Contents

# JEE Main 2020 Question Paper Answer Keys Solutions 3 September Evening Shift

Hi Students, welcome to **Amans Maths Blogs (AMB)**. On this post, you will get * JEE Main 2020 Question Paper Answer Keys Solutions 3 September Evening Shift*. As you know that Joint Entrance Examination means

*is one of the most important entrance exam in engineering entrance examination.*

**JEE Main and JEE Advanced***is Computer Based Test (CBT) and it was conducted by the National Testing Agency (NTA).*

**JEE Main 2020***duration is three hours and the exam consists of 300 marks (Maximum Marks).*

**JEE Main 2020 exam***has 2 sections in all three Subject Papers (Physics, Chemistry, Mathematics) and each subject has 25 questions.*

**JEE Main 2020 Questions Paper**## JEE Main 2020 Physics Questions Paper with Answer Keys & Solutions

In * JEE Main 2020 Question Paper Answer Keys Solutions 3 September Evening Shift*, Physics question paper’s answer keys and solutions by Resonance.

**JEE Main 2020 Physics Question Paper with Answer Keys and Solutions (By Resonance)**

## JEE Main 2020 Chemistry Questions Paper with Answer Keys & Solutions

In * JEE Main 2020 Question Paper Answer Keys Solutions 2 September Evening Shift*, Chemistry question paper’s answer keys and solutions by Resonance.

**JEE Main 2020 Chemistry Question Paper with Answer Keys and Solutions (By Resonance)**

## JEE Main 2020 Mathematics Questions Paper with Answer Keys & Solutions

In * JEE Main 2020 Question Paper Answer Keys Solutions 3 September Evening Shift*, Mathematics question paper’s answer keys and solutions by

**Amans Maths Blogs (AMB)**.

**Instructions for SECTION 1 : (Maximum Marks : 80): **

This section contains 20 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4) for its answer, out of which Only One is correct.

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 1**

Let A be a 3 x 3 matrix such that

and B = adj (adj A). If |A| = λ and |(B^{-1})^{T}| = μ, then ordered pair, (|λ|, μ) is equal to

**Options:**

A. (3, 1/81)

B. (9, 1/9)

C. (3, 81)

D. (9, 1/81)

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 2**

If x^{3}dy + xy.dx = x^{2}dy + 2ydx ; y(2) = e and x > 1, then y(4) is equal to

**Options:**

A. √e / 2

B. 1/2 + √e

C. 3√e / 2

D. 3/2 + √e

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 3**

If the sum of the series 20 + 19 3/5 + 19 1/5 + 18 4/5 + … upto n^{th} term is 488 and the n^{th} term is negative, then :

**Options:**

A. n^{th} term is -4 2/5

B. n = 41

C. n^{th} term is -4

D. n = 60

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 4**

The set of all real values of λ for which the quadratic equation (λ^{2} + 1) x^{2} – 4λx + 2 = 0 always have

exactly one root in the interval (0, 1) is :

**Options:**

A. (-3, -1)

B. (0, 2)

C. (1, 3]

D. (2, 4]

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 5**

Let R_{1} and R_{2} be two relations defined as follows : R_{1} = {(a, b) ∈ R^{2} : a^{2} + b^{2} ∈ Q} and R_{2} = {(a, b) ∈ R^{2} : a^{2} + b^{2} ∉ Q}, where Q is the set of all rational numbers, then

**Options:**

A. R_{1} is transitive but R_{2} is not transitive

B. R_{2} is transitive but R_{1} is not transitive.

C. Neither R_{1} nor R_{2} is transitive

D. R_{1} and R_{2} are both transitive.

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 6**

The Plane which bisects the line joining the points (4, –2, 3) and (2, 4, –1) at right angles also passes through the point :

**Options:**

A. (0, –1, 1)

B. (4, 0, –1)

C. (4, 0, 1)

D. (0, 1, –1)

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 7**

Let p, q, r be three statements such that the truth value of (p ∧ q) → (~ q V r) is F. Then the truth values of p, q, r are respectively :

**Options:**

A. T, T, F

B. T, T, T

C. T, F, T

D. F, T, F

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 8**

If a triangle ABC has vertices A (–1, 7), B (–7, 1) and C (5, –5), then its orthocentre has coordinates

**Options:**

A. (-3, 3)

B. (3, -3)

C. (-3/5, 3/5)

D. (3/5, -3/5)

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 9**

Suppose f(x) is a polynomial of degree four, having critical points at –1, 0, 1. If T = {x ∈ R |f(x) = f(0)}, then the sum of squares of all the elements of T is :

