JEE Main 22 January 2025 Mathematics Question Paper with Answer Key Solutions (Available)
Download here the memory-based JEE Main 22 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 22 January 2025 Mathematics Question Paper : Applicants can find JEE Main 22 January 2025 Mathematics question paper with answer key solutions provided by our experts on the page below for Shift 1 and 2. The question paper will be collected from the candidates, and all 25 questions from the Mathematics sections will be provided here, along with unofficial answers for each. Apart from the CLD answer key, the pdf links to Resonance, Vedantu, BYJU, and Aakash will also be provided below.
| Toughest Shift of JEE Main January 2025 (Session 1) | Easiest Shift of JEE Main January 2025 (Session 1) |
JEE Main 22 January 2025 Mathematics Shift 1 Question Paper with Answer Key Solutions
Here is JEE Main 22 January 2025 Mathematics question paper with answer key solutions for Shift 1:
| Q.No. | Questions | Answers |
| 1 | The shortest distance between the lines (x - 1)/2 = (y - 2)/3 = (z - 1)/4 and (x + 2)/7 = (y - 2)/8 = (z + 1)/2 | 88/√1277 |
| 2 | In a bag, there are 6 white and 4 black balls two balls are drawn at random, then the probability that both balls are white are | 1/3 |
| 3 | If A be a 3 x 3 square matrix such that det(A) = -2. If det(3 adj(-6 adj(3A))) = 2 n x 3 m , where m ≥ n, then 4m + 2n is equal to | 104 |
| 4 | If a 1 , a 2 , a 3 ..., a n are in geometric progression such that a 1 a 5 = 28, a 2 + a 4 = 29, then the value of a 6 is | 784 |
| 5 | Let A = {1, 2, 3}. Then number of non-empty equivalence relations from A to A are | 5 |
| 6 | If f(x) = 16(sec -1 x) 2 + (cosec -1 x) 2 . Then the maximum and minimum value of f(x) is respectively | 1105π 2 /68 and 4π 2 /17 |
| 7 | If 8 = 3 + (1/4)*(3+p) + (1/4 2 )*(3+p 2 )+ ... ∞, then the value of p is | 16/5 |
| 8 | If dx/dy + x/y 2 = 1/y 3 and x(1) = 1. Then find the value of x (1/2). | 3 - e |
| 9 | Let T r = [ (2r - 1) (2r + 1) (2r +3) (2r + 5) / 64 ], then find the value of lim (n→∞)∑ n r=1 (1/r r ) | 32/45 |
| 10 | Coefficient of x 2012 in the expansion of (1-x) 2008 (1 + x + x 2 ) 2007 | 0 |
| 11 | If the mirror images of the points A(1, 3), B(3, 1) and C(2, 4) in the line x + 2y = 4 are D, E and F respectively, then the centroid of the triangle DEF is | (2/5, -1/5) |
| 12 | If A = {1, 2, 3, ...., 10} and B = {m/n. m,n∈ A, m<n and gcd of (m, n) = 1}. Then find the total number of elements in set B. | 31 |
| 13 | How many ways are there to select 5 letters from English alphabets such that M is in the middle of the letters if repetition is not allowed. | 25 C 4 |
| 14 | Let |z i | = 1 ∀ i = 1, 2, 3 satisfying | z̄ 1 z 2 + z̄ 2 z 3 + z̄ 3 z 1 | 2 = a + b√2, where a, b are rational numbers such that arg(z 1 ) = π/4, arg(z 2 ) = 0 and arg(z 3 )=-π/4, then ordered pair (a, b) is | (5, -2) |
| 15 | Let a coin is tossed thrice. Let the random variable X is tail follows a head and the mean of X is µ and variance is σ 2 respectively. Then 64 (μ + σ 2 ) is | 48 |
| 16 | Let g(x) = 3 f(x/3) + f(3 - x) ∀ x ∈ (0,3) and f"(x) > 0 ∀ x ∈ (0,3), then g(x) decreases in interval (0, α), then α is | 9/4 |
| 17 | Let b = λî + 4k, a > 0 and the projection vector of b on a = 2î + 2j - k is c. If l a + c | = 7, then the area of the parallelogram formed by vectors b and c is (in square units) | 32 |
| 18 | Let the parabola y = x 2 + Px - 3 cuts the coordinate axes at P, Q and R. A circle with centre (-1,-1) passes through P, Q and R, then the area of triangle PQR is (in square units) | 3/2 |
| 19 | If the circle (x - 2√3) 3 + y 2 = 12 and parabola y 2 = 2√3x intersects at P, Q and R. Then the area of triangle PQR is | 12 sq. units |
| 20 | A hyperbola with foci (1, 14) and (1, -12) passes through the point (1, 6). The length of the latus rectum of the hyperbola is | 288/5 |
Also Read | JEE Main 22 Jan 2025 vs 27 Jan 2024 Shift Analysis: Hardest vs Easiest
JEE Main 22 January 2025 Mathematics Shift 2 Question Paper with Answer Key Solutions
Here is JEE Main 22 January 2025 Mathematics question paper with answer key solutions for Shift 2:
| Q.No. | Questions | Answers |
| 1 | If 2x 2 + (cosθ)x - 1 = 0, θ ∈ (0, 2π) has roots α and β. Then the sum of maximum and minimum value of α 4 + β 4 is | 25/16 |
| 2 | If θ ∈ [0, 2π] satisfying the system of equations 2sin2θ = cos2θ and 2cos2θ = 3cosθ. Then the sum of all real values of θ. | π |
| 3 | Let A = {1, 2, 3, 4) and B = {1, 4, 9, 16). If f: A→B, then number of many-one functions from A to B are | 232 |
