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.

Predict your Rank
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: 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.


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.QuestionsAnswers
1If the 5th, 6th and 7th term of the binomial expansion of (1 + x2)n+4 are in A.P. Then the greatest binomial coefficient in the expansion of (1 + x2)n+4 is35
2The number of 3 digit numbers which is divisible by 2 and 3 but not divisible by 4 and 9.125
3If A is 3 x 3 matrix such that det(A) = 2. Then det(adj (adj(adj (adj))))216
4Evaluate
lim (x→0) [cosecx. (2cos2x + 3cosx)1/2 - (cos2x + sin x + 4)1/2)
-1/2√5
5If 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
6The area of the region bounded by S(x, v) such that S = {(x, y) : x2 + 4x + 2 ≤ y ≤ |x + 2|} is (in sq. units)20/3
7If dy/dx - (x/(1 + x2))y = √x / √(1 + x2) and y(0) = 0, then find the value of y(1).√2/3
8If α and β are real numbers such that sec2(tan-1(α)) + cosec2(cot-1(β)) = 36 and α + β = 8, then (α2 + β) is (α > β)28
9Two 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, is9/19
10For a distribution of 10 observations, Σ(i = 1 to 10) xi = 55 and Σ(i = 1 to 10) xi2 = 328.
If the observations 4 and 5 are replaced by 6 and 8 respectively, then the new variance is
2.7
11Find the product of all real roots of equation (x2 - 9x + 11)2- (x - 4) (x - 5) = 2 is99
12If 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 to5110
13If I(m, n) = ∫01xm-1(1 - x)n-1dx, m, n > 0, then I(9, 14) + l(10, 13) is equal tol(9, 13)
14If 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.S2025)1/2. The absolute value of difference between 20th and 15th term in A.P. is25
15If 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) is4

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.QuestionsAnswers
1If 7 = 5 + (1/7) (5 + a) + (1/72) (5 + 2a) + .... ∞, then find the value of a.6
2If 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 is21
3The equation of chord of the ellipse (x2)/25 + (y2)/16 = 1 with (3, 1) as mid-point is48x + 25y - 169 = 0
4If 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
5Let S denotes the sum of the first n terms of an arithmetic progression. If S40 = 1030 and S12 = 57, then the value of S30 - S10 is515
6Consider 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
7The area of region enclosed by the curves y = ex, y = | e- 1 | and y-axis is (in sq. units)1 - ln2
8The number of real roots of the equation x2 + 3x + 2 =  min ( |x + 2|, |x - 3| ) is2
9A function f: R → (-1, 1) such that f(x) = ( 2x - 2-x)/(2x + 2-x). The function f isBoth one-one and onto
10Let 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
11The 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 to55

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:

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:

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:

You may also find important |

Subject-wise JEE Mains Marks vs Percentile 2025 |

Keep visiting CollegeDekho for the latest Education News on entrance exams, board exams and admissions. You can also write to us at our email ID news@collegedekho.com.

Get Help From Our Expert Counsellors

JEE Main Previous Year Question Paper

2024 Physics Paper Morning Shift

Be the First to Know

Get Access to Latest Updates

Do you have a question? Ask us.

  • Typical response between 24-48 hours

  • Get personalized response

  • Free of Cost

  • Access to community

Recent News