Practice problems on JEE Mains, JEE Mains 2021 July 25 Shift 1

Question 1

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Moment of inertia of a circular disc of mass ' M ' and radius 'R' about X,Y axes (passing through its plane) and Z -axis which is perpendicular to its plane were found to be Ix​,Iy​&Iz​ respectively. The respective radii of gyration about all the three axes will be the same.Reason R: A rigid body making rotational motion has fixed mass and shape.In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

A is not correct but R is correct.

Answer

Both A and R are correct and R is the correct explanation of A .

Answer

Both A and R are correct but R is NOT the correct explanation of A .

Answer

A is correct hut R is not correct.

Question 2

Let 9 distinct balls distributed among 4 boxes, B1​,B2​,B3​ and B4​ . If the probability that B3​ contains exactly 3 balls is k(43​)9 then k lies in the set:

Accepted Answer

{x∈R:∣x−3∣<1}

Answer

{x∈R:∣x−1∣<1}

Answer

{x∈R:∣x−2∣≤1}

Answer

{x∈R:∣x−5∣≤1}

Question 3

Which one of the following compounds of Group- 14 elements is not known?

Accepted Answer

[SiCl6​]2−

Answer

[SiF6​]2−

Answer

[GeCl6​]2−

Answer

[Sn(OH)6​]2−

Question 4

Given below are two statements :Assertion I: None of the alkaline earth metal hydroxides dissolve in alkali.Reason II : Solubility of alkaline earth metal hydroxide in water increases down the group.In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

Statement I is incorrect but Statement II is correct.

Answer

Statement I is correct but Statement II is incorrect.

Answer

Statement I and Statement II both are incorrect.

Answer

Statement I and Statement II both are correct.

Question 5

Two billiard balls of equal mass 30 g strike a right wall with same speed of 108kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along ' X ' direction is :

Accepted Answer

2​:1

Answer

1:2​

Answer

2:1

Answer

1:1

Question 6

The given reaction can occur in the presence of :(a) Bromine water(b) Br2​ in CS2​,273 K (c) Br2​/FeBr3​ (d) Br2​ in CHCl3​,273 K

Accepted Answer

(b), (c) and (d) only

Answer

(a), (b) and (d) only

Answer

(b) and (d) only

Answer

(a) and (c) only

Question 7

Identify the given polymer

Accepted Answer

Novolac

Answer

Buna-N

Answer

Acrilan

Answer

Neoprene

Question 8

The half-life of 198Au is 3 days. If atomic weight of 198Au is 198 g/mol then the activity of 2mg198Au is [in disintegration/second]

Accepted Answer

16.18×1012

Answer

2.67×1012

Answer

6.06×1018

Answer

32.36×1012

Question 9

Which one of the following chemical agent is not being used for dry-cleaning of clothes?

Accepted Answer

CCl4​

Answer

H2​O2​

Answer

Cl2​C=CCl2​

Answer

Liquid CO2​

Question 10

Water droplets are coming from an open tap at a particular rate. The spacing between a droplets observed at 4th  second after its fall to the next droplet is 34.3 m . At what rate the droplets are coming from the tap ?( Take g=9.8 m/s2) )

Accepted Answer

1 drop/second

Answer

1 drop/7seconds

Answer

2 drops/second

Answer

3 drops/2 seconds

Question 11

Let the foot of perpendicular from a point P(1,2,−1) to the straight line L=1x​=0y​=−1z​ be N . Let a line be drawn from P parallel to the plane x+y+2z=0 which meets L at point Q . If α is the acute angle between the lines PN and PQ , then cosα is equal to

Accepted Answer

3​1​

Answer

23​​

Answer

23​1​

Answer

5​1​

Question 12

Let ellipse E:a2x2​+b2y2​=1,a2>b2 passes through (23​​,1) and the has eccentricity 3​1​. If a circle. centered at focus F(α,0),α>0 of E and radius 3​2​ , intersects E at two points P and Q , then PQ2 is equal to :

Accepted Answer

316​

Answer

3

Answer

38​

Answer

34​

Question 13

The locus of the centroid of the triangle formed by any point P on the hyperbola 16x2−9y2+32x+36y−164=0 and its foci is:

Accepted Answer

16x2−9y2+32x+36y−36=0

Answer

9x2−16y2+36x+32y−36=0

Answer

16x2−9y2+32x+36y−144=0

Answer

9x2−16y2+36x+32y−144=0

Question 14

A monoatomic ideal gas, initially at temperature T1​ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to temperature T2​ by releasing the piston suddenly. If l1​ and l2​ are the lengths of the gas column, before and after the expansion respectively, then the value of T2​T1​​ will be.

Accepted Answer

(I1​I2​​)32​

Answer

I1​I2​​

Answer

I2​I1​​

Answer

(I2​I1​​)32​

Question 15

Given below are two statements, one is labelled as Assertion (A) and other is labelled as Reason (R).Assertion (A) : Gabriel phthalimide synthesis cannot be used to prepare aromatic primary amines.Reason (R): Aryl halides do not undergo nucleophilic substitution reaction.In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

Both (A) and (R) are true but (R) is correct explanation of (A)

Answer

(A) is true but (R) is false

Answer

(A) is false but (R) is true

Answer

Both (A) and (R) are true but (R) is not the correct explanation of (A)