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.

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

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.QuestionsAnswers
1If π/2-π/2 [ 96(x2 + cosx)/(1 + ex) ] dx = απ3 + β (where α, β are positive integers), then find the value of α + β.100
2Number 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 to5119
3If 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
4If ∫0x t . f(t)dt = x2f(x) and f(2) = 3, then f(6) equals to1
5Let R be a relation such that R = {(x, y): x, y ∈ Z and (x + y) is even), then the relation R isEquivalence Relation
6cos(sin-1(3/5) + sin-1(5/13) + sin-1(33/65)) = ?0
7The sum of squares of real roots of the equation: x2 + |2x - 3| - 4 = 0 is6(2 - √2)
8Area bounded by 0 < y < 2|x| + 1 and y > x2 + 1 is (in sq. units)8/3
9There 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 is49/162
102an + 2 = 5an + 1 - 3an' prime where n = 0, 1, 2 If a0 = 3 and a1 = 4 then the find the value of ∑ ak from k = 1 to 100.3a100 - 91
11Let k1 and k2 be two randomly selected natural numbers. The probability that (i)k1 + (i)k2 is non-zero is (where i = √-1)3/4
12In ∆ABC, A(4sinθ, 4cosθ), B(-2cosθ, 0) and C(2, 2sinθ). If locus of centroid is (3x - 2)2 + (3y)2 = α, then α is20
13Let E1 : x2/9 + y2/4 = 1 be an ellipse and a series of ellipses are drawn in that Ei + 1 has the same centre, eccentricity as E1 and Ei + 1's major axis is the minor axis of Ei. If Si be the area of Ei, then ( (5/π) ∑ Si from i = 1 to ∞ ) is equal to54

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.QuestionsAnswers
1Let f(x) = ∫ dx / (x1/4(x1/4 + 1))
If f(0) = -6, then find f(2) = ?
4[(1/21/2) - 21/4 + ln |1 + 21/4| - 6
2Area bounded between the curves C1: x(1 + y2) - 1 = 0 and C2: y2 - 2x = 0 is (in sq. unit)π/2 - 1/3
3There 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
4If 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
5In 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 is2/3
6If α, β, γ, δ are real numbers such that α + iβ and γ + iδ are roots of the equation x2 - (3 - 2i)x - (2i - 2) = 0 (where i = √-1), then (αγ + βδ) is equal to2
7The domain of the function f(x) = sec-1(2[x] + 1) is (where [.] represents greatest integer function)(-∞, ∞)
8If p is the number of possible values of r such that Tr, Tr+1, Tr+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 (31/4 + 41/3)12 then (p + q) is283
9Let P, be image of parabola P: y2 = 4x with respect to line x + y + 1 = 0. Let the line y + 5 = 0 intersect Pi 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 Pi. Then (a + d) is20

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:

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