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IIT JAM Mathematics Practice Test- 10 - Mathematics MCQ


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30 Questions MCQ Test - IIT JAM Mathematics Practice Test- 10

IIT JAM Mathematics Practice Test- 10 for Mathematics 2024 is part of Mathematics preparation. The IIT JAM Mathematics Practice Test- 10 questions and answers have been prepared according to the Mathematics exam syllabus.The IIT JAM Mathematics Practice Test- 10 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for IIT JAM Mathematics Practice Test- 10 below.
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IIT JAM Mathematics Practice Test- 10 - Question 1

if  find (p.q) where  at ( 1 - 1, 1).

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 1

IIT JAM Mathematics Practice Test- 10 - Question 2

if   then the point (1,-1,2), we have

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 2

i[9x2z] - j[-6xyz] + k[3x2z2 + 4y2] at the point (1,-1, 2), we have 

    (1)

then


By (1) and (2) both the option are true.

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IIT JAM Mathematics Practice Test- 10 - Question 3

Let   


 then is equal to,

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 3

we have 

IIT JAM Mathematics Practice Test- 10 - Question 4

if  is equal to

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 4

IIT JAM Mathematics Practice Test- 10 - Question 5

If  at the p oin t (1, -2, 1), is

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 5

IIT JAM Mathematics Practice Test- 10 - Question 6

A non - zero vector is parallel to the line of intersection of the plane determined by the vectors i, i +j and the plane determined by the vectors i - j, i + k. Then the angle between and the vector i - 2j + 2k is ,

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 6

IIT JAM Mathematics Practice Test- 10 - Question 7

The unit normal to the surface xy2 + 2xz = 4 at the point (2, -2, 3) is

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 7

IIT JAM Mathematics Practice Test- 10 - Question 8

The values of x for which the angle between the vectors is obtuse,

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 8

The angle 0 between  is given by

Now θ is obtuse 

IIT JAM Mathematics Practice Test- 10 - Question 9

The value of line integral  and C is the boundary curve of the upper half surface of the sphere x2 + y2 + z2 = 1.

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 9

The Stoke’s theorem is

IIT JAM Mathematics Practice Test- 10 - Question 10

The value of   where F = 2xi + 3yj + 4zk and S is the surface of sphere x2 + y2 + z2 = 1

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 10

IIT JAM Mathematics Practice Test- 10 - Question 11

Let  then

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 11

We are given that 

Let us take e > 0 and x2 + y2 ≠ 0

Now consider

Therefore , for given ε > 0, there exists δ > 0 such that

Thus, f(x,y) is continuous at (0,0).
Hence , option(a) is correct.
Now,


so that A = 0, B = 0 which does not depends on h and k and 

Now approaching along h = mk, we get

which dpends on . Therefore

d o e s not exists.Hence,f(x,y) is not 

differentiable at origin.
Hence , option(b) is incorrect.

Hence, option(c) is incorrect.


Hence, option(d) is incorrect.

IIT JAM Mathematics Practice Test- 10 - Question 12

The differential equation of the family of parabolas with foci at the arigin and axis along the x-axis is)

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 12

Let 4a be the lotusrectam of the parabola with facus Sat ( 0 ,0 ). Then the equation of the directrix will be x + 2 a = 0. now let p (x,y) be any point on the parabola, let PM be the \ drawn from pon the directrix . Then by the definition of the parabola, we have

IIT JAM Mathematics Practice Test- 10 - Question 13

The solution of differential equation  is

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 13

IIT JAM Mathematics Practice Test- 10 - Question 14

Solution of  is equal to,

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 14

Let x-y = v

IIT JAM Mathematics Practice Test- 10 - Question 15

Let y(x) = 4(x) sinx + v(x) cos x be a solution of the differential equation, y”+y sec x, Then 4(x) is

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 15

(D2+1) y = sec x

A . E . M2+ 1 = 0 = M = I i

C.F. = C1 Cos x + C2 sin x

*Multiple options can be correct
IIT JAM Mathematics Practice Test- 10 - Question 16

Let W be the region inside the solid cylinder x2 + y2 < 9 between the plane z = - 2 and the parabolio d z = x2 + y2. Let S is the boundary of W and  be a vector field. Then the value of cannot be ?

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 16

Here S be a closed surface so we can apply GDT hen


*Multiple options can be correct
IIT JAM Mathematics Practice Test- 10 - Question 17

If  then at the point (1 -1 ,1 ), select the correct statements:

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 17

*Multiple options can be correct
IIT JAM Mathematics Practice Test- 10 - Question 18

The value of line integral where C is the circle x2 + y2 = 16 , z = -1, is

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 18



 

*Multiple options can be correct
IIT JAM Mathematics Practice Test- 10 - Question 19

The value of the line integral 

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 19

*Multiple options can be correct
IIT JAM Mathematics Practice Test- 10 - Question 20

if  are unit vectors, then the possible values of  is/are

Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 20

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 21

The directional derivative of f at P in the direction of   with 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 21

we have 

Then directional derivative at P(2, 0, 3) along 

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 22

The value of  for the vector field  for a plane rectangular area with vertics at  in x-y plane, is ____________.


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 22

stoke's Theorem is

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 23

Evaluate  for the vector  take over 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 23

The Gauss divergence theorem is

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 24

The value of surface integral

Where S is closed Sufrace 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 24

We have F1 = yz, F2 = zx, F3 = xy. therefore

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 25

Let S be the surface with the indicated orientaton then the value of 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 25

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 26

Let S be the portion of the cylinder y = Inx in the first octant whose projection parallel to the y-axis on to the xz-plane is the rectangle Rxz  Let  be the unit vector normal to S that points away from the xz-plane. Let  be a rector field, then the value of integral 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 26

Given y = In x

So S: In x-y

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 27

The circulation of the field   around the curve C in which the plane z = 2 meets the cone  Counterclock wise as viewed  from above, is equal to  ....... (correct upto two decimal places)


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 27

so to fine I we will use s toke's theorem here, so

I= 0

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 28

The direcitional derivative of  in the direction of the unit  vector 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 28

The derivative of f at P0(x0,y0) in the direction of the unit vector u = u1i + u2j is the number

= 3.536

 

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 29

Find the directional derivative of    at the point 


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 29

8/5 = 1.6

*Answer can only contain numeric values
IIT JAM Mathematics Practice Test- 10 - Question 30

Find the derivation of  in the direction v = 2i - 3j + 6k


Detailed Solution for IIT JAM Mathematics Practice Test- 10 - Question 30

The partial derivatives of f at P0 are

The gradient of f at p0  is

The derivative of f at P0 in the direction of v is therefore

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