Attempting question papers is best way to practice. In this blog you have JEE Main 2021 Solved question paper for 24^{th} February shift 2.

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## JEE Main 2021 Solved Question Paper- 24 February Shift 1

### Mathematics

#### Question 1

Give f(0)=1, f(2)=e^{2}, f'(x)=f'(2-x), then the value of _{0}∫^{2} f(x)dx is

- 1-e
^{2} - 1+e
^{2} - 3e
- e
^{2}

Correct answer: 2

#### Question 2

The area of region defined by 5x^{2}≤y≤2x^{2}+9

- 6√3
- 12√3
- 18√3
- 9√3

Correct answer: 2

#### Question 3

A plane is flying horizontally with speed 120 m/s. Its angle of elevation from a point on ground is 60° . After 20s angle of elevation is 30° . Find height of plane

- 1200√3
- 2400√3
- 600√3
- 1500√3

Correct answer: 1

#### Question 4

Negation of the statement ~p∨(p∧q)

- p∧~q
- p∨~q
- ~p∧q
- ~p∨~q

Correct answer: 2

#### Question 5

Vertices of Δ are (a, c), (2, b) and (a, b), a, b, c are in A.P. centroid is (10/3 , 7/3). If α, β are roots of ax^{2}+bx+1=0 then α^{2}+β^{2}-αβ=

- -71/256
- 71/256
- 69/256
- -69/256

Correct answer: 1

#### Question 6

⨍(x)=1, ⨍'(0)=2, ⨍”(x)≠0 then ⨍(1) lies in

- (0,3)
- (6,9)
- [9,12]
- [5,7]

Correct answer: 2

#### Question 7

The value of tan(0.25 sin^{-1}(√63 / 8)) is

- 1/√7
- 1/√5
- 2/√3
- None of these

Correct answer: 1

#### Question 8

The number of natural numbers less than 7,000 which can be formed by using the digits 0,1, 3, 7, 9 (repetition of digits allowed) is equal to

- 250
- 374
- 372
- 375

Correct answer: 2

#### Question 9

The value of ^{n+1}C_{2}+2(^{2}C_{2}+^{3}C_{2}+…+^{n}C_{2})=

- n(n+1)(2n-1)/6
- n(n+1)(2n+1)/6
- n(n-1)(n+1)/6
- n(n+1)/2

Correct answer: 2

#### Question 10

If A and B are subsets of X = {1, 2, 3, 4, 5} then find the probability such that n(A∩B)=2

- 65/2
^{7} - 65/2
^{9} - 35/2
^{9} - 135/2
^{9}

Correct answer: 4

#### Question 11

A curve y=f(x) passing through the point (1,2) satisfies the differential equation xdx/dy+y=bx^{2} such that _{1}∫^{2} f(y)dy=62/5. The value of b is

- 10
- 11
- 32/5
- 62/5

Correct answer: 1

#### Question 12

A curve y=ax^{2}+bx+c passing through the point (1, 2) has slope at origin equal to 1, then ordered triplet (a, b, c) may be

- (1,1,0)
- (0.5,1,0)
- (-0.5,1,1)
- (2,-1,0)

Correct answer: 1

#### Question 13

The value of _{1}∫^{3} [x^{2}-2x-2]dx ([.] denotes greatest integer function)

- -4
- -5
- -1-√2-√3
- 1-√2-√3

Correct answer: 3

#### Question 14

Which of the following conic has tangent x+√3y-2V3 at pont (1.5√3, 0.5)

- x
^{2}+9 y^{2}=9 - y
^{2}=x/6√3 - x
^{2}-9y^{2}=10 - x
^{2}=y/6√3

Correct answer: 1

#### Question 15

Equation of plane passing through (1, 0, 2) and line of intersection of planes r^{→}.(i+j+k)=1 and r^{→}.(i-2j)=-2 is

- r
^{→}.(i+7j+3k)=7 - r
^{→}.(3i+10j+3k)=7 - r
^{→}.(i+j-3k)=4 - r
^{→}.(i+4j-1k)=-7

Correct answer: 1

#### Question 16

A is 3×3 square matrix and B is 3×3 skew symmetric matrix and X is a 3×1 matrix, then equation ( A^{2}B^{2}-B^{2}A^{2})X=O (Where O is a null matrix) has/have

- Infinite solution
- No solution
- Exactly one solution
- Exactly two solution

Correct answer: 1

#### Question 17

Find a point on the curve y=x^{2}+4 which is at shortest distance from the line y=4x-1.

- (2,8)
- (1,5)
- (3,13)
- (-1,5)

Correct answer: 1

#### Question 18

Then interval in which f(x) is monotonically increasing is

- (-5,-4)∪(4,∞)
- (-∞,-4)∪(5,∞)
- (-5,4)∪(5,∞)
- (-5,-4)∪(3,∞)

Correct answer: 1

#### Question 19

If variance of ten numbers 1, 1, 1, 1, 1, 1, 1, 1, 1, ; k where k N ∈ , is less than or equal to 10 then maximum value of k is.

Correct answer: 11.00

#### Question 20

If a+α=1, β+b=2 and a(⨍(x))+α⨍(1/x)=β/x + bx, then the value of

Correct answer: 2.00

#### Question 21

(x-2)^{2}+(y-3)^{2}=25, Normal and tangent are drawn to it at (5, 7 .) Area of ∆ made by normal, tangent and x – axis is A. Find 24A.

Correct answer: 1225.00

#### Question 22

Sum of first four terms of GP=65/12. Sum of their reciprocals is 65/18. Product of first 3 terms is 1. If 3rd term is α, then 2α=

Correct answer: 3.00

#### Question 23

S_{1}, S_{2}, S_{3} …., S_{10} are 10 students, in how many ways they can be divided in 3 groups A, B and C such that all groups have at least one student and C has maximum 3 students.

Correct answer: 31650.00

#### Question 24

A(5, 0) and B(-5, 0) are two points PA=3PB. Then locus of P is a circle with radius ‘r’. Then 4r^{2}=

Correct answer: 525.00

## 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 Main 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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