JEE Main 23 January 2025 Mathematics Question Paper with Answer Key Solutions (Available)
Download here the memory-based JEE Main 23 January 2025 Mathematics question paper with answer key solutions for both Shift 1 and Shift 2. Mathematics question paper PDFs by top coaching institutes will also be available here.
JEE Main 23 January 2025 Mathematics Question Paper: Examineess can find memory-based questions with answer key solutions by our experts and top coaching institutes for JEE Main 23 January 2025 Mathematics Shift 1 on this page. Candidates can find most of the 25 questions of JEE Main 23 January 2025 Mathematics exam bifurcated into 20 MCQs and 5 NVQs, with no optional questions. Test takers can review the question paper with answer key solutions for Mathematics Shift 1 exam which will help aspirants appearing in the coming shifts and sessions.
| Toughest Shift of JEE Main January 2025 (Session 1) | Easiest Shift of JEE Main January 2025 (Session 1) |
JEE Main 23 January 2025 Mathematics Shift 1 Question Paper with Answer Key Solutions
Examinees can find JEE Main 23 January 2025 Mathematics questions along with the answer key solutions for Shift 1 (morning session) below:
| Q.No. | Questions | Answers |
| 1 | If for an arithmetic progression, if first term is 3 and sum of first four terms is equal to of the sum of next four terms, then the sum of first 20 terms is | -1080 |
| 2 | How many words can be formed from the word DAUGHTER such that any vowels are not together | 36000 |
| 3 | Two biased dies are tossed. Die 1 has 1 on two faces, 2 on two faces, 3 and 4 on other faces, while die 2 has 2 on 2 faces, 4 on 2 faces and 1 and 3 on other faces. Then the probability that when throwing these dices we get sum 4 or 5. | 4/9 |
| 4 |
If f(x) is continuous at x = 0, where
f(x) = { (2/x) (sin(k 1 + 1)x + sin(k 2 + 1)x), x < 0 = { 4 x = 0 = { (2/x) (log(k 2 x + 1)/log(k 1 x + 1) x > 0 Find the value of k 1 2 + k 2 2 . | 2 |
| 5 | Find cos -1 [ (12/13) cosx + (5/13) sinx ] if x ∈ [ π/2, π ] | x - tan -1 (5/12) |
| 6 |
If for the system of linear equations having infinite solutions
(λ - 4)x + (λ - 2)y + λz = 0 2x + 3y + 5z = 0 x + 2y + 6z = 0 then λ 2 + λ is | 90 |
| 7 | A relation defined on set A = {1, 2, 3, 4), then how many ordered pairs are added to R = {(1, 2), (2, 3), (3, 3)) so that it becomes equivalence relation? | 7 |
| 8 | The sum of all rational terms in the expansion ( 1 + 2 1/3 + 3 1/2 )6 is | 638 |
| 9 | If | z/(z + i) | = 2 represents a circle with centre P then distance of P from D is (where D: (1,5)) | (370/9) 1/2 |
| 10 | If the equation a(b - c)x 2 + b(c - a)x + c(a - b) = 0 has equal roots and if a + c = 5 and b = 16/5, then the value of a 2 + c 2 is equal to | 9 |
| 11 | Consider the set S = {1, 2, 3, ..., 1000). Then the number of arithmetic progression that can be formed using elements of set S such that first term is 1 and last term is 1000 is | 8 |
| 12 | Let A and B are non-singular commutative matrices. Then A[(adj A -1 ) (adj(B -1 ))] -1 B is equal to | |A| |B| I n |
| 13 | The area of larger portion enclosed by curves y = | x - 1 | and x 2 + y 2 = 25 is equal to (απ + β)/4 (where α, β are natural numbers), then α + β equals to | 77 |
| 14 | Let f(x) = log e x and g(x) = [ (2x 4 - 2x 3 - x 2 + 2x - 1)/(2x 2 - 2x + 1) ], then the domain of f(g(x) for x > 0 is | (1, ∞) |
| 15 | If the curve satisfying the differential equation dy/dx = (6 - 2e 2x y)/(1 + e 2x )passes through (0, 0) and (In 2, k), then k is | (6/5)*(ln 2) |
| 16 | Find I = ∫ dx /((x - 1) 11/13 *(x + 15) 15/13 ) | (13/32)((x - 1)/(x + 15)) 2/13 + C |
Also Read | JEE Main 23 Jan 2025 vs 29 Jan 2024 Shift Analysis: Hardest vs Easiest
JEE Main 23 January 2025 Mathematics Shift 2 Question Paper with Answer Key Solutions
For Shift 2, Session 1 JEE Main 23 January 2025 Mathematics exam, check the question paper with answer key solutions below.
