Practice problems on JEE Mains, JEE Mains 2021 July 20 Shift 1

Question 1

Identify the incorrect statement from the following:

Accepted Answer

Amylose is a branched chain polymer of glucose

Answer

Starch is a polymer of alpha-D glucose

Answer

Glycogen is called as animal starch

Answer

beta-Glycosidic linkage makes cellulose polymer

Question 2

Let a function f:R→R be defined as f(x)=⎩⎨⎧​sinx−ex; if x≤0a+[−x]; if 0<x<1 where [x] is the greatest integer less 2x−b; if x≥1​ than or equal to x. If f is continuous on R, then (a+b) is equal to:

Accepted Answer

3

Answer

4

Answer

5

Answer

2

Question 3

The normal reaction 'N ' for a vehicle of 800 kg mass, negotiating a turn on a 302 banked road at maximum possible speed without skidding is ×103 kg m/s2. (Given $cos30∘=0.87,μs=0.2 )

Accepted Answer

10.2

Answer

7.2

Answer

12.4

Answer

6.96

Question 4

Orlon fibres are made up of :

Accepted Answer

Polyacrylonitrile

Answer

Cellulose

Answer

Polyamide

Answer

Polyesters

Question 5

Compound A is converted to B on reaction with CHCl3​ and KOH. The compound B is toxic and can be decomposed by C. A, B and C respectively are :

Accepted Answer

Primary amine, isonitrile compound, conc.{HCl}

Answer

Secondary amine, nitrile compound, conc NaOH

Answer

Primary amine, nitrile compound, conc. {HCl}

Answer

Secondary amine, isonitrile compound, conc {NaOH}

Question 6

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason RAssertion A : Sharp glass becomes smooth on heating it up to its melting point.Reason R : The viscosity of glass decreases on melting.Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

A is false but R is true.

Answer

A is true but R is false.

Answer

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

Question 7

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2,4 , 5 and 7 , then the remaining two observations are :

Accepted Answer

10,11

Answer

3,18

Answer

1,20

Answer

8,13

Question 8

The value of tension in a long thin metal wire has been changed from T1​ to T2​. The lengths of the metal wire at two different values of tension T1​ and T2​ are I1​ and I2​ respectively. The actual length of the metal wire is :

Accepted Answer

T1​−T2​T1​I2​−T2​I1​​

Answer

T1​−T2​T1​l1​−T2​l2​​

Answer

2I1​+I2​​

Answer

T1​ T2​I1​I2​​

Question 9

The species given below that does NOT show disproportionation reaction is :

Accepted Answer

BrO4−​

Answer

BrO−

Answer

BrO3−​

Answer

BrO2−​

Question 10

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

Accepted Answer

111​

Answer

661​

Answer

112​

Answer

91​

Question 11

Let the tangent to the parabola S:y2=2x at the point P(2,2) meet the x -axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle P Q R is equal to :

Accepted Answer

225​

Answer

35/2

Answer

215​

Answer

25