| 4 | 4 boys and 3 girls are to be seated in a row such that all girls seat together and two particular boys B 1 and B 2 are not adjacent to each other. Then the number of ways in which this arrangement can be done. | 432 |
| 5 | If the sum ∑ 30 r=0 [ (r 2 ( 30 C r ) 2 ) / ( 30 C r-1 ) = α.2 29 , then find the value of α. | 465 |
| 6 | Let a and b be two unit vectors such that angle between a and b is π/3. If λa + 3b and 2a + λb are perpendicular to each other, then the product of all possible values of λ is | 6 |
| 7 | Consider a function f(x) = ∫ 0 x^2 [(t 2 - 8t + 15) / e t ] dt. The number of points of exterma are: | 5 |
| 8 | Let A and B are two events such that P(A ∩ B) = 1/10, then P(AUB) P(A∩B) = and P(A/B) and P(B/A) are the roots of the equation 10 is equal to 12x 2 -7x + 1 = 0 then P(Abar U Bbar)/P(Abar ∩ Bbar) = ? | 9/4 |
| 9 | Number of terms in an arithmetic progression is 2n. Sum of terms occurring at even places is 40 and sum of terms occurring at odd places is 55. If the first term exceeds the last term by 27, then n equals to | 5 |
| 10 | If A is the 3 x 3 matrix of order 3 x 3, such that det(A) = 1/2, tr(A) = 10 and B be another matrix of order 3 x 3 and defined as B = adj(adj(2A)) then det(B) + tr(B) is equal to (where tr(A) denotes trace of matrix A) | 336 |
| 11 | The perpendicular distance of point P(3, 4, 5) from the line 7 = 2î - j + k + λ(4î – j + 5k) is | (19/42) 1/2 |
| 12 | In the expansion of (x + √x 3 -1) 5 + (x - √x 3 −1) 5 , where α, β, γ and δ are the coefficients of x x 3 , x 5 and x 7 respectively. If αu – βν = 18 and γu + δv = 20, then u + v is equal to | -14/15 |
| 13 | Let A(6, 8), B(10 cosα - 10sinα) and C(-10sinα, -10cosα) be 3 points and if orthocenter of the triangle ABC is (0, 9), then 100sin 2 α is equal to | 25/4 |
| 14 | If z be a complex number such that |z - 3| <= 1, then the equation of line with the largest slope passing through origin and z | x - 2√2y = 0 |
| 15 | A relation R is defined on set A, A = (1, 2, 3) and R = {(1, 2), (2, 3)). Elements are added such that R becomes reflexive and transitive but not symmetric. Find the number of such relations. | 3 |
| 16 | Consider two curves E 1 : x 2 /a 2 + y 2 /b 2 = 1 with eccentricity e1 and E 2 : x 2 /A 2 + y 2 /B 2 = 1 with eccentricity e 2 . If e 1 /e 2 = 1/3 and distance between foci of both curves is 2√3 and a - A = 4, then the sum of lengths of latus rectum of both curves is | 12 |
| 17 | The number of maximum number of common tangents to the curves y = (x - 2) 2 and y 2 = 16 - 8x is | 1 |
| 18 | Let P(10, -2, -1) and Q be the point of perpendicular drawn from point R(1, 7, 6) on the line joining the points (2,-5, 11) and (-6, 7, -5). Then the length PQ is | 13 |
Latest | JEE Main Question Paper 24 January 2025 Live Updates
JEE Main 22 January 2025 Mathematics Question Paper PDF Download
Download here JEE Main 22 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 22 January Shift 1 PDF |
| Shift 2 | JEE Main 2025 Question Paper Mathematics 22 January Shift 2 PDF |
| Physics | JEE Main 22 Jan Physics Topic vs No. of Questions Analysis 2025 |
| Chemistry | JEE Main 22 Jan Chemistry Topic vs No. of Questions Analysis 2025 |
| Mathematics | JEE Main 22 Jan Mathematics Topic vs No. of Questions Analysis 2025 |
JEE Main 22 January 2025 Question Paper: Physics and Chemistry
For other subjects across both shifts, check and download JEE Main 22 January 2025 question paper here:
| Parameter | Question Paper Link |
| Physics | JEE Main 22 January 2025 Physics Question Paper with Answer Key Solutions |
| Chemistry | JEE Main 22 January 2025 Chemistry Question Paper with Answer Key Solutions |
JEE Main 22 January 2025 Mathematics Question Paper PDFs by Coaching Institutions
For both Shift 1 and Shift 2, JEE Main 22 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 |
| Resonance | Shift 1 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 1 |
| Shift 2 | Resonance JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 2 | |
| Aakash | Shift 1 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 1 |
| Shift 2 | Aakash JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 2 | |
| Vedantu | Shift 1 | Vedantu JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 1 |
| Shift 2 | Vedantu JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 2 | |
| Narayana | Shift 1 | Narayana JEE Main Mathematics Question Paper and Answer Key 2025 January 22 Shift 1 |
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 |
| Exam Analysis (All Days) | JEE Main 2025 Session 1 Exam Analysis |
| 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 |
| 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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