Practice problems on JEE Mains, JEE Mains 2021 Mar 17 Shift 2

Question 1

Let y=y(x) be the solution of the differential equationcosx(3sinx+cosx+3)dy=(1+ysinx(3sinx+cosx+3)dx,0≤x≤2π​,y(0)=0. Then,y(3π​) is equal to:

Accepted Answer

2log6​(1123​+10​)

Answer

2log6​(23​+7​)

Answer

2loge​(623​+9​)

Answer

2loge​(433​−8​)

Question 2

The value of limn→∞​n2[r]+[2r]+….+[nr]​ , where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r , is equal to:

Accepted Answer

2r​

Answer

2r

Answer

0

Answer

r

Question 3

Match List-I with List-II

Accepted Answer

(a) - (ii), (b) - (iii), (c) - (i), (d) - (iv)

Answer

(a) - (ii), (b) - (iv), (c) - (iii), (d) - (i)

Answer

(a) - (i), (b) - (iii), (c) - (iv), (d) - (ii)

Answer

(a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)

Question 4

The number of solutions of the equation x+2tanx=2π​ in the interval [0,2π] is :

Accepted Answer

3

Answer

5

Answer

4

Answer

2

Question 5

A sound wave of frequency 245 Hz travels with the speed of 300 ms−1 along the positive x axis. Each point of the wave moves to and fro through a total distance of 6 cm . What will be the mathematical expression of this travelling wave?

Accepted Answer

Y(x,t)=0.03[sin5.1x−(1.5×103)t]

Answer

Y(x,t)=0.06[sin0.8x−(0.5×103)t]

Answer

Y(x,t)=0.06[sin5.1x−(0.5×103)t]

Answer

Y(x,t)=0.03[sin5.1x−(0.2×103)t]

Question 6

Match List-I with List-II: Choose the correct answer from the options given below:

Accepted Answer

(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

Answer

(a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)

Answer

(a)-(i), (b)-(iii), (c) -(ii), (d)-(iv)

Answer

(a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)

Question 7

Two tangents are drawn from a point P to the circlex2+y2−2x−4y+4=0 , such that the angle between these tangents is tan−1(512​) , where tan−1(512​)∈(0,π). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of △PAB and △CAB is:

Accepted Answer

9:4

Answer

11:4

Answer

3:1

Answer

2:1

Question 8

If the Boolean expression (p∧q)⊛(p⊗q) is a tautology, then ⊗ and ⊗ are respectively given by :

Accepted Answer

→,→

Answer

⋀i​∨

Answer

v,→

Answer

∧,→

Question 9

Let the tangent to the circle x2+y2=25 at the point R(3,4) meet x -axis and y -axis at points P and Q , respectively. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ , then r2 is equal to :

Accepted Answer

72625​

Answer

66585​

Answer

64529​

Answer

72125​

Question 10

The set of elements that differ in mutual relationship from those of the other sets is:

Accepted Answer

Li−Na

Answer

Li−Mg

Answer

B−Si

Answer

Be−Al

Question 11

If the sides AB,BC and CA of a triangle ABC have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to:

Accepted Answer

333

Answer

364

Answer

240

Answer

360

Question 12

Which one of the following will be the output of the given circuit?

Accepted Answer

XOR Gate

Answer

NAND Gate

Answer

NOR Gate

Answer

AND Gate