Attempting question papers is best way to practice. In this blog you have JEE Mains 2021 Solved question paper for 24^{th} February shift 1.

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

### Mathematics

#### Question 1

The area bounded by region inside the circle x^{2}+y^{2}=36 and outside the parabola y^{2}=9x is

- 12π+3√3
- 36π+3√3
- 24π+3√3
- 24π-3√3

Correct answer: 3

#### Question 2

The locus of mid – point of the line segment joining focus of parabola y^{2}=4ax to a point moving on it, is a parabola equation of whose directrix is

- y=0
- x=0
- x=a
- y=a

Correct answer: 2

#### Question 3

The equation of plane perpendicular to plans 3x+y-2z+1=0 and 2x-5y-z+3=0 such that it passes through point (1, 2, -3)

- 11x+y+17z+38=0
- 11x-y-17z+40=0
- 11x+y-17z+36=0
- x+11y+17z+3=0

Correct answer: 1

#### Question 4

There are 6 Indians 8 foreigners. Find number of committee form with atleast 2 Indians such numbers of foreigners is twice the number of Indians.

- 1625
- 1050
- 1400
- 575

Correct answer: 1

#### Question 5

If f:R→R is a function defined by f(x)=[x-1]cos((2x-1)π/2) where [x] denotes the greatest integer function, then f is

- continuous for every real x.
- discontinuous only at x = 1.
- discontinuous only at non-zero integral values of x
- continuous only at x = 1.

Correct answer: 1

#### Question 6

There are two positive number p and q such that p+q=2 and p^{4}+q^{4}=272. Find the quadratic equation whose roots are p and q

1. x^{2}-2x+2=0

2. x^{2}-2x+135=0

3. x^{2}-2x+16=0

4. x^{2}-2x+130=0

Correct answer: 3

#### Question 7

A point is moving on the line such that the AM of reciprocal of intercepts on axis is 1/4. There are 3 stones whose position are (2, 2) (4, 4) and (1, 1). Find the stone which satisfies the line

- (2,4)
- (4,4)
- (1,1)
- None of these

Correct answer: 1

#### Question 8

A fair die is thrown n times. The probability of getting an odd number twice is equal to that getting an even number thrice. The probability of getting an odd number, odd number of times is

- 1/3
- 1/6
- 1/2
- 1/8

Correct answer: 3

#### Question 9

If

is the root of equation t^{2}-9t+8 then value of 2sinθ/(sinθ + √3sinθ) when 0<θ<π/2, is

- 1/2
- 1
- 2
- 4

Correct answer: 1

#### Question 10

Population of a town at time t is given by the differential equation dP/dt=0.5P(t)-450. Also P(0)=850, find the time when population of town becomes zero

- ln9
- 3ln4
- 2ln18
- ln18

Correct answer: 3

#### Question 11

then ordered pair (a,b) is

- (1,3)
- (3,1)
- (1,1)
- (-1,3)

Correct answer: 1

#### Question 12

Which of following is tautology ?

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

Correct answer: 1

#### Question 13

Let f:R→R, f(x)=2x-1, g(x)=(x-0.5)/(x-1), then f(g(x)) is?

- one-one, onto
- many-one, onto
- one-one, into
- many-one, into

Correct answer: 3

#### Question 14

The value of (^{15}C_{1} + 2. ^{15}C_{2} – 3. ^{15}C_{3} +…..- 15. ^{15}C_{15}) + (^{14}C_{1} + ^{14}C_{3} +……+ ^{14}C_{11}) is

1. 2^{16}-14

2. 2^{13}-14

3. 2^{13}-13

4. 2^{14}

Correct answer: 2

#### Question 15

The distance of the point P(1, 1, 9) from the point of intersection of plane x+y+z=17 and line (x-3)=(y-4)/2=(z-5)/2

