# JEE Main 2020 Question Paper Answer Keys Solutions 4 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 4 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 4 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 4 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 4 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 f : (0, ∞) → (0, ∞) be a differentiable function such that f(1) = e and. If f(x) = 1, then x is equal to :

**Options:**

A. 1/e

B. 2e

C. 1/2e

D. e

**Answer Key: **

**Solution:**

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

Contrapositive of the statement :

If a function f is differentiable at a, then it is also continuous at a’, is :

**Options:**

A. If a function f is not continuous at a, then it is not differentiable at a.

B. If a function f is continuous at a, then it is differentiable at a.

C. If a function f is not continuous at a. then it is differentiable at a.

D. If a function f is continuous at a, then it is not differentiable at a.

**Answer Key: **

**Solution:**

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

The solution of the differential equation is (where C is a constant of integration).

**Options:**

A. x – 2log_{e}(y + 3x) = C

B. x – log_{e}(y + 3x) = C

C. y + 3x – [(log_{e}x)^{2}]/2 = C

D. y – [(log_{e}(y + 3x))^{2} ]/2 = C

**Answer Key: **

**Solution:**

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

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)^{n+5} are in the ratio 5 : 10 : 14, then the largest coefficient in the expansion is :

**Options:**

A. 330

B. 252

C. 792

D. 462

**Answer Key: **

**Solution:**

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

The circle passing through the intersection of the circles, x^{2} + y^{2} – 6x = 0 and x^{2} + y^{2} – 4y = 0, having its centre on the line, 2x – 3y + 12 = 0, also passes through the point :

**Options:**

A. (1, –3)

B. (–1, 3)

C. (–3, 6)

D. (–3, 1)

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 6**

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is:

**Options:**

A. 30/61

B. 5/6

C. 5/31

D. 31/61

**Answer Key: **

**Solution:**

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

The angle of elevation of a cloud C from a point P, 200 m above a still take is 30°. If the angle of

depression of the image of C in the lake from the point P is 60°, then PC (in m) is equal to

**Options:**

A. 100

B. 400√3

C. 200√3

D. 400

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 8**

The function is

**Options:**

A. continuous on R – {–1} and differentiable on R – {–1, 1}.

B. both continuous and differentiable on R – {–1}.

C. both continuous and differentiable on R – {1}

D. continuous on R – {1} and differentiable on R – {–1, 1}.

**Answer Key: **

**Solution:**

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

Suppose the vectors x_{1}, x_{2} and x_{3} are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b_{1}, b_{2} and b_{3} respectively. If

then the determinant of A is equal of A is equal to :

**Options:**

A. 3/2

B. 4

C. 1/2

D. 2

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 10**

Let a_{1}, a_{2}, …. a_{n} be a given A.P. whose common difference is an integer and S_{n} = a_{1} + a_{2} + … + a_{n}. If a_{1} = 1, a_{n} = 300 and 15 ≤ n ≤ 50, then the ordered pair (S_{n–4}, a_{n–4}) is equal to :

**Options:**

A. (2490, 248)

B. (2490, 249)

C. (2480, 249)

D. (2480, 248)

**Answer Key: **

**Solution:**

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

Let , where each X_{i} contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi’s and exactly 6 of sets Y_{i}‘s then n is equal to :

**Options:**

A. 45

B. 15

C. 30

D. 50

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 12**

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x^{2} – 1 below the x-axis, is :

**Options:**

A. 1/3√3

B. 4/3

C. 4/3√3

D. 2/3√3

**Answer Key: **

**Solution:**

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

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1/2. If P(1, β) β > 0 is a point on this ellipse, then the equation of the normal to it at P is

**Options:**

A. 7x– 4y = 1

B. 4x – 2y = 1

C. 8x – 2y = 5

D. 4x – 3y = 2

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 14**

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line x/2 = y/3 = z/-6 is

**Options:**

A. 1/7

B. 7

C. 1

D. 7/5

**Answer Key: **

**Solution:**

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

If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to –4, then a value of k is ;

**Options:**

A. √15

B. –4

C. –2

D. √14

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 16**

The integral is equal to

**Options:**

A. -1/9

B. 9/2

C. -1/18

D. 7/18

**Answer Key: **

**Solution:**

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

The minimum value of 2^{sinx} + 2^{cosx} is :

**Options:**

A.

B.

C.

D.

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 18**

If a and b are real numbers such that (2 + α)^{4} = a + bα, where α = (-1 + i√3) / 2, then (a + b) is equal to

**Options:**

A. 33

B. 24

C. 9

D. 57

**Answer Key: **

**Solution:**

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

Let λ ≠ 0 be in R. If α and β are the roots of the equation, x^{2} – x + 2λ = 0 and α and γ are the roots of the equation, 3x^{2} – 10x + 27λ = 0, then βγ / λ is equal to

**Options:**

A. 27

B. 36

C. 9

D. 18

**Answer Key: **

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 20**

If the system of equations

x + y + z = 2

2x + 4y – z = 6

3x + 2y + λz = μ,

**Options:**

A. λ + 2μ = 14

B. 2λ – μ = 5

C. 2λ + μ = 14

D. λ – 2μ = -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**

Let PQ be a diameter of the circle x^{2} + y^{2} = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is ……

**Answer Key: 07.00**

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 22**

If the variance of the following frequency distribution :

Class : 10-20 20-30 30-40

Frequency : 2 x 2

is 50, then x is equal to …..

**Answer Key: 04.00**

**Solution:**

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

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ……

**Answer Key: 135.00**

**Solution:**

**JEE Main 2020 Maths Questions Answer Keys Solutions 4th Sep Shift 2 : Ques No 22**

Let {x} and [x] denote the fractional part of x and the greatest integer ≤ x respectively of a real number x.

If and 10(n^{2} – n), (n ∈ N, n > 1) are three consecutive terms of a G.P. then n is equal

**Answer Key: 21.00**

**Solution:**

**JEE Main 2020 Mathematics Questions with Answer Keys and Solutions : Ques No 25**

If a = 2* i* +

*+ 2*

**j***, then the value of |*

**k***x (a x*

**i***)|*

**i**^{2}+ |

*x (a x*

**j***)|*

**j**^{2}+ |

*x (a x*

**k***)|*

**k**^{2}is equal to

**Answer Key: 18.00**

**Solution:**