# Mathematical Physics-Linear Differential Equations [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 6 - 10 of 12

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## Question 6

Appeared in Year: 2013

### Write in Short Short Answer▾

In a constant magnetic field of also the direction, find the value of the path integral in the units of (Tesla ) on a square loop of side length meters. The normal to the loop makes an angle of to the axis, as shown in the figure. The answer should be up to two decimal places. ________

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## Question 7

Appeared in Year: 2011

### Question MCQ▾

The solutions to the differential equation are a family of

### Choices

Choice (4)Response

a.

b.

Straight lines with different slopes

c.

Circles with different centers

d.

Straight lines with different intercepts on the

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## Question 8

Appeared in Year: 2011

### Question MCQ▾

If a force is derivable from a potential function , where is the distance from the origin of the coordinate system, it follows that –

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 9

Appeared in Year: 2010

### Question MCQ▾

The solution of the differential equation for , subject to the initial conditions and , is –

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 10

Appeared in Year: 2009

### Question MCQ▾

Which one of the following curves given the solution of the differential equation , where and are positive constant with initial conditions and ?

### Choices

Choice (4)Response

a.

b.