| Q.No. | Questions | Answers |
| 1 | A square is divided in 4 x 4 squares. If two squares are chosen randomly then the probability that the squares doesn't share common side is | 4/5 |
| 2 | There are 5 boys and 4 girls. The sum of number of ways to sit them such that all boys together and number of ways such that no boys sit together is equal to | 17280 |
| 3 | Let f(x) = 6 + 16cos((π/3) - x)cos((π/3) + x)*cosx*sin3x*cos6x if range of f(x) is [α, β], then distance of (α, β) from 3x + 4y + 12 = 0 is | 11 |
| 4 | Consider the terms 8, 21, 34, 47,... 320. The variance of the given data set is | 8788 |
| 5 | Let M (1/2, 1) be the midpoint of a chord to the ellipse x2/2 + y2/4 = 1, then the length of the chord is | 2√(5/3) |
| 6 | If the square of the shortest distance between the lines (x - 2)/1 = (y - 1)/2 = (2 + 3)/-3 and (x + 1)/2 = (y + 3)/4 = (2 + 5)-5 is m/n (where m and n are coprime number) then m + m = ? | 9 |
| 7 |
A = {(x, y)| |x + y ≥ 3};
B = {(x, y)| |x + y ≤3} Let C = A ∩ B. Find the sum of x + y ∀ x, y ε C. | 0 |
| 8 | A rod of length 8 units having two end points always lie on x - y + 2 = 0 and x + y + 2 = 0. A point P divides this line in ratio 2: 1. Then locus of P is | 9x 2 + 9y 2 +36x - 28 = 0 |
| 9 |
If system of linear equations
x + y + z = 6 x + 2y + 5z = 9 x + 5y + λz = μ has no solutions. Then value of λ equals to | 17 |
| 10 | Let S be the region consisting of points (x, y) such that -1 ≤ x ≤ 1 and 0 ≤ y ≤ α + e|x| - e|-x|. If the area bounded by the region is 2(e2 +8e + 1)/e square units, then find the value of α. | 10 |
| 11 | If z is a complex number such that |z| and | z/z̄ + z̄/z | = 1, then the number of complex number z is | 8 |
| 12 | Let (a, 0) be a point such that its shortest distance from the parabola y 2 = 4x is 4. equation of the circle passing through (a, 0) and focus of the parabola having centre on the axis of the parabola is | x 2 + y 2 - 6x + 5 = 0 |
| 13 | If 10th and 11th terms of an arithmetic progression are roots of equation 3x2 - px +q = 0 and the common difference of the arithmetic progression arithmetic progression is 3/2. Also, the sum of first 11 terms of the arithmetic progression is 88, then q - 2p is | 474 |
JEE Main 23 January 2025 Mathematics Question Paper PDF Download
Download here JEE Main 23 Jan 2025 Mathematics question paper and answer key by CollegeDekho as provided above in PDF format:
| Shift | Mathematics Question Paper with Answers Links |
| Shift 1 | JEE Main 2025 Question Paper Mathematics 23 January Shift 1 PDF |
| Shift 2 | JEE Main 2025 Question Paper Mathematics 23 January Shift 2 PDF |
JEE Main 23 January 2025 Question Paper: Physics and Chemistry
For other subjects across both shifts, check and download JEE Main 23 January 2025 question paper here:
| Parameter | Question Paper Link |
| Physics | JEE Main 23 January 2025 Physics Question Paper with Answer Key Solutions |
| Chemistry | JEE Main 23 January 2025 Chemistry Question Paper with Answer Key Solutions |
JEE Main 23 January 2025 Mathematics Question Paper PDFs by Coaching Institutions
For both Shift 1 and Shift 2, JEE Main 23 January 2025 Mathematics answer key and question paper PDF links have been provided as released by Resonance, Aakash BYJU's, and Vedantu in the below table:
| Coaching Institute | Shifts | Mathematics Question Paper with Answer Key PDFs |
| Resonance | Shift 1 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 23 Shift 1 |
| Shift 2 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 23 Shift 2 | |
| Vedantu | Shift 1 | Vendantu JEE Main Mathematics Question Paper and Answer Key 2025 January 23 Shift 1 |
| Shift 2 | Vedantu JEE Main Mathematics Question Paper and Answer Key 2025 January 23 Shift 2 | |
| Aakash | Shift 1 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 23 Shift 1 |
| Shift 2 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 23 Shift 2 |
You may also find important |
| Parameter | Link |
| Safe Score | Expected Safe Score in JEE Mains January 2025 |
| Safe Percentile | Expected Safe Percentile in JEE Main 2025 Session 1 |
| Question Paper (All Days) | JEE Main Question Paper January 2025 Shift 1 and 2 |
| Answer Key (All Days) | JEE Main Answer Key Solutions January 2025 |
| Exam Analysis (All Days) | JEE Main 2025 Session 1 Exam Analysis |
| Percentile to Marks | Expected Marks for JEE Main Percentile January 2025 |
| Marks to Percentile | JEE Main Expected Percentile Score January 2025 |
| Cutoff Percentile | JEE Main Expected Cutoff Percentile January 2025 |
| Cutoff Marks | Minimum Marks in JEE Mains to Qualify for JEE Advanced 2025 |
Subject-wise JEE Mains Marks vs Percentile 2025 |
| Name of the Subject | Link |
| Physics | JEE Main Physics Expected Marks vs Percentile 2025 |
| Chemistry | JEE Main Chemistry Expected Marks vs Percentile 2025 |
| Mathematics | JEE Main Mathematics Expected Marks vs Percentile 2025 |
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