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

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## JEE Mains 2021 Question Paper with Solutions- 24 February Shift 1

### Physics

#### Question 1

Match the following for the value of ‘α’ for following process represented by

PV^{α} = constant?

a) constant pressure | p) α = 0 |

b) constant volume | q) α = 1 |

c) constant temperature | r) α → ∞ |

d) No heat exchange | s) α = γ |

1. a → q, b → s, c → p, d → r

2. a → p, b → r, c → q, d → s

3. a → s, b → p, c → r, d → q

4. a → p, b → r, c → q, d → s

Correct answer: 2

#### Question 2

In a double star system. Find w.

1. w = √(G(m_{1}+m_{2})/r^{3})

2. w = √((Gm_{1}m_{2})/(m_{1}+m_{2})*r^{3})

3. w = √((Gm_{1})/r^{3})

4. w = √((Gm_{2})/r^{3})

Correct answer: 1

#### Question 3

What is the sign of focal length of convex mirror?

- +ve
- -ve
- Can be +ve or -ve
- None of these

Correct answer: 1

#### Question 4

Find field at center of cube of side a.

- (4kQ)/(3a
^{2}) - (8kQ)/(3a
^{2}) - (16kQ)/(3a
^{2}) - None of these

Correct answer: 2

#### Question 5

Two equal capacitors are as shown in the two figure 1 and 2. The ratio of the equivalent capacitance in the two diagrams is:-

1. C_{1}/C_{2} =1/2

2. C_{1}/C_{2} =1

3. C_{1}/C_{2} = 1/4

4. None of these

Correct answer: 3

#### Question 6

Compare the magnitudes of moment of Inertia of (masses & Radius are equal)

(a) Ring About Diameter (I_{a})

(b) Disc About ⊥ axis passing through centre (I_{b})

(c) SOLID cylinder about (Axis) (I_{c})

(d) SOLID sphere (I_{D})

1. I_{a}= I_{b} = I_{c } >I_{D}

2. I_{a}= I_{b} > I_{c} >I_{D}

3. I_{a}< I_{b} < I_{c} <I_{D}

4. None of these

Correct answer: 1

#### Question 7

A horizontal spring block system (mass m_{2} spring constant k) is oscillating on a smooth surface with amplitude A. If at the mean position an identical block is kept on it so that they move together after what is the new amplitude?

- A
- A/2
- A/√2
- A/(2√2)

Correct answer: 3

#### Question 8

How does the energy of photon change if the corresponding wavelength increases?

- Increases
- Decreases
- May increase or decrease
- Doesn’t depend on wavelength

Correct answer: 2

#### Question 9

In the shown circuit the following the battery is of EMF 4 and internal resistance 8 Ω. Find the potential difference between points x and y is shown in the circuit.

1. V_{x} -V_{y} = 2.4V

2. V_{y } -V_{x} = -2V

3. V_{x} -V_{y} = 4V

4. V_{y} -V_{x}= -4V

Correct answer: 1

#### Question 10

Choose the correct a v/s t graph

1.

2.

3.

4.

Correct answer: 2

#### Question 11

If µ_{r} & ε_{r} represents relative permeability of Medium & Relative permittivity of medium & speed of light in medium is , c/µ

where μ (refractive Index) will be –

- µ
_{r}ε_{r} - √(µ
_{r}ε_{r}) - 1/√(µ
_{r}ε_{r}) - None of these

Correct answer: 2

#### Question 12

A body cools from 100^{o}C to 90^{o}C in 20 mins. Find the time to cool from 110^{o}C to 100^{o}C.

- Equal to 20 mins
- Less than 20 mins
- More than 20 mins
- 30 min

Correct answer: 2

#### Question 13

An object is moving with speed v and collides with an identical mass at rest. After collision, they both move at an angle of 30^{o} with original direction. Find ratio of final speed of mass to the initial speed?