**Options:**

A. 4

B. 6

C. 2

D. 8

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 10**

If the term independent of x in the expansion of is k, then 18k is equal to

**Options:**

A. 11

B. 5

C. 9

D. 7

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 11**

If z_{1}, z_{2} are complex numbers such that Re(z_{1}) = |z_{1} – 1| and Re(z_{2}) = |z_{2} – 1| and arg (z_{1} – z_{2}) =

π/6, then *Im* (z_{1} + z_{2}) is equal to :

**Options:**

A. 2√3

B. √3 / 2

C. 1 / √3

D. 2 / √3

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 12**

Let x_{i} (1 ≤ i ≤ 10) be ten observation of a random variable X. If where 0 ≠ p ∈ R, then the standard deviation of these observations is:

**Options:**

A. 4/5

B. √(3/5)

C. 9/10

D. 7/10

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 13**

The probability that a randomly chosen 5-digit number is made from exactly two digits is:

**Options:**

A. 135 / 10^{4}

B. 150 / 10^{4}

C. 134 / 10^{4}

D. 121 / 10^{4}

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 14**

Let a, b, c ∈ R be such that a^{2} + b^{2} + c^{2} = 1. If a cos θ = b cos (θ + 2π/3) = c cos (θ + 4π/3), where θ = π/9, then the angle between the vectors a* i* + b

*+ c*

**j***and b*

**k***+ c*

**i***+ a*

**j***is*

**k****Options:**

A. 0

B. 2π/3

C. π/2

D. π/9

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 15**

If the surface area of a cube is increasing at a rate of 3.6 cm^{2}/sec, retaining its shape; then the rate of change of its volume (in cm^{3}/sec.), when the length of a side of the cube is 10 cm, is:

**Options:**

A. 20

B. 10

C. 18

D. 9

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 16**

, (a ≠ 0) is equal to:

**Options:**

A. (2/9)(2/3)^{1/3}

B. (2/3)^{4/3}

C. (2/9)^{1/3}

D. (2/3)(2/9)^{1/3}

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 17**

Let e_{1} and e_{2} be the eccentricities of the ellipse, x^{2} / 25 + y^{2} / b^{2} = 1 (b < 5) and the hyperbola, x^{2} / 16 – y^{2} / b^{2} = 1, respectively satisfying e_{1}e_{2} = 1. If α and β are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair (α, β) is equal to:

**Options:**

A. (8, 10)

B. (20/3, 12)

C. (8, 12)

D. (24/5, 10)

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 18**

If where C is a constant of integration, then the ordered pair (A(x), B(x)) can be :

**Options:**

A. (x – 1, √x)

B. (x – 1, -√x)

C. (x + 1, √x)

D. (x + 1, -√x)

**Answer Key: **

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 19**

If the value of the integral is k/6, then k is equal to

**Options:**

A. 2√3 + π

B. 2√3 – π

C. 3√2 + π

D. 3√2 – π

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 20**

Let the latus rectum of the parabola y^{2} = 4x be the common chord to the circles C_{1} and C_{2} each of them having radius 2√5. Then, the distance between the centres of the circles C_{1} and C_{2} is:

**Options:**

A. 12

B. 8

C. 8√5

D. 4√5

**Answer Key: **

**Solution:**

**Instructions for SECTION 2 : (Maximum Marks : 20): **

This section contains FIVE (05) questions. The answer to each question is NUMERICAL VALUE with two digit integer and decimal upto one digit.

If the numerical value has more than two decimal places truncate/round-off the value upto TWO decimal places.

Full Marks : +4 If ONLY the correct option is chosen

Zero Marks : 0 In all other cases

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 21**

If the tangent to the curve, y = e^{x} at a point (c, e^{c}) and the normal to the parabola, y^{2} = 4x at the point (1,2) intersect at the same point on the x-axis, then the value of c is…..

**Answer Key: 04.00**

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 22**

Let a plane P contain two lines * r* =

*+ λ(*

**i***+*

**i***), λ ∈ R and*

**j***= –*

**r***+ μ(*

**j***–*

**j***), μ ∈ R. If Q(α, β, γ) is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3(α + β + γ) equals to*

**k****Answer Key: 05.00**

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 23**

If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4^{th} A.M. is equal to 2^{nd} G.M., then m is equal to :

**Answer Key: 39.00**

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 24**

The total number of 3-digit numbers, whose sum of digits is 10, is…….

**Answer Key: 54.00**

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 3rd Sep Shift 2 : Ques No 25**

Let S be the set of all integer solutions, (x, y, z), of the system of equations: x – 2y + 5z = 0, –2x + 4y + z = 0, –7x + 14y + 9z = 0 Such that 15 ≤ x2 + y2 + z2 ≤ 150. Then, the number of elements in the set S is equal to….

**Answer Key: 08.00**

**Solution:**