JEE Main 28 January 2025 Mathematics Question Paper with Answer Key Solutions (Available)

Rini Maria

Updated On: January 30, 2025 02:06 PM

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 with Answer Key SolutionsJEE Main 28 January 2025 Mathematics Question Paper with Answer Key Solutions

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.

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:

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:

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:

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 |

Upcoming Important Dates of JEE Mains 2025 Session 1

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JEE Main Previous Year Question Paper

2022 Physics Shift 1

2022 Physics Shift 2

2022 Chemistry Shift 1

2022 Chemistry Shift 2

2022 Mathematics Shift 1

2022 Mathematics Shift 2

2023 Chemistry Shift 1

2023 Mathematics Shift 1

2023 Physics Shift 2

2023 Mathematics Shift 2

2023 Chemistry Shift 2

2023 Physics Shift 1

2024 Chemistry Shift 1

2024 Mathematics Shift 2

2024 Physics Paper Morning Shift

2024 Mathematics Morning Shift

2024 Physics Shift 2

2024 Chemistry Shift 2

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