- 1/2
- 2
- √3
- 1/√3

Correct answer: 4

#### Question 14

In a cyclic process ABCA, the process BC is isothermal. Find the work done by gas in cycle ABCA? (Given: P_{1} = P)

- 2ln2 PV
- (2ln2 – 1) PV
- PV ln2
- None of these

Correct answer: 2

#### Question 15

A proton & Li^{3+} are accelerated through same potential difference. If

mass of Li^{3+} is 8.3 times the mass of proton, then find the ratio of de-Broglie wavelength λ_{Li3}+ / λ_{p}

- 0.1
- 0.2
- 0.3
- 0.4

Correct answer: 2

#### Question 16

For a transistor emitter current is 40 mA and collector current is 35 mA, then the β of the transistor is?

- 8/7
- 1/7
- 7
- 1/8

Correct answer: 3

#### Question 17

Choose the correct option (s) regarding the Hydrogen spectrum

- A is the series limit of Lyman
- B is the third line of Balmer
- C is the second line of Paschen
- All of the above are correct

Correct answer: 4

#### Question 18

If W = work done, T = Temperature, K_{b} = Boltzmann constant, x=Displacement & W=αβ^{2} e^{-(x2)/(αTKB)} then find dimensions of β?

1. [M^{1} L^{2} T^{-2} ]

2. [M^{-1} L^{2} T^{-2} ]

3. [M^{1} L^{1} T^{-2} ]

4. None of these

Correct answer: 3

#### Question 19

Find the current at time t = 3 seconds, If the charge as a function of time is given as q(t) =3t^{2} + 2t + 1.

- 34A
- 21A
- 20A
- 15A

Correct answer: 3

#### Question 20

Two satellites are revolving in the orbit around a planet. The ratio of their time periods is 1 : 8. Find the ratio of their angular velocities.

1. w_{1} /w_{2} = 1/2

2. w_{1} /w_{2} = 8

3. w_{1} /w_{2} = 2

4. w_{1} /w_{2} = 2/3

Correct answer: b

#### Numerical value type questions

#### Question 21

Find the minimum force Fo that should be applied to the block of mass m = 0.5 kg, so that the block stays in equilibrium with the rough vertical wall having friction coefficient μ = 0.2. (Take g = 10 m/s^{2} ) (Answer to the nearest integer).

Correct answer: 25.00

#### Question 22

A vertical cross-section of plane is y= x^{2} /4 coefficient of friction is 0.5. Find

maximum height at which particle can stay (in cm).

Correct answer: 25.00

#### Question 23

Two identical particles of same mass are shown just before collision and just after collision than v_{1} /v_{2} is :

Correct answer: 1.00

#### Question 24

i =20t +8t^{2}

Find charge flown during 0≤t≤15

Correct answer: 11250.00

#### Question 25

A Zener diode is connected in the circuit as shown. The current in the 2k Ω

resistance is x ×10^{-4} A , where x is:

Correct answer: 25.00

**Question 26**

A 220 volts AC supply is given to the primary circuit of transformer and as output of 12 volts DC is taken out using rectifier. If secondary number of urns was 24, then find the no. of turns in primary coil.

Correct answer: 440

**Question 2**7

A 100 kg block can be lift by placing a mass m on a piston (hydraulic lift). If diameter of piston placed at one and is increased by 4 times and that of second piston is decreased by 4 times. Now same mass m is placed at piston than how many kg weight can be lift up for the new set up?

Correct answer: 25600

**Question 2**8

An electromagnetic wave is propagating in medium, where µ_{r}=ε_{r}=2. If speed of light in medium is x×10^{7} m/s. Find out x.

Correct answer: 15.00

**Question 2**9

V_{m} = 20sin[100πt + π/4]

V_{c} = 80sin[10^{4}πt + π/6]

For amplitude modulation wave find out percentage modulation index.

Correct answer: 25.00

**Question **30

In AC series R-L-C resonance circuit Resistance R = 6.28 ohm, frequency 10 MH Z and self inductance L=2×10^{-4} Henry is given. Find Quality factor of circuit.

Correct answer: 2000

## 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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