JEE Main 2024 Question Paper Answer Keys Solutions
Hi Students, welcome to Amans Maths Blogs (AMB). As you know that Joint Entrance Examination means JEE Main and JEE Advanced is one of the most important entrance exam in engineering entrance examination. JEE Main 2024 is Computer Based Test (CBT) and it was conducted by the National Testing Agency (NTA). On this post, you will get JEE Mains 2024 Shift 2 Question Paper 27 January Answer Keys Solutions PDF.
NTA is conducting this year of JEE Mains 2024 on 27, 29, 30, 31 January and 1 February. This exam is going to schedule in two shifts as Shift 1 from 9 AM to 12 PM and Shift 2 as from 3 PM to 6 PM.
JEE Main 2024 (27 Jan Shift 2) Physics Question Paper Answer Keys Solutions
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JEE Mains 2024 Physics 27 January Shift 2 Questions Paper Answer Keys & Solutions by AAKASH.
JEE Mains 2024 Physics 27 January Shift 2 Questions Paper Answer Keys & Solutions by ALLEN.
JEE Mains 2024 Physics 27 January Shift 2 Questions Paper Answer Keys & Solutions by RELIABLE.
JEE Main 2024 Physics Questions Answer Keys Solutions Shift 2 : Ques No 1
Which among the following is forward biased:
Option A :
Option B :
Option C :
Option D :
Answer Key:
Solution:
JEE Main 2024 (27 Jan Shift 2) Chemistry Question Paper Answer Keys Solutions
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JEE Mains 2024 Chemistry 27 January Shift 2 Questions Paper Answer Keys & Solutions by AAKASH.
JEE Mains 2024 Chemistry 27 January Shift 2 Questions Paper Answer Keys & Solutions by ALLEN.
JEE Mains 2024 Chemistry 27 January Shift 2 Questions Paper Answer Keys & Solutions by RELIABLE.
JEE Main 2024 Chemistry Questions Answer Keys Solutions Shift 2 : Ques No 1
Which among the following is forward biased:
Option A :
Option B :
Option C :
Option D :
Answer Key:
Solution:
JEE Main 2024 (27 Jan Shift 2) Mathematics Question Paper Answer Keys Solutions
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JEE Mains 2024 Mathematics 27 January Shift 2 Questions Paper Answer Keys & Solutions by AAKASH.
JEE Mains 2024 Mathematics 27 January Shift 2 Questions Paper Answer Keys & Solutions by ALLEN.
JEE Mains 2024 Mathematics 27 January Shift 2 Questions Paper Answer Keys & Solutions by RELIABLE.
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 1
An urn contains 6 black and 9 red balls. Four balls are drawn from the urn twice without replacement. The probability that first four balls are black & 2nd four balls are red in colour is:
Option A : 3 / 765
Option B : 6 / 715
Option C : 3 / 715
Option D : 6 / 615
Answer Key: C
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 2
A line x + y = 0 touches the circle (x – α)2 + (y – β)2 = 50, α, β > 0. The distance of origin from its points of contact is 4√2. Find the value of α2 + β2
Option A :
Option B :
Option C :
Option D :
Answer Key: 82
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 3
Let 2tan2x – 5sec x – 1 = 0 has 7 solutions in x ∈ [0, nπ/2], then the minimum value of n is N, find the value of 
.
Option A : 
Option B : 
Option C : 
Option D : 
Answer Key: A
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 4
The vertices of a triangle are A(1, 2, 2), B(2, 1, 2) & C(2, 2, 1). The perpendicular distance of its orthocentre from the given sides are l1, l2, l3. Find the value of (l1)2 + (l2)2 + (l3)2.
Option A : 1
Option B : 1/2
Option C : 1/3
Option D : 1/4
Answer Key: B
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 5
Let two sets A and B having ‘m’ & ‘n’ elements respectively such that difference of the number of subsets of A and that of B is 56, then (m, n) is
Option A : (8, 3)
Option B : (8, 5)
Option C : (6, 3)
Option D : (7, 4)
Answer Key: C
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 6
If ‘A’ is a square matrix of order ‘2’ such that roots of the equation det(A – λI) = 0 are 1 and –3, then sum of diagonal elements of matrix ‘A2‘ is
Option A : 2
Option B : -3
Option C : 9
Option D : 10
Answer Key: D
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 7
Let tan-1x + tan-12x = π/4, x > 0, then the number of positive values of x is/are
Option A : 0
Option B : 1
Option C : 2
Option D : 3
Answer Key: B
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 8
Find the coefficient of x2012 in (1 – x)2008.(1 + x + x2)2007.
