JEE Main 2021 Solved Question Paper- 25 Feb M2

JEE Main 2021 solved question paper (Official) for February session has been released. It is released separately for four session in February, March, April and May sessions. JEE Main is conducted for providing admission into UG engineering (B.Tech) / architecture courses (B.Arch). These courses are offered by various IITs, NITs and IIITs and other government and non-government engineering institutions. JEE Main question paper and answer key is released by the National Testing Agency (NTA). And solutions are prepared by Kunduz tutors for you. Through this blog, candidates can get the JEE Main 2021 solved question paper and also previous year answer key and question papers with all solutions.

Important Material for JEE Aspirants

Download JEE Advanced 2020 answer key and question paper with solutions

Must read JEE Mains chapter wise weightage

Must read Important Name Reactions in Organic Chemistry

Clear your concepts with best tutors at Kunduz. Click here to know more.

NCERT Books – Best Ways to Study

JEE Main 2021 Solved Question Paper- 25 February Shift 2

Mathematics JEE Main 2021 solved question paper 25 Feb shift 2

Question 1

then:

1. 1/(I₂+I₄), 1/(I₃+I₅), 1/(I₄+I₆) are in G.P.
2. I₂+I₄, I₃+I₅, I₄+I₆, are in A.P.
3. I₂+I₄, (I₃+I₅)², I₄+I₆ are in G.P.
4. 1/(I₂+I₄), 1/(I₃+I₅), 1/(I₄+I₆) are in A.P.

Correct answer: 4

Question 2

Let α and β be the roots of x²-6x-2=0. If a_n=αⁿ-βⁿ for n≥1, then the value of (a₁₀-2a₈)/3a₉ is

1. 2
2. 4
3. 3
4. 1

Correct answer: 1

Question 3

A hyperbola passes through the foci of the ellipse x²/25 + y²/16 = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :

1. x²/9 – y²/16 = 1

2. x² – y² = 9

3. x²/9 – y²/4 = 1

4. x²/9 – y²/25 = 1

Correct answer: 1

Question 4

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then :

1. 2y=273x
2. 2y=91x
3. y=273x
4. y=91x

Correct answer: 2

Question 5

A function f(x) is given by f(x)=5^x/(5^x+5), then the sum of the series f(1/20)+f(2/20)+f(3/20)+…..+f(39/20) is equal to:

1. 19/2
2. 29/2
3. 49/2
4. 39/2

Correct answer: 4

Question 6

The minimum value of

where a, x∈R and a>0, is equal to :

1. a+1
2. 2Va
3. a + 1/a
4. 2a

Correct answer: 2

Question 7

If the curve x²+2y²=2 intersects the line x+y=1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

1. π/2 – tan^-1(1/4)

2. π/2 – tan^-1(1/3)

3. π/2 + tan^-1(1/3)

4. π/2 + tan^-1(1/4)

Correct answer: 4

Question 8

1. 1/2
2. 1/3
3. 1
4. 1/4

Correct answer: 1

Question 9

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is :

1. 2/9
2. 97/297
3. 122/297
4. 1/5

Correct answer: 2

Question 10

A plane passes through the points A(1,2,3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, –1, 1), then the projection of OP on this plane is of length:

1. √(2/5)
2. √(2/7)
3. √(2/3)
4. √(2/11)

Correct answer: 4

Question 11

The integral

x>0, is equal to :

1. 4log_e|x²+5x-7|+c
2. log_e|x²+5x-7|+c
3. 0.25 log_e|x²+5x-7|+c
4. 4log_e√(x²+5x-7)+c

Correct answer: 1

Question 12

If for the matrix

AA^T=I₂, then the value of α⁴+β⁴ is:

1. 1
2. 2
3. 4
4. 3

Correct answer: 1

Question 13

The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x – y + 4z = 8

1. has a solution (α, β, γ) satisfying α+β²+γ³=12
2. has a unique solution
3. does not have any solution
4. has infinitely many solutions

Correct answer: 2

Question 14

is equal to:

1. 65/56
2. 65/33
3. 75/56
4. 56/33

Correct answer: 1

Question 15

If α, β ∈ R are such that 1 – 2i (here i² = –1) is a root of z²+αz+β=0, then (α-β) is equal to:

1. -3
2. -7
3. 7
4. 3

Correct answer: 2

Question 16

The contrapositive of the statement “If you will work, you will earn money” is :

1. If you will earn money, you will work
2. You will earn money, if you will not work
3. If you will not earn money, you will not work
4. To earn money, you need to work

Correct answer: 3

Question 17

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :

