JEE Main 2025 January 24 Shift 1, 2 Mathematics Question Paper (Available): Unofficial answer key solutions PDF
JEE Main 2025 January 24 Mathematics question paper along with the unofficial answer key solutions PDF can be checked here for both Shift 1 and 2.
JEE Main 2025 January 24 Mathematics Question Paper:
Candidates who have appeared for the JEE Main 24 January 2025 exam, can check the question paper PDF for mathematics subject along with the answer key solutions below. This JEE Main 24 January 2025 Mathematics Question Paper & Answer Key is intended to assist candidates in evaluating their performance and estimating their scores prior to the official release. It is crucial to note that the unofficial answer key may contain minor differences when compared to the official release.
Subject matter experts have created these solutions based on their analysis of the question paper, and candidates can use them to assess their answers and determine their estimated scores.
| Toughest Shift of JEE Main January 2025 (Session 1) | Easiest Shift of JEE Main January 2025 (Session 1) |
JEE Main 2025 January 24 Shift 1 Mathematics Question Paper with Answer Key Solutions
Below we have provided the JEE Main 24 January 2025 Mathematics question paper with answer key solutions for Shift 1:
| Q.No. | Questions | Answers |
| 1 | If the 5th, 6th and 7th term of the binomial expansion of (1 + x 2 ) n+4 are in A.P. Then the greatest binomial coefficient in the expansion of (1 + x 2 ) n+4 is | 35 |
| 2 | The number of 3 digit numbers which is divisible by 2 and 3 but not divisible by 4 and 9. | 125 |
| 3 | If A is 3 x 3 matrix such that det(A) = 2. Then det(adj (adj(adj (adj)))) | 2 16 |
| 4 |
Evaluate
lim (x→0) [cosecx. (2cos 2 x + 3cosx) 1/2 - (cos 2 x + sin x + 4) 1/2 ) | -1/2√5 |
| 5 | If a = i + 2j + 3k, b=3i + j - k and ĉ is coplanar with a and b. Also a - c = 5 and ĉ is perpendicular to b. Then | c | is | (11/6) 1/2 |
| 6 | The area of the region bounded by S(x, v) such that S = {(x, y) : x 2 + 4x + 2 ≤ y ≤ |x + 2|} is (in sq. units) | 20/3 |
| 7 | If dy/dx - (x/(1 + x 2 ))y = √x / √(1 + x 2 ) and y(0) = 0, then find the value of y(1). | √2/3 |
| 8 | If α and β are real numbers such that sec 2 (tan -1 (α)) + cosec2(cot -1 (β)) = 36 and α + β = 8, then (α 2 + β) is (α > β) | 28 |
| 9 | Two persons A and B throws a pair of dice alternatively. For A to win he should throw sum of 5 before B throws sum of 8. If A throws first, then the probability that A wins, is | 9/19 |
| 10 |
For a distribution of 10 observations, Σ(i = 1 to 10) x
i
= 55 and Σ(i = 1 to 10) x
i
2
= 328.
If the observations 4 and 5 are replaced by 6 and 8 respectively, then the new variance is | 2.7 |
| 11 | Find the product of all real roots of equation (x2 - 9x + 11) 2 - (x - 4) (x - 5) = 2 is | 99 |
| 12 | If S be the set of 10 distinct primes and let A be the set of product of two or more elements from the set S. If P = {(x, y) : x ∈ S and y ∈ A and y is divided by x}. Then n(P) is equal to | 5110 |
| 13 | If I(m, n) = ∫01x m-1 (1 - x) n-1 dx, m, n > 0, then I(9, 14) + l(10, 13) is equal to | l(9, 13) |
| 14 | If Sn = 1/2 + 1/6 + 1/12 + ...n terms. The sum of first six terms in A.P. with first term equal to -p and common difference p is (2026.S 2025 ) 1/2 . The absolute value of difference between 20th and 15th term in A.P. is | 25 |
| 15 | If f(x) satisfies the functional equation f(x) + 6 f(1/x)) = 35/3x - 7/2, x ∈ R - {0} and if lim (x→0) (1/αx + f(x)) exist finitely and is equal to β, then (α - 2β) is | 4 |
Also Read | JEE Main 24 Jan 2025 vs 30 Jan 2024 Shift Analysis: Hardest vs Easiest
JEE Main 2025 January 24 Shift 2 Mathematics Question Paper with Answer Key Solutions
Below we have provided JEE Main 24 January 2025 Mathematics question paper with answer key solutions for Shift 2:
| Q.No. | Questions | Answers |
| 1 | If 7 = 5 + (1/7) (5 + a) + (1/7 2 ) (5 + 2a) + .... ∞, then find the value of a. | 6 |
| 2 | If A and B are binomial coefficients of 30th and 12th term of binomial expansion (1 + x) 2n - 1 . If 2A= 5B, then the value of n is | 21 |
| 3 | The equation of chord of the ellipse (x 2 )/25 + (y 2 )/16 = 1 with (3, 1) as mid-point is | 48x + 25y - 169 = 0 |
| 4 |
If system of equations
x + 2y - 3z = 2 2x + λy + 5z = 5 4x + 3y + μz = 33 has infinite solutions, then λ. + μ is equal to | 1334/5 |
| 5 | Let S denotes the sum of the first n terms of an arithmetic progression. If S 40 = 1030 and S 12 = 57, then the value of S 30 - S 10 is | 515 |
| 6 | Consider an event E such that a matrix of order 2 x 2 is invertible with entries 0 or 1. Then P(E) is (where P(X) denotes the probability of event X) | 3/8 |
| 7 | The area of region enclosed by the curves y = e x , y = | e x - 1 | and y-axis is (in sq. units) | 1 - ln2 |
| 8 | The number of real roots of the equation x 2 + 3x + 2 = min ( |x + 2|, |x - 3| ) is | 2 |
| 9 | A function f: R → (-1, 1) such that f(x) = ( 2 x - 2 -x )/(2 x + 2 -x ). The function f is | Both one-one and onto |
| 10 | Let a = 3î + 2j - k, b = a × (î - 2j)) and d = b × k, then projection of c - 2j on a is equal to | (3√14)/14 |
| 11 | The point P (11/2, α) lies on or inside the triangle formed by the lines x + y = 11, x + 2y = 16, and 2x + 3y = 29, then minimum value of 10α is equal to | 55 |
JEE Main 24 January 2025 Mathematics Question Paper PDF Download
Download here JEE Main 24 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 24 January Shift 1 PDF |
| Shift 2 | JEE Main 2025 Question Paper Mathematics 24 January Shift 2 PDF |
JEE Main 24 January 2025 Question Paper: Physics and Chemistry
For other subjects across both shifts, check and download JEE Main 24 January 2025 question paper here:
| Parameter | Question Paper Link |
| Physics | JEE Main 2025 January 24 Physics Question Paper |
| Chemistry | JEE Main 2025 January 24 Chemistry Question Paper |
JEE Main 24 January 2025 Mathematics Question Paper PDFs by Coaching Institutions
For both Shift 1 and Shift 2, JEE Main 24 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 |
| Vedantu | Shift 1 | Vendantu JEE Main Mathematics Question Paper and Answer Key 2025 January 24 Shift 1 |
| Shift 2 | Vendantu JEE Main Mathematics Question Paper and Answer Key 2025 January 24 Shift 2 | |
| Resonance | Shift 1 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 24 Shift 1 |
| Shift 2 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 24 Shift 2 | |
| Aakash | Shift 1 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 24 Shift 1 |
| Shift 2 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 24 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 |
| JEE Main 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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