JEE Main 28 January 2025 Mathematics Question Paper with Answer Key Solutions (Available)
Download here the memory-based JEE Main 28 January 2025 Mathematics question paper with answer key solutions for both Shift 1 and Shift 2. Mathematics question paper PDF by top coaching institutes will also be available here.
JEE Main 28 January 2025 Mathematics Question Paper: After each shift is over, candidates can access the JEE Main 28 January 2025 Mathematics question paper with answer key solutions from our experts on the page below. After the candidates' question paper is gathered, all 25 of the mathematics section's questions will be available here, along with their unofficial answers. In addition to the CLD answer key, the following will provide PDF links to Resonance, Vedantu, and Aakash.
| Toughest Shift of JEE Main January 2025 (Session 1) | Easiest Shift of JEE Main January 2025 (Session 1) |
JEE Main 28 January 2025 Mathematics Shift 1 Question Paper with Answer Key Solutions
Find the Shift 1 question paper and answer key solutions for JEE Main 28 January 2025 here:
| Q.No. | Questions | Answers |
| 1 | If π/2 ∫ -π/2 [ 96(x 2 + cosx)/(1 + e x ) ] dx = απ 3 + β (where α, β are positive integers), then find the value of α + β. | 100 |
| 2 | Number of ways to form 5 digit numbers greater than 50000 with the use of digits 0, 1, 2, 3, 4, 5, 6, 7 such that sum of first and last digit is not more than 8, is equal to | 5119 |
| 3 | If the image of the point P(4, 4, 3) in the line (x - 1)/2 = (y - 2)/1 = (z - 1)/1 is Q (α, β, γ), then find the value of (α + β + γ). | 31/3 |
| 4 | If ∫ 0 x t . f(t)dt = x 2 f(x) and f(2) = 3, then f(6) equals to | 1 |
| 5 | Let R be a relation such that R = {(x, y): x, y ∈ Z and (x + y) is even), then the relation R is | Equivalence Relation |
| 6 | cos(sin -1 (3/5) + sin -1 (5/13) + sin -1 (33/65)) = ? | 0 |
| 7 | The sum of squares of real roots of the equation: x 2 + |2x - 3| - 4 = 0 is | 6(2 - √2) |
| 8 | Area bounded by 0 < y < 2|x| + 1 and y > x 2 + 1 is (in sq. units) | 8/3 |
| 9 | There are 2 bad oranges mixed with 7 good oranges and 2 oranges are drawn at random. Ket X be the number of bad oranges. The variance of X is | 49/162 |
| 10 | 2a n + 2 = 5a n + 1 - 3a n' prime where n = 0, 1, 2 If a 0 = 3 and a 1 = 4 then the find the value of ∑ a k from k = 1 to 100. | 3a 100 - 91 |
| 11 | Let k 1 and k 2 be two randomly selected natural numbers. The probability that (i) k1 + (i) k2 is non-zero is (where i = √-1) | 3/4 |
| 12 | In ∆ABC, A(4sinθ, 4cosθ), B(-2cosθ, 0) and C(2, 2sinθ). If locus of centroid is (3x - 2) 2 + (3y) 2 = α, then α is | 20 |
| 13 | Let E 1 : x 2 /9 + y 2 /4 = 1 be an ellipse and a series of ellipses are drawn in that E i + 1 has the same centre, eccentricity as E 1 and E i + 1 's major axis is the minor axis of E i . If Si be the area of E i , then ( (5/π) ∑ S i from i = 1 to ∞ ) is equal to | 54 |
JEE Main 28 January 2025 Mathematics Shift 2 Question Paper with Answer Key Solutions
The detailed answer key along with the question paper for JEE Main 28 January 2025 Mathematics Shift 2 is provided here:
| Q.No. | Questions | Answers |
| 1 |
Let f(x) = ∫ dx / (x
1/4
(x
1/4
+ 1))
If f(0) = -6, then find f(2) = ? | 4[(1/2 1/2 ) - 2 1/4 + ln |1 + 2 1/4 | - 6 |
| 2 | Area bounded between the curves C 1 : x(1 + y 2 ) - 1 = 0 and C 2 : y 2 - 2x = 0 is (in sq. unit) | π/2 - 1/3 |
| 3 | There are three bags such that bag 1 has 4 white, 6 blue, bag 2 has 6 white and 4 blue and bag 3 has 5 white and 5 blue balls. A bag is randomly selected and a ball is randomly picked out of it, it comes out to be white then probability that selected bag was bag 2. | 2/5 |