- √38
- √39
- 6
- 7

Correct answer: 1

#### Question 16

Two towers are 150 m distance apart. Height of one tower is thrice the other tower. The angle of elevation of top of tower from midpoint of their feet are complement to each other height of smaller tower is

- 25√3 m
- 25/√3 m
- 75√3 m
- 25 m

Correct answer: 1

#### Question 17

Find the value of

- 1/15
- 2/3
- 3
- 2

Correct answer: 2

#### Question 18

Tangent at point P(t,t^{3}), of curve y=x^{3} meets the curve again at Q then ordinate of point which divides PQ in 1:2 internally, is

- 0
- 2t
^{3} - -2t
^{3} - 8t

Correct answer: 3

#### Question 19

The values of k and m such that system of equations 3x+2y-kz=10, x-2y+3z=3, x+2y-3z=5m are inconsistent.

- k=3 and m≠7/3
- k=3 and m≠7/10
- k≠3 and m=7/10
- k=2 and m≠7/10

Correct answer: 1

#### Question 20

Let f(x)=(4x^{3}-3x^{2})/6 – 2sinx + (2x-1)cosx, then f(x)

- decreases in [0.5, ∞)
- increase in [0.5, ∞)
- decreases in (-∞, ∞)
- increase in (-∞, 0.5]

Correct answer: 2

#### Question 21

The least value of α such that (4/sinx)+(1/(1-sinx))=α has at least one solution in x∈(0,π/2)

Correct answer: 9.00

#### Question 22

One of the diameter of circle C_{1}😡^{2}+y^{2}-2x-6y+6=0 is chord of circle C_{2} with centre (2, 1) then radius of C_{2} is

Correct answer: 3.00

#### Question 23

Correct answer: 1.00

#### Question 24

where α ∈ R . Suppose Q=q_{ij }is a matrix such that PQ=kI, where k∈R, k≠0 and I is the identity matrix of order 3. If q_{23}=-k/8 and det(Q)=k^{2}/2, then value of k^{2}+α^{2} is equal to

Correct answer: 17.00

#### Question 25

Of the three independent events B_{1}, B_{2} and B_{3} , the probability that only B_{2} occurs is β and only B_{3} occurs is γ. Let the probability p that none of events B_{1}, B_{2} or B_{3} occurs satisfy the equations (α-2β)p=αβ and (β-3γ)p=2βγ. All the given probabilities are assumed to lie in the interval (0, 1).

Then (Probability of occurrence of B_{1})/(Probability of occurrence of B_{2})=

Correct answer: 6.00

#### Question 26

How many 3 × 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of M^{T}M is 7?

Correct answer: 540.00

#### Question 27

c^{→} is coplanar with a^{→}=-i+j+k and b^{→}=2i+k, a^{→}.c^{→}=7 and c^{→} is perpendicular to b^{→}, then the value of 2|a^{→}+b^{→}+c^{→}| is

Correct answer:75.00

#### Question 28

z+α|z-1|+2i=0; z∈C and α∈R, then the value of 2[(α_{max})^{2}+(α_{min})^{2}] is

Correct answer: 10.00

#### Question 29

Let A={x:x is 3 digit number}, B={x:x=9k+2, k∈I} and C={x:x=9k+l, k∈I, l∈I, 0<l<9}. If sum of elements in A∩B∩C is 274 × 400 then l is

Correct answer: 5.00

#### Question 30

_{-a}∫^{a} |x|+|x-2| = 22, a>2 then the value of _{-a}∫^{a} x+[x] is, (where [.] represents greatest integer function)

Correct answer: -3.00

## JEE Main Frequently Asked Questions (FAQs)

**Question 1: **When is JEE Mains 2021 exams?

**Answer: **National Testing Agency has announced dates for all phases of JEE Mains. 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 Mains click here.

**Question 2:** Can I challenge JEE Mains 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 Mains 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 Mains 2021 Counseling?

**Answer: **Joint Seat Allocation Authority (JoSAA) is responsible for counseling of JEE Mains 2021 qualified students.

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