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.

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## 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/(I
_{2}+I_{4}), 1/(I_{3}+I_{5}), 1/(I_{4}+I_{6}) are in G.P. - I
_{2}+I_{4}, I_{3}+I_{5}, I_{4}+I_{6}, are in A.P. - I
_{2}+I_{4}, (I_{3}+I_{5})^{2}, I_{4}+I_{6}are in G.P. - 1/(I
_{2}+I_{4}), 1/(I_{3}+I_{5}), 1/(I_{4}+I_{6}) are in A.P.

Correct answer: 4

**Question **2

Let α and β be the roots of x^{2}-6x-2=0. If a_{n}=α^{n}-β^{n} for n≥1, then the value of (a_{10}-2a_{8})/3a_{9} is

- 2
- 4
- 3
- 1

Correct answer: 1

**Question **3

A hyperbola passes through the foci of the ellipse x^{2}/25 + y^{2}/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. x^{2}/9 – y^{2}/16 = 1

2. x^{2} – y^{2} = 9

3. x^{2}/9 – y^{2}/4 = 1

4. x^{2}/9 – y^{2}/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 :

- 2y=273x
- 2y=91x
- y=273x
- 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:

- 19/2
- 29/2
- 49/2
- 39/2

Correct answer: 4

**Question **6

The minimum value of

where a, x∈R and a>0, is equal to :

- a+1
- 2Va
- a + 1/a
- 2a

Correct answer: 2

**Question **7

If the curve x^{2}+2y^{2}=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

- 1/2
- 1/3
- 1
- 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 :

- 2/9
- 97/297
- 122/297
- 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:

- √(2/5)
- √(2/7)
- √(2/3)
- √(2/11)

Correct answer: 4

**Question **11

The integral

x>0, is equal to :

- 4log
_{e}|x^{2}+5x-7|+c - log
_{e}|x^{2}+5x-7|+c - 0.25 log
_{e}|x^{2}+5x-7|+c - 4log
_{e}√(x^{2}+5x-7)+c

Correct answer: 1

**Question **12

If for the matrix

AA^{T}=I_{2}, then the value of α^{4}+β^{4} is:

- 1
- 2
- 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

- has a solution (α, β, γ) satisfying α+β
^{2}+γ^{3}=12 - has a unique solution
- does not have any solution
- has infinitely many solutions

Correct answer: 2

**Question **14

is equal to:

- 65/56
- 65/33
- 75/56
- 56/33

Correct answer: 1

**Question **15

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

- -3
- -7
- 7
- 3

Correct answer: 2

**Question **16

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

- If you will earn money, you will work
- You will earn money, if you will not work
- If you will not earn money, you will not work
- 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 :

- 7/45
- 28/45
- 14/45
- 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+√3)/2
- √3 / 2
- 1/2
- (1-V3)/2

Correct answer: 1

**Question **19

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

- 1/√2
- 1/2
- 0
- 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 R_{2}→2R_{2}+5R_{3} on 2A, then det(B) is equal to :

- 64
- 128
- 80
- 16

Correct answer: 1

**Question **21

If the curve, y = y(x) represented by the solution of the differential equation (2xy^{2} – 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

I_{1} : r^{→} = (3+t)i+(-1+2t)j+(4+2t)k

I_{2} : r^{→} = (3+2s)i+(3+2s)j+(2+s)k

If the co-ordinates of the point in the first octant on ‘l_{2}” at a distance of √17 from the point of intersection of ‘l’ and ‘I_{1}’ 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}+y^{2}=9 and the parabola y^{2}=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 3^{n}+7^{n} 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=y^{4} 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.

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