Option A :
Option B :
Option C :
Option D :
Answer Key: 0
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 9
If H: x2 / 16 – y2 / 9 = 1 and E: x2 / a2 – y2 / b2 = 1 (a > b). Ellipse passes through the foci of the hyperbola and the product of their eccentricities is 1. then find the length of the chord of the ellipse passes through (0, 2) and parallel to x-axis.
Option A : 5√5 / 3
Option B : 3 / 5√5
Option C : 10√5 / 3
Option D : 20√5 / 3
Answer Key: C
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 10
If α and 1/α bar are two complex numbers which satisfy the equation |z – z0|2 = 4and |z – z0|2 = 16 respectively, where z0 = 1 + i, then find the value of 5|α|2.
Option A :
Option B :
Option C :
Option D :
Answer Key: 1
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 11
Let x2 – x – 1 = 0 has roots α and β such that Sn = 2023αn + 2024βn, then
Option A : S12 = S11 – S10
Option B : S12 = S10 – S11
Option C : S12 = S10 + S11
Option D : S12 = – S10 – S11
Answer Key: A
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 12
For the series 20, 19 1/4, 18 1/2, …., -129 1/4, then find 20th term from end.
Option A : -115
Option B : -119
Option C : -117
Option D : -120
Answer Key: A
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 13
Option A : 
Option B : 
Option C : 
Option D : None of these
Answer Key: A
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 13
If 
, then find the value of (2α – β)
Option A : 10
Option B : 7
Option C : 8
Option D : 5
Answer Key: D
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 14
Let a1, a2, a3 ……. a15 are 15 observations having mean and variance as 12 & 9 respectively. One of the observation which was 12, misread as 10. The correct mean and variance are μ and σ2 respectively, then find the value of
Option A : 2521
Option B : 2522
Option C : 2518
Option D : 2621
Answer Key: A
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 15
Values of α for which 
lies in the interval
Option A : (0, 3)
Option B : (-3, 0)
Option C : (-2, 1)
Option D : (-2, 0)
Answer Key: B
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 16
Let g(x) = 3f(x/3) + f(3 – x), where f”(x) > 0 and x ∈ (0, 3), g(x) is decreasing in x ∈ (0, α) and increasing in (α, 3), then find the value of 8α.
Option A :
Option B :
Option C :
Option D :
Answer Key: 18
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 17
Let a triangle ABC have vertices A(2, 2, 3), B(2, –3, 3) C(–1, –2, 3) and length of internal angle bisector of angle A is L. then the value of 2L2 is
Option A :
Option B :
Option C :
Option D :
Answer Key: 45
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 18
Let S1 = (4!)! / (4!)3! and S2 = (5!)! / (5!)4!, then
Option A : S1 ∈ N and S2 ∉ N
Option B : S1 ∈ N and S2 ∈ N
Option C : S1 ∉ N and S2 ∈ N
Option D : S1 ∉ N and S2 ∉ N
Answer Key: B
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 19
Let the area bounded by 0 ≤ y ≤ min (2x, 6x – x2) and x-axis is A, then find the value of 12A.
Option A :
Option B :
Option C :
Option D :
Answer Key: 304
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 20
Let (x2 – 4)dy = y(y – 3)dx satisfying y(4) = 3/2, then find the value of y(10).
Option A :
Option B :
Option C :
Option D :
Answer Key: 304
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 21
Three lines 2x – y – 3 = 0, 6x + 3y + 4 = 0, αx + 2y + 4 = 0 does not form triangle then find [∑α2] (where [.] denotes the greatest integer function)
Option A :
Option B :
Option C :
Option D :
Answer Key: 32
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 22
Let 
(where g(x) is cont. odd function). If 
then find the value of α.
Option A :
Option B :
Option C :
Option D :
Answer Key: 2
Solution:
JEE Main 2024 Mathematics Questions Answer Keys Solutions Shift 2 : Ques No 23
If dy/dx = (x + y – 2) / (x – y) and y(0) = 2, find y(2).
Option A : 0
Option B : 2
Option C : e
Option D : e2
Answer Key: A
Solution:
| JEE Mains 2024 Session 1 | Physics | Chemistry | Mathematics |
|---|---|---|---|
| 27 January | Shif 1 | Shif 1 | Shif 1 |
| Shif 2 | Shif 2 | Shif 2 | |
| 29 January | Shif 1 | Shif 1 | Shif 1 |
| Shif 2 | Shif 2 | Shif 2 | |
| 30 January | Shif 1 | Shif 1 | Shif 1 |
| Shif 2 | Shif 2 | Shif 2 | |
| 31 January | Shif 1 | Shif 1 | Shif 1 |
| Shif 2 | Shif 2 | Shif 2 | |
| 01 February | Shif 1 | Shif 1 | Shif 1 |
| Shif 2 | Shif 2 | Shif 2 |
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