1. 7/45
2. 28/45
3. 14/45
4. 8/45

Correct answer: 2

Question 18

If 0>x<y<π and cos x + cos y – cos (x + y) = 3/2 , then sin x + cos y is equal to :

1. (1+√3)/2
2. √3 / 2
3. 1/2
4. (1-V3)/2

Correct answer: 1

Question 19

The shortest distance between the line x – y = 1 and the curve x² = 2y is :

1. 1/√2
2. 1/2
3. 0
4. 1/2√2

Correct answer: 4

Question 20

Let A be a 3 × 3 matrix with det(A) = 4. Let R_i denote the i^th row of A. If a matrix B is obtained by performing the operation R₂→2R₂+5R₃ on 2A, then det(B) is equal to :

1. 64
2. 128
3. 80
4. 16

Correct answer: 1

Question 21

If the curve, y = y(x) represented by the solution of the differential equation (2xy² – y) dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to _.

Correct answer: 1

Question 22

A function f is defined on [–3, 3] as

where [x] denotes the greatest integer ≤ x. The number of points, where f is not differentiable in (–3, 3) is _

Correct answer: 5

Question 23

The value of

is

Correct answer: 19

Question 24

Let a^→=i+aj+3k and b^→=3i-aj+k. If the area of the parallelogram whose adjacent sides
are represented by the vectors a^→ and b^→ 8√3 square units, then a^→.b^→ is equal to _____.

Correct answer: 2

Question 25

A line ‘l’ passing through origin is perpendicular to the lines

I₁ : r^→ = (3+t)i+(-1+2t)j+(4+2t)k

I₂ : r^→ = (3+2s)i+(3+2s)j+(2+s)k

If the co-ordinates of the point in the first octant on ‘l₂” at a distance of √17 from the point of intersection of ‘l’ and ‘I₁’ are (a, b, c) then 18(a + b + c) is equal to __.

Correct answer: 44

Question 26

If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)²⁰²² is divided by 8 is __.

Correct answer: 1

Question 27

A line is a common tangent to the circle (x – 3)²+y²=9 and the parabola y²=4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a + c) is equal to _.

Correct answer: 9

Question 28

The total number of two digit numbers ‘n’, such that 3ⁿ+7ⁿ is a multiple of 10, is __.

Correct answer: 45

Question 29

If

exists and is equal to b, then the value of a –2b is _.

Correct answer: 5

Question 30

If the curves x=y⁴ and xy=k cut at right angles, then (4k)⁶ is equal to _.

Correct answer: 4

JEE Main Frequently Asked Questions (FAQs)

Question 1: When is JEE Main 2021 exams?

Answer: National Testing Agency has announced dates for all phases of JEE Main. First phase is in February 2021 (23, 24, 25 and 26). Second phase is in March 2021 (15, 16, 17 & 18) , third in April 2021 (27, 28, 29 & 30) and fourth in May 2021 (24, 25, 26, 27 & 28). To get more details about JEE Main click here.

Question 2: Can I challenge JEE Main 2021 answer key? How?

Answer: Yes, candidates who have objection to the answer key given by National Testing Agency can go to jeemain.nta.nic.in , from where they can challenge answer key.

Question 3: Does National Testing Agency refund JEE Mains 2021 answer key fees.

Answer: Yes, National Testing Agency refund fees if objection is found valid with proper supporting documents.

Question 4: Who will conduct JEE Main 2021 Counseling?

Answer: Joint Seat Allocation Authority (JoSAA) is responsible for counseling of JEE Main 2021 qualified students.

Importance of Doubt Clearing with Solving JEE Main Question Paper

The more questions you solve, the better your JEE Score! You can see best questions asked for JEE inside the app which gets updated daily with 1000+ questions. You can always take help from Kunduz which will help you when you are stuck in between and need some help from topmost tutors from IITs!  We will update you with such blog posts. So, keep checking this space.  Stay awesome, Keep Learning!?

Why Study with Kunduz?

• Get personalized solutions & answers to all questions.
• Doubts are solved in 15 mins by our doubt solving expert teachers
• Chat with our tutors like private tutoring to get your doubts cleared.
• Doubt solving experts available 24*7.
• Do not stand in a queue at a doubt corner to get your doubts solved.
• Save hours exploring online to find solutions to your doubts.
• Do your own revision using the Kunduz Question bank that is free.
• Revise with questions and solutions asked by other students preparing for JEE / NEET from our question bank.

You may also like

• JEE Main 2021 Question Paper with Solutions- 24 February
• JEE Mains Registration Process, Dates, Fees, Eligibility
• How to Concentrate Study – Increasing Concentration Power

To solve and ask more and more questions download Kunduz app for free.