JEE Mains 2021 Answer Key (Official) for February session has been released. It is released separately for four session in February, March, April and May sessions. JEE Mains 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 Mains answer key is released by the National Testing Agency (NTA). Through this blog, candidates can get the JEE Mains Answer Keys 2021 and also previous year answer key and question papers with all solutions.

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## JEE Mains 2021 Answer Key with Solutions- 25 February Shift 1

### Mathematics Answer Key JEE Mains 2021 25 Feb Shift 1

**Question 1**

Let α be the angle between the lines whose direction cosines satisfy the equations l+m-n=0, l^{2}+m^{2}-n^{2}=0. Then the value of sin^{4}α+cos^{4}α is :

- 3/4
- 5/8
- 1/2
- 3/8

Correct answer: 2

**Question **2

If Rolle’s theorem holds for the function f(x)=x^{3}-ax^{2}+bx-4, x∈[1,2] with f'(4/3)=0, then ordered pair (a, b) is equal to :

1. (5, -8)

2. (5, 8)

3. (-5, -8)

4. (-5, 8)

Correct answer: 2

**Question **3

All possible values of θ∈[0, 2π] for which sin^{2}θ+tan^{2}θ>0 lie in :

- (0,π/2) ⋃ (π,3π/2)
- (0.π/2) ⋃ (π/2,3π/4) ⋃ (π,7π/6)
- (0,π/4) ⋃ (π/2,3π/4) ⋃ (3π/2,11π/6)
- (0,π/4)⋃(π/2,3π/4)⋃(π/5π/4)⋃(3π/2,7π/4)

Correct answer: 4

**Question **4

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At the point, angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B, where the angle of depression is 45°. Then the time taken (in seconds) by the boat from B to reach the base of the tower is :

- 10√3
- 10
- 10(√3+1)
- 10(√3-1)

Correct answer: 3

**Question **5

The value of

where [t] denotes the greatest integer ≤ t, is :

- (e+1)/3
- 1/(3e)
- (e+1)/(3e)
- (e-1)/(3e)

Correct answer: 3

**Question **6

The statement A → (B→ A) is equivalent to :

- A→(A⟷B)
- A→(A∧B)
- A→(A→B)
- A→(A∨B)

Correct answer: 4

**Question **7

Let f, g : N→N such that f(n+1)=f(n)+f(1) ∀ n∈N and g be any arbitrary function. Which of the following statements is NOT true ?

- If g is onto, then fog is one-one
- If f is onto, then f(n)=n ∀ n∈N
- f is one-one
- If fog is one-one, then g is one-one

Correct answer: 1

**Question **8

The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

- 36
- 30
- 45
- 24

Correct answer: 2

**Question **9

When a missile is fired a ship, the probability that it is intercepted is 1/3 and the probability that the missile hits the target, given that it is not intercepted, is 3/4. If three missiles are fired independently from the ship, then the probability that all three hit the target, is :

- 1/27
- 3/8
- 3/4
- 1/8

Correct answer: 4

**Question 1**0

Let the lines (2-i)z=(2+i)z’ and (2+i)z+(i-2)z’-4i=0, be normal to a circle C. If the line iz+z’+1+i=0 is tangent to this circle C, then its radius is :

- 3√2
- 3/√2
- 3/2√2
- 1/2√2

Correct answer: 3

**Question 1**1

If the curves, x^{2}/a+y^{2}/b=1 and x^{2}/c+y^{2}/d=1 intersect each other at an angle of 90º, then which of the following relations is TRUE?

- a-c=b+d
- a+b=c+d
- a-b=c-d
- ab=(c+d)/(a+b)

Correct answer: 3

**Question 1**2

The image of the point (3, 5) in the line x – y + 1 = 0, lies on :

1. (x – 4)^{2}+(y + 2)^{2}= 16

2. (x – 4)^{2}+(y – 4)^{2}= 8

3. (x – 2)^{2}+(y – 2)^{2}= 12

4. (x – 2)^{2}+(y – 2)^{2}= 4

Correct answer: 4

**Question 1**3

The value of the integral

where c is a constant of integration

Correct answer: 2

**Question 1**4

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x^{2}-4x+y+8)/(x-2), then this curve also passes through the point :

- (5, 5)
- (4, 5)
- (4, 4)
- (5, 4)

Correct answer: 1

**Question 1**5

- xyz=4
- xy-z=(x+y)z
- xy+yz+zx=z
- xy+z=(x+y)z

Correct answer: 4

**Question 1**6

The equation of the line through the point (0, 1, 2) and perpendicular to the line (x-1)/2=(y+1)/3=(z-1)/-2

- x/3=(y-1)/4=(z-2)/-3
- x/3=(y-1)/4=(z-2)/3
- x/-3=(y-1)/4=(z-2)/3
- x)/3=(y-1)/-4=(z-2)/3

Correct answer: 3

**Question 1**7

- 1/2
- 0
- 1
- 1/e

Correct answer: 3

**Question 1**8

The coefficients a, b and c of the quadratic equation, ax^{2}+bx+c=0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

- 1/54
- 1/36
- 5/216
- 1/72

Correct answer: 3

**Question 1**9

A tangent is drawn to the parabola y^{2}=6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it ?

- (0, 3)
- (–6, 0)
- (4, 5)
- (5, 4)

Correct answer: 4

**Question **20

The integer ‘k’, for which the inequality x^{2}-2(3k-1)x+8k^{2}-7>0 is valid for every x in R, is :

- 2
- 3
- 4
- 0

Correct answer: 2

**Question **21

Let A_{1}, A_{2}, A_{3},….. be squares such that for each n≥1, the length of the side of A_{n} equals the length of diagonal of A_{n+1}. If the length of A_{1} is 12 cm, then the smallest value of n for which area of A_{n} is less than one, is___________.

Correct answer: 9

**Question **22

The number of points, at which the function f(x)=|2x+1|-3|x+2|+|x^{2}+x-2|, x∈R is not differentiable is ** _**.

Correct answer: 2

**Question **23

The total number of numbers, lying between 100 and 1000 than can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is ** __**.

Correct answer: 32

**Question **24

Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x^{6} is unity and it has extrema at x = –1, and x = 1. If

then 5.f(2) is equal to ** _**.

Correct answer: 144

**Question **25

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A^{4} is equal to ** __**.

Correct answer: 64

**Question **26

Correct answer: 13

**Question **27

The locus of the point of intersection of the lines √3 kx+ky-4V3=0 and √3 x-y-4V3 k=0 is a conic, whose eccentricity is **__**.

Correct answer: 2

**Question **28

If the system of equations

kx+y+2z=1

3x-y-2z=2

-2x-2y-4z=3

has infinitely many solutions, then k is equal to _______.

Correct answer: 21

**Question **29

where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If A^{2}= I_{3}, then the value of x^{3}+y^{3}+z^{3} is ___.

Correct answer: 7

**Question **30

Correct answer: 12

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