JEE Mains 2024 Shift 2 Question Paper 27 January Answer Keys Solutions PDF

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

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

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

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 S_n = 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

 

jee mains 2024 27 january paperjee mains 2024 27 january paper analysisjee mains 2024 27 january paper pdfjee mains 2024 27 january paper pdf downloadjee mains 2024 27 january paper shift 1jee mains 2024 27 january paper shift 1 answer keysjee mains 2024 27 january paper shift 1 solutionsjee mains 2024 27 january paper shift 2jee mains 2024 27 january paper shift 2 answer keysjee mains 2024 27 january paper shift 2 solutionsjee mains 2024 admit cardjee mains 2024 chemistry question paper answer keysjee mains 2024 chemistry syllabusjee mains 2024 marks vs percentilejee mains 2024 maths question paper answer keysjee mains 2024 maths syllabusjee mains 2024 paperjee mains 2024 paper 1 pdfjee mains 2024 physics question paper answer keysjee mains 2024 physics syllabusjee mains 2024 question paperjee mains 2024 registrationjee mains 2024 syllabus