Practice problems on JEE Mains, JEE Mains 2021 Feb 25 Shift 2

Question 1

If the curve x2 + 2﻿y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

Accepted Answer

2π​+tan−1(41​)

Answer

2π​−tan−1(41​)

Answer

2π​−tan−1(31​)

Answer

2π​+tan−1(31​)

Question 2

The truth table for the following logic circuit is :

Accepted Answer

A 0011​ B 0101​ Y 0110​​

Answer

A0011​B0101​Y1010​​

Answer

A 0011​ B 0101​ Y 1001​​

Answer

A0011​B0101​Y0101​​

Question 3

Which one of the following statements is FALSE for hydrophilic sols ?

Accepted Answer

Their viscosity is of the order of that of H2​O

Answer

They do not require electrolytes for stability

Answer

These sols are reversible in nature

Answer

The sols cannot be easily coagulated

Question 4

Given below are two statements :Statement I: α and β forms of sulphur can change reversibly between themselves with slow heating or slow cooling.Statement II: At room temperature the stable crystalline form of sulphur is monoclinic sulphur.In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

Statement I is true but Statement II is false.

Answer

Both Statement I and Statement II are true.

Answer

Both Statement I and Statement II are false.

Answer

Statement I is false but Statement II is true.

Question 5

Which of the following compound is added to the sodium extract before addition of silver nitrate for testing of halogens?

Accepted Answer

Nitric acid

Answer

Hydrochloric acid

Answer

Sodium hydroxide

Answer

Ammonia

Question 6

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is :

Accepted Answer

29797​

Answer

92​

Answer

297122​

Answer

51​

Question 7

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are nonsmokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :

Accepted Answer

28/45

Answer

7/45

Answer

14/45

Answer

8/45

Question 8

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then :

Accepted Answer

2y = 91x

Answer

2y = 273x

Answer

y = 273x

Answer

y = 91x

Question 9

If 0 π and cos x + cos y – cos (x + y) = 23​, then sin x + cos y is equal to :

Accepted Answer

21+3​​

Answer

23​​

Answer

21​

Answer

21−3​​

Question 10

The solubility of Ca(OH)2​ in water is :[Given : The solubility product of Ca(OH)2​ in water =5.5×10−6 ]

Accepted Answer

1.11×10−2

Answer

1.77×10−2

Answer

1.77×10−6

Answer

1.11×10−6

Question 11

An LCR circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45°. If on the other hand, only inductor is removed the current leads by 45° with the applied voltage. The rms current flowing in the circuit will be :

Accepted Answer

2 A

Answer

1.5 A

Answer

1 A

Answer

2.5 A

Question 12

The method used for the purification of Indium is :

Accepted Answer

Zone refining

Answer

Vapour phase refining

Answer

Liquation

Answer

van Arkel method

Question 13

If a message signal of frequency ′fm​ ’  ’ is amplitude modulated with a carrier signal of frequency ′fc​ ' and radiated through an antenna, the wavelength of the corresponding signal in air is :

Accepted Answer

fc​c​

Answer

fm​c​

Answer

fc​+fm​c​

Answer

fc​−fm​c​

Question 14

Let A be a 3 x 3 matrix with det(A)=4. Let Ri​ denote the ith  row of A. If a matrix B is obtained by performing the operation R2​→2R2​ +5R3​ on 2 A, then det(B) is equal to :

Accepted Answer

64

Answer

128

Answer

80

Answer

16