameter range for exactly one root in interval
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Both Roots Positivecount integer parameters for root condition	2	2	Numerical valueMulti-step	1
Both roots greater than klocation of roots with eccentricity constraints	1	1	Single correctMulti-step	–
Both roots in intervalroots in interval after limit-determined coefficients	1	1	Single correctMulti-step	–
Both Roots Negativeparameter range for negative roots	1	1	Single correctCalculation	–
Exactly one root in intervalparameter range for exactly one root in interval	1	1	Single correctMulti-step	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Location of Roots questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.