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# JEE Mains 2021 Answer Key and Solutions- 25 Feb M1

Get the JEE Mains February 2021 answer key for 25 February here. The official question papers of JEE Main 2021 are available and Kunduz provide solutions for you.

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Posted by Mahak Jain, 31/3/2021 Hesap Oluştur

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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, l2+m2-n2=0. Then the value of sin4α+cos4α is :

1. 3/4
2. 5/8
3. 1/2
4. 3/8

#### Question 2

If Rolle’s theorem holds for the function f(x)=x3-ax2+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)

#### Question 3

All possible values of θ∈[0, 2π] for which sin2θ+tan2θ>0 lie in :

1. (0,π/2) ⋃ (π,3π/2)
2. (0.π/2) ⋃ (π/2,3π/4) ⋃ (π,7π/6)
3. (0,π/4) ⋃ (π/2,3π/4) ⋃ (3π/2,11π/6)
4. (0,π/4)⋃(π/2,3π/4)⋃(π/5π/4)⋃(3π/2,7π/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 :

1. 10√3
2. 10
3. 10(√3+1)
4. 10(√3-1)

#### Question 5

The value of

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

1. (e+1)/3
2. 1/(3e)
3. (e+1)/(3e)
4. (e-1)/(3e)

#### Question 6

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

1. A→(A⟷B)
2. A→(A∧B)
3. A→(A→B)
4. A→(A∨B)

#### 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 ?

1. If g is onto, then fog is one-one
2. If f is onto, then f(n)=n ∀ n∈N
3. f is one-one
4. If fog is one-one, then g is one-one

#### Question 8

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

1. 36
2. 30
3. 45
4. 24

#### 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. 1/27
2. 3/8
3. 3/4
4. 1/8

#### Question 10

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 :

1. 3√2
2. 3/√2
3. 3/2√2
4. 1/2√2

#### Question 11

If the curves, x2/a+y2/b=1 and x2/c+y2/d=1 intersect each other at an angle of 90º, then which of the following relations is TRUE?

1. a-c=b+d
2. a+b=c+d
3. a-b=c-d
4. ab=(c+d)/(a+b)

#### Question 12

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

#### Question 13

The value of the integral

where c is a constant of integration

#### Question 14

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x2-4x+y+8)/(x-2), then this curve also passes through the point :

1. (5, 5)
2. (4, 5)
3. (4, 4)
4. (5, 4)

1. xyz=4
2. xy-z=(x+y)z
3. xy+yz+zx=z
4. xy+z=(x+y)z

#### Question 16

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

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

1. 1/2
2. 0
3. 1
4. 1/e

#### Question 18

The coefficients a, b and c of the quadratic equation, ax2+bx+c=0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

1. 1/54
2. 1/36
3. 5/216
4. 1/72

#### Question 19

A tangent is drawn to the parabola y2=6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it ?

1. (0, 3)
2. (–6, 0)
3. (4, 5)
4. (5, 4)

#### Question 20

The integer ‘k’, for which the inequality x2-2(3k-1)x+8k2-7>0 is valid for every x in R, is :

1. 2
2. 3
3. 4
4. 0

#### Question 21

Let A1, A2, A3,….. be squares such that for each n≥1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one, is___________.

#### Question 22

The number of points, at which the function f(x)=|2x+1|-3|x+2|+|x2+x-2|, x∈R is not differentiable is _.

#### 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 __.

#### Question 24

Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x = –1, and x = 1. If

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

#### 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 A4 is equal to __.

#### 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 __.

#### 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 _______.

#### Question 29

where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If A2= I3, then the value of x3+y3+z3 is ___.

#### Question 30

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