| 4 | If S is a set of words formed by all the letters of word "GARDEN", then find the probability that the vowels are not in alphabetical order. | 1/2 |
| 5 | In an isosceles triangle two sides are x + 2y = 4, x + y = 4, then the sum of all possible value of slope of third side of triangle is | 2/3 |
| 6 | If α, β, γ, δ are real numbers such that α + iβ and γ + iδ are roots of the equation x 2 - (3 - 2i)x - (2i - 2) = 0 (where i = √-1), then (αγ + βδ) is equal to | 2 |
| 7 | The domain of the function f(x) = sec -1 (2[x] + 1) is (where [ . ] represents greatest integer function) | (-∞, ∞) |
| 8 | If p is the number of possible values of r such that T r , T r+1 , T r+2 are three terms of (a + b) 12 are in a geometric progression and if q is the sum of rational terms in the expansion of (3 1/4 + 4 1/3 ) 12 then (p + q) is | 283 |
| 9 | Let P, be image of parabola P: y 2 = 4x with respect to line x + y + 1 = 0. Let the line y + 5 = 0 intersect P i at A and B. If a is the distance between A and B and d be the area of triangle SAB where S is the focus of parabola P i . Then (a + d) is | 20 |
Also Read| Expected Important Topics for JEE Main 29 January 2025
JEE Main 28 January 2025 Mathematics Question Paper PDF Download
The JEE Main 28 Jan 2025 Mathematics question paper and answer key is provided here for both Shift 1 and Shift 2 in PDF format for reference:
| Shift | Mathematics Question Paper with Answers Links |
| Shift 1 | JEE Main 2025 Question Paper Mathematics 28 January Shift 1 PDF |
| Shift 2 | JEE Main 2025 Question Paper Mathematics 28 January Shift 2 PDF |
JEE Main 28 January 2025 Question Paper: Physics and Chemistry
For other subjects across both shifts, check and download the JEE Main 28 January 2025 question paper here:
| Parameter | Question Paper Link |
| Physics | JEE Main 2025 January 28 Shift 1, 2 Physics Question Paper with Answer Key Solutions |
| Chemistry | JEE Main 28 January 2025 Shift 1,2 Chemistry Question Paper with Answer Key Solutions |
JEE Main 28 January 2025 Mathematics Question Paper PDFs by Coaching Institutions
In the table below, Resonance, Aakash BYJU, and Vedantu have released the JEE Main 28 January 2025 Mathematics answer key and question paper PDF links for both Shifts 1 and 2:
| Coaching Institute | Shifts | Mathematics Question Paper with Answer Key PDFs |
| Resonance | Shift 1 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 28 Shift 1 |
| Shift 2 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 28 Shift 2 | |
| Aakash | Shift 1 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 28 Shift 1 |
| Shift 2 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 28 Shift 2 | |
| Vedantu | Shift 1 | Vedantu JEE Main Mathematics Question Paper and Answer Key 2025 January 28 Shift 1 |
| Shift 2 | Vedantu JEE Main Mathematics Question Paper and Answer Key 2025 January 28 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 |
| JEE Main Percentile to Marks | Expected Marks for JEE Main Percentile January 2025 |
| Cutoff Percentile | JEE Main Expected Cutoff Percentile January 2025 |
| Percentile Score | JEE Main Expected Percentile Score 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 |
Upcoming Important Dates of JEE Mains 2025 Session 1
| Event | Link for Expected/ Official Dates |
| Response Sheet | JEE Main Response Sheet January 2025 Expected Release Date |
| Answer Key | JEE Main Answer Key January 2025 Expected Release Date |
| Result | JEE Main Result Date January 